Thursday, 5 November 2015

P versus NP problem........................

 

The following could have some serious "indirect" bearing on the Universal Debating Project, and hence, its inclusion here. See http://www.p2pfoundation.net/Universal_Debating_Project
 
Also, please note the following link on this self same subject.
 
 
 
 
 
Melvyn Bragg and guests discuss the problem of P versus NP, which has a bearing on online security. There is a $1,000,000 prize on offer from the Clay Mathematical Institute for the first person to come up with a complete solution. At its heart is the question "are there problems for which the answers can be checked by computers, but not found in a reasonable time?" If the answer to that is yes, then P does not equal NP. However, if all answers can be found easily as well as checked, if only we knew how, then P equals NP. The area has intrigued mathematicians and computer scientists since Alan Turing, in 1936, found that it's impossible to decide in general whether an algorithm will run forever on some problems. Resting on P versus NP is the security of all online transactions which are currently encrypted: if it transpires that P=NP, if answers could be found as easily as checked, computers could crack passwords in moments.
With
Colva Roney-Dougal
Reader in Pure Mathematics at the University of St Andrews
Timothy Gowers
Royal Society Research Professor in Mathematics at the University of Cambridge
And
Leslie Ann Goldberg
Professor of Computer Science and Fellow of St Edmund Hall, University of Oxford
Producer: Simon Tillotson.
 
 
 
 
LINKS AND FURTHER READING
Colva Roney-Dougal at the University of St Andrews
Timothy Gowers at the University of Cambridge
Leslie Ann Goldberg at the University of Oxford
P versus NP problem - Wikipedia
P vs. NP for Dummies
Gödel’s Lost Letter and P=NP
MacTutor History of Mathematics archive

READING LIST:
Scott Aaronson, Quantum Computing Since Democritus (Cambridge University Press, 2013)
William J. Cook, In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation (Princeton University Press, 2012)
Lance Fortnow, The Golden Ticket: P, NP, and the Search for the Impossible (Princeton University Press, 2013)
Dennis Shasha, Out of their Minds: The Lives and Discoveries of 15 Great Computer Scientists (first published 1995; Springer, 2008)
 
 
 
 
 
 
 
Wikipedia Article Per Se
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Vraagteken.svgOpen problem in computer science:
If the answer to a problem is easy to check, is the problem itself easy to solve?
(more open problems in computer science)
Millennium Prize Problems


Diagram of complexity classes provided that P ≠ NP. The existence of problems within NP but outside both P and NP-complete, under that assumption, was established by Ladner's theorem.[1]
The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time.[2] The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures"[3] and is considered by many to be the most important open problem in the field.[4] It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution.
The informal term quickly, used above, means the existence of an algorithm for the task that runs in polynomial time. The general class of questions for which some algorithm can provide an answer in polynomial time is called "class P" or just "P". For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The class of questions for which an answer can be verified in polynomial time is called NP.
Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute. Given a set of integers, does some nonempty subset of them sum to 0? For instance, does a subset of the set {−2, −3, 15, 14, 7, −10} add up to 0? The answer "yes, because the subset {−2, −3, −10, 15} adds up to zero" can be quickly verified with three additions. However, there is no known algorithm to find such a subset in polynomial time (there is one, however, in exponential time, which consists of 2n-n-1 tries), but such an algorithm exists if P = NP; hence this problem is in NP (quickly checkable) but not necessarily in P (quickly solvable).
An answer to the P = NP question would determine whether problems that can be verified in polynomial time, like the subset-sum problem, can also be solved in polynomial time. If it turned out that P ≠ NP, it would mean that there are problems in NP (such as NP-complete problems) that are harder to compute than to verify: they could not be solved in polynomial time, but the answer could be verified in polynomial time.
Aside from being an important problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence, game theory, multimedia processing, philosophy, economics and many other fields.


Context[edit]

The relation between the complexity classes P and NP is studied in computational complexity theory, the part of the theory of computation dealing with the resources required during computation to solve a given problem. The most common resources are time (how many steps it takes to solve a problem) and space (how much memory it takes to solve a problem).
In such analysis, a model of the computer for which time must be analyzed is required. Typically such models assume that the computer is deterministic (given the computer's present state and any inputs, there is only one possible action that the computer might take) and sequential (it performs actions one after the other).
In this theory, the class P consists of all those decision problems (defined below) that can be solved on a deterministic sequential machine in an amount of time that is polynomial in the size of the input; the class NP consists of all those decision problems whose positive solutions can be verified in polynomial time given the right information, or equivalently, whose solution can be found in polynomial time on a non-deterministic machine.[5] Clearly, P ⊆ NP. Arguably the biggest open question in theoretical computer science concerns the relationship between those two classes:
Is P equal to NP?
In a 2002 poll of 100 researchers, 61 believed the answer to be no, 9 believed the answer is yes, and 22 were unsure; 8 believed the question may be independent of the currently accepted axioms and therefore is impossible to prove or disprove.[6]
In 2012, 10 years later, the same poll was repeated. The number of researchers who answered was 151: 126 (83%) believed the answer to be no, 12 (9%) believed the answer is yes, 5 (3%) believed the question may be independent of the currently accepted axioms and therefore is impossible to prove or disprove, 8 (5%) said either don't know or don't care or don't want the answer to be yes nor the problem to be resolved.[7]

NP-complete[edit]



Euler diagram for P, NP, NP-complete, and NP-hard set of problems
Main article: NP-complete
To attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are a set of problems to each of which any other NP-problem can be reduced in polynomial time, and whose solution may still be verified in polynomial time. That is, any NP problem can be transformed into any of the NP-complete problems. Informally, an NP-complete problem is an NP problem that is at least as "tough" as any other problem in NP.
NP-hard problems are those at least as hard as NP problems, i.e., all NP problems can be reduced (in polynomial time) to them. NP-hard problems need not be in NP, i.e., they need not have solutions verifiable in polynomial time.
For instance, the Boolean satisfiability problem is NP-complete by the Cook–Levin theorem, so any instance of any problem in NP can be transformed mechanically into an instance of the Boolean satisfiability problem in polynomial time. The Boolean satisfiability problem is one of many such NP-complete problems. If any NP-complete problem is in P, then it would follow that P = NP. Unfortunately, many important problems have been shown to be NP-complete, and not a single fast algorithm for any of them is known.
Based on the definition alone it is not obvious that NP-complete problems exist, a trivial and contrived NP-complete problem can be formulated as: given a description of a Turing machine M guaranteed to halt in polynomial time, does there exist a polynomial-size input that M will accept?[8] It is in NP because (given an input) it is simple to check whether M accepts the input by simulating M; it is NP-complete because the verifier for any particular instance of a problem in NP can be encoded as a polynomial-time machine M that takes the solution to be verified as input. Then the question of whether the instance is a yes or no instance is determined by whether a valid input exists.
The first natural problem proven to be NP-complete was the Boolean satisfiability problem. As noted above, this is the Cook–Levin theorem; its proof that satisfiability is NP-complete contains technical details about Turing machines as they relate to the definition of NP. However, after this problem was proved to be NP-complete, proof by reduction provided a simpler way to show that many other problems are also NP-complete, including the subset-sum problem discussed earlier. Thus, a vast class of seemingly unrelated problems are all reducible to one another, and are in a sense "the same problem".

Harder problems[edit]

See also: Complexity class
Although it is unknown whether P = NP, problems outside of P are known. A number of succinct problems (problems that operate not on normal input, but on a computational description of the input) are known to be EXPTIME-complete. Because it can be shown that P ⊊ EXPTIME, these problems are outside P, and so require more than polynomial time. In fact, by the time hierarchy theorem, they cannot be solved in significantly less than exponential time. Examples include finding a perfect strategy for chess (on an N × N board)[9] and some other board games.[10]
The problem of deciding the truth of a statement in Presburger arithmetic requires even more time. Fischer and Rabin proved in 1974 that every algorithm that decides the truth of Presburger statements has a runtime of at least 2^{2^{cn}} for some constant c. Here, n is the length of the Presburger statement. Hence, the problem is known to need more than exponential run time. Even more difficult are the undecidable problems, such as the halting problem. They cannot be completely solved by any algorithm, in the sense that for any particular algorithm there is at least one input for which that algorithm will not produce the right answer; it will either produce the wrong answer, finish without giving a conclusive answer, or otherwise run forever without producing any answer at all.

Problems in NP not known to be in P or NP-complete[edit]

Main article: NP-intermediate
It was shown by Ladner that if P ≠ NP then there exist problems in NP that are neither in P nor NP-complete.[1] Such problems are called NP-intermediate problems. The graph isomorphism problem, the discrete logarithm problem and the integer factorization problem are examples of problems believed to be NP-intermediate. They are some of the very few NP problems not known to be in P or to be NP-complete.
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. An important unsolved problem in complexity theory is whether the graph isomorphism problem is in P, NP-complete, or NP-intermediate. The answer is not known, but it is believed that the problem is at least not NP-complete.[11] If graph isomorphism is NP-complete, the polynomial time hierarchy collapses to its second level.[12][13] Since it is widely believed that the polynomial hierarchy does not collapse to any finite level, it is believed that graph isomorphism is not NP-complete. The best algorithm for this problem, due to Laszlo Babai and Eugene Luks has run time 2O(√nlog(n)) for graphs with n vertices.
The integer factorization problem is the computational problem of determining the prime factorization of a given integer. Phrased as a decision problem, it is the problem of deciding whether the input has a factor less than k. No efficient integer factorization algorithm is known, and this fact forms the basis of several modern cryptographic systems, such as the RSA algorithm. The integer factorization problem is in NP and in co-NP (and even in UP and co-UP[14]). If the problem is NP-complete, the polynomial time hierarchy will collapse to its first level (i.e., NP = co-NP). The best known algorithm for integer factorization is the general number field sieve, which takes expected time
O\left (\exp \left ( \left (\tfrac{64n}{9} \log(2) \right )^{\frac{1}{3}} \left ( \log(n\log(2)) \right )^{\frac{2}{3}} \right) \right )
to factor an n-bit integer. However, the best known quantum algorithm for this problem, Shor's algorithm, does run in polynomial time. Unfortunately, this fact doesn't say much about where the problem lies with respect to non-quantum complexity classes.

Does P mean "easy"?[edit]



The graph shows time (average of 100 instances in ms using a 933 MHz Pentium III) vs.problem size for knapsack problems for a state-of-the-art specialized algorithm. Quadratic fit suggests that empirical algorithmic complexity for instances with 50–10,000 variables is O((log(n))2).[15]
All of the above discussion has assumed that P means "easy" and "not in P" means "hard", an assumption known as Cobham's thesis. It is a common and reasonably accurate assumption in complexity theory; however, it has some caveats.
First, it is not always true in practice. A theoretical polynomial algorithm may have extremely large constant factors or exponents thus rendering it impractical. On the other hand, even if a problem is shown to be NP-complete, and even if P ≠ NP, there may still be effective approaches to tackling the problem in practice. There are algorithms for many NP-complete problems, such as the knapsack problem, the traveling salesman problem and the Boolean satisfiability problem, that can solve to optimality many real-world instances in reasonable time. The empirical average-case complexity (time vs. problem size) of such algorithms can be surprisingly low. An example is the simplex algorithm in linear programming, which works surprisingly well in practice; despite having exponential worst-case time complexity it runs on par with the best known polynomial-time algorithms.[16]
Second, there are types of computations which do not conform to the Turing machine model on which P and NP are defined, such as quantum computation and randomized algorithms.

Reasons to believe P ≠ NP[edit]

According to polls,[6][17] many computer scientists believe that P ≠ NP. A key reason for this belief is that after decades of studying these problems no one has been able to find a polynomial-time algorithm for any of more than 3000 important known NP-complete problems (see List of NP-complete problems). These algorithms were sought long before the concept of NP-completeness was even defined (Karp's 21 NP-complete problems, among the first found, were all well-known existing problems at the time they were shown to be NP-complete). Furthermore, the result P = NP would imply many other startling results that are currently believed to be false, such as NP = co-NP and P = PH.
It is also intuitively argued that the existence of problems that are hard to solve but for which the solutions are easy to verify matches real-world experience.[18]
If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in "creative leaps," no fundamental gap between solving a problem and recognizing the solution once it's found.
— Scott Aaronson, MIT
On the other hand, some researchers believe that there is overconfidence in believing P ≠ NP and that researchers should explore proofs of P = NP as well. For example, in 2002 these statements were made:[6]
The main argument in favor of P ≠ NP is the total lack of fundamental progress in the area of exhaustive search. This is, in my opinion, a very weak argument. The space of algorithms is very large and we are only at the beginning of its exploration. [...] The resolution of Fermat's Last Theorem also shows that very simple questions may be settled only by very deep theories.
— Moshe Y. Vardi, Rice University
Being attached to a speculation is not a good guide to research planning. One should always try both directions of every problem. Prejudice has caused famous mathematicians to fail to solve famous problems whose solution was opposite to their expectations, even though they had developed all the methods required.
— Anil Nerode, Cornell University

Consequences of solution[edit]

One of the reasons the problem attracts so much attention is the consequences of the answer. Either direction of resolution would advance theory enormously, and perhaps have huge practical consequences as well.

P = NP[edit]

A proof that P = NP could have stunning practical consequences, if the proof leads to efficient methods for solving some of the important problems in NP. It is also possible that a proof would not lead directly to efficient methods, perhaps if the proof is non-constructive, or the size of the bounding polynomial is too big to be efficient in practice. The consequences, both positive and negative, arise since various NP-complete problems are fundamental in many fields.
Cryptography, for example, relies on certain problems being difficult. A constructive and efficient solution[Note 1] to an NP-complete problem such as 3-SAT would break most existing cryptosystems including:
  • public-key cryptography,[19] a foundation for many modern security applications such as secure financial transactions over the Internet; and
  • symmetric ciphers such as AES or 3DES,[20] used for the encryption of communications data.
  • one-way functions used in cryptographic hashing. The problem of finding a pre-image that hashes to a given value[21] must be difficult to be useful, and ideally should require exponential time. However, if P=NP, then finding a pre-image M can be done in polynomial time, through reduction to SAT.[22]
These would need to be modified or replaced by information-theoretically secure solutions not inherently based on P-NP equivalence.
On the other hand, there are enormous positive consequences that would follow from rendering tractable many currently mathematically intractable problems. For instance, many problems in operations research are NP-complete, such as some types of integer programming and the travelling salesman problem. Efficient solutions to these problems would have enormous implications for logistics. Many other important problems, such as some problems in protein structure prediction, are also NP-complete;[23] if these problems were efficiently solvable it could spur considerable advances in life sciences and biotechnology.
But such changes may pale in significance compared to the revolution an efficient method for solving NP-complete problems would cause in mathematics itself. Gödel, in his early thoughts on computational complexity, noted that a mechanical method that could solve any problem would revolutionize mathematics:[24][25]
If there really were a machine with φ(n) ∼ k ⋅ n (or even ∼ k ⋅ n2), this would have consequences of the greatest importance. Namely, it would obviously mean that in spite of the undecidability of the Entscheidungsproblem, the mental work of a mathematician concerning Yes-or-No questions could be completely replaced by a machine. After all, one would simply have to choose the natural number n so large that when the machine does not deliver a result, it makes no sense to think more about the problem.
Similarly, Stephen Cook says[26]
...it would transform mathematics by allowing a computer to find a formal proof of any theorem which has a proof of a reasonable length, since formal proofs can easily be recognized in polynomial time. Example problems may well include all of the CMI prize problems.
Research mathematicians spend their careers trying to prove theorems, and some proofs have taken decades or even centuries to find after problems have been stated—for instance, Fermat's Last Theorem took over three centuries to prove. A method that is guaranteed to find proofs to theorems, should one exist of a "reasonable" size, would essentially end this struggle.
Donald Knuth has stated that he has come to believe that P = NP, but is reserved about the impact of a possible proof:[27]
[...] I don't believe that the equality P = N P will turn out to be helpful even if it is proved, because such a proof will almost surely be nonconstructive.

P ≠ NP[edit]

A proof that showed that P ≠ NP would lack the practical computational benefits of a proof that P = NP, but would nevertheless represent a very significant advance in computational complexity theory and provide guidance for future research. It would allow one to show in a formal way that many common problems cannot be solved efficiently, so that the attention of researchers can be focused on partial solutions or solutions to other problems. Due to widespread belief in P ≠ NP, much of this focusing of research has already taken place.[28]
Also P ≠ NP still leaves open the average-case complexity of hard problems in NP. For example, it is possible that SAT requires exponential time in the worst case, but that almost all randomly selected instances of it are efficiently solvable. Russell Impagliazzo has described five hypothetical "worlds" that could result from different possible resolutions to the average-case complexity question.[29] These range from "Algorithmica", where P = NP and problems like SAT can be solved efficiently in all instances, to "Cryptomania", where P ≠ NP and generating hard instances of problems outside P is easy, with three intermediate possibilities reflecting different possible distributions of difficulty over instances of NP-hard problems. The "world" where P ≠ NP but all problems in NP are tractable in the average case is called "Heuristica" in the paper. A Princeton University workshop in 2009 studied the status of the five worlds.[30]

Results about difficulty of proof[edit]

Although the P = NP? problem itself remains open despite a million-dollar prize and a huge amount of dedicated research, efforts to solve the problem have led to several new techniques. In particular, some of the most fruitful research related to the P = NP problem has been in showing that existing proof techniques are not powerful enough to answer the question, thus suggesting that novel technical approaches are required.
As additional evidence for the difficulty of the problem, essentially all known proof techniques in computational complexity theory fall into one of the following classifications, each of which is known to be insufficient to prove that P ≠ NP:
ClassificationDefinition
Relativizing proofsImagine a world where every algorithm is allowed to make queries to some fixed subroutine called an oracle, and the running time of the oracle is not counted against the running time of the algorithm. Most proofs (especially classical ones) apply uniformly in a world with oracles regardless of what the oracle does. These proofs are called relativizing. In 1975, Baker, Gill, and Solovay showed that P = NP with respect to some oracles, while P ≠ NP for other oracles.[31] Since relativizing proofs can only prove statements that are uniformly true with respect to all possible oracles, this showed that relativizing techniques cannot resolve P = NP.
Natural proofsIn 1993, Alexander Razborov and Steven Rudich defined a general class of proof techniques for circuit complexity lower bounds, called natural proofs. At the time all previously known circuit lower bounds were natural, and circuit complexity was considered a very promising approach for resolving P = NP. However, Razborov and Rudich showed that, if one-way functions exist, then no natural proof method can distinguish between P and NP. Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof or disproof of their existence would be a much stronger statement than the quantification of P relative to NP. Thus it is unlikely that natural proofs alone can resolve P = NP.
Algebrizing proofsAfter the Baker-Gill-Solovay result, new non-relativizing proof techniques were successfully used to prove that IP = PSPACE. However, in 2008, Scott Aaronson and Avi Wigderson showed that the main technical tool used in the IP = PSPACE proof, known as arithmetization, was also insufficient to resolve P = NP.[32]
These barriers are another reason why NP-complete problems are useful: if a polynomial-time algorithm can be demonstrated for an NP-complete problem, this would solve the P = NP problem in a way not excluded by the above results.
These barriers have also led some computer scientists to suggest that the P versus NP problem may be independent of standard axiom systems like ZFC (cannot be proved or disproved within them). The interpretation of an independence result could be that either no polynomial-time algorithm exists for any NP-complete problem, and such a proof cannot be constructed in (e.g.) ZFC, or that polynomial-time algorithms for NP-complete problems may exist, but it's impossible to prove in ZFC that such algorithms are correct.[33] However, if it can be shown, using techniques of the sort that are currently known to be applicable, that the problem cannot be decided even with much weaker assumptions extending the Peano axioms (PA) for integer arithmetic, then there would necessarily exist nearly-polynomial-time algorithms for every problem in NP.[34] Therefore, if one believes (as most complexity theorists do) that not all problems in NP have efficient algorithms, it would follow that proofs of independence using those techniques cannot be possible. Additionally, this result implies that proving independence from PA or ZFC using currently known techniques is no easier than proving the existence of efficient algorithms for all problems in NP.

Claimed solutions [edit]

While the P versus NP problem is generally considered unsolved,[35] many amateur and some professional researchers have claimed solutions. Gerhard J. Woeginger has a comprehensive list.[36] An August 2010 claim of proof that P ≠ NP, by Vinay Deolalikar, a researcher at HP Labs, Palo Alto, received heavy Internet and press attention after being initially described as "seem[ing] to be a relatively serious attempt" by two leading specialists.[37] The proof has been reviewed publicly by academics,[38][39] and Neil Immerman, an expert in the field, had pointed out two possibly fatal errors in the proof.[40] In September 2010, Deolalikar was reported to be working on a detailed expansion of his attempted proof.[41] However, opinions expressed by several notable theoretical computer scientists indicate that the attempted proof is neither correct nor a significant advancement in the understanding of the problem.[42] This assessment prompted a May 2013 The New Yorker article to call the proof attempt "thoroughly discredited."[43]

Logical characterizations[edit]

The P = NP problem can be restated in terms of expressible certain classes of logical statements, as a result of work in descriptive complexity.
Consider all languages of finite structures with a fixed signature including a linear order relation. Then, all such languages in P can be expressed in first-order logic with the addition of a suitable least fixed-point combinator. Effectively, this, in combination with the order, allows the definition of recursive functions. As long as the signature contains at least one predicate or function in addition to the distinguished order relation, so that the amount of space taken to store such finite structures is actually polynomial in the number of elements in the structure, this precisely characterizes P.
Similarly, NP is the set of languages expressible in existential second-order logic—that is, second-order logic restricted to exclude universal quantification over relations, functions, and subsets. The languages in the polynomial hierarchy, PH, correspond to all of second-order logic. Thus, the question "is P a proper subset of NP" can be reformulated as "is existential second-order logic able to describe languages (of finite linearly ordered structures with nontrivial signature) that first-order logic with least fixed point cannot?".[44] The word "existential" can even be dropped from the previous characterization, since P = NP if and only if P = PH (as the former would establish that NP = co-NP, which in turn implies that NP = PH).

Polynomial-time algorithms[edit]

No algorithm for any NP-complete problem is known to run in polynomial time. However, there are algorithms for NP-complete problems with the property that if P = NP, then the algorithm runs in polynomial time (although with enormous constants, making the algorithm impractical). The following algorithm, due to Levin (without any citation), is such an example below. It correctly accepts the NP-complete language SUBSET-SUM. It runs in polynomial time if and only if P = NP:
// Algorithm that accepts the NP-complete language SUBSET-SUM.
//
// this is a polynomial-time algorithm if and only if P = NP.
//
// "Polynomial-time" means it returns "yes" in polynomial time when
// the answer should be "yes", and runs forever when it is "no".
//
// Input: S = a finite set of integers
// Output: "yes" if any subset of S adds up to 0.
// Runs forever with no output otherwise.
// Note: "Program number P" is the program obtained by
// writing the integer P in binary, then
// considering that string of bits to be a
// program. Every possible program can be
// generated this way, though most do nothing
// because of syntax errors. 
FOR N = 1...∞
  FOR P = 1...N
    Run program number P for N steps with input S
    IF the program outputs a list of distinct integers
      AND the integers are all in S
      AND the integers sum to 0
    THEN
      OUTPUT "yes" and HALT
If, and only if, P = NP, then this is a polynomial-time algorithm accepting an NP-complete language. "Accepting" means it gives "yes" answers in polynomial time, but is allowed to run forever when the answer is "no" (also known as a semi-algorithm).
This algorithm is enormously impractical, even if P = NP. If the shortest program that can solve SUBSET-SUM in polynomial time is b bits long, the above algorithm will try at least 2b−1 other programs first.

Formal definitions[edit]

P and NP[edit]

Conceptually speaking, a decision problem is a problem that takes as input some string w over an alphabet Σ, and outputs "yes" or "no". If there is an algorithm (say a Turing machine, or a computer program with unbounded memory) that can produce the correct answer for any input string of length n in at most cnk steps, where k and c are constants independent of the input string, then we say that the problem can be solved in polynomial time and we place it in the class P. Formally, P is defined as the set of all languages that can be decided by a deterministic polynomial-time Turing machine. That is,
\mathbf{P} = \{ L : L=L(M) \text{ for some deterministic polynomial-time Turing machine } M \}
where
L(M) = \{ w\in\Sigma^{*}: M \text{ accepts } w \}
and a deterministic polynomial-time Turing machine is a deterministic Turing machine M that satisfies the following two conditions:
  1. M halts on all input w and
  2. there exists k \in N such that T_M(n)\in O(n^k), where O refers to the big O notation and
T_M(n) = \max\{ t_M(w) : w\in\Sigma^{*}, |w| = n \}
t_M(w) = \text{ number of steps }M\text{ takes to halt on input }w.
NP can be defined similarly using nondeterministic Turing machines (the traditional way). However, a modern approach to define NP is to use the concept of certificate and verifier. Formally, NP is defined as the set of languages over a finite alphabet that have a verifier that runs in polynomial time, where the notion of "verifier" is defined as follows.
Let L be a language over a finite alphabet, Σ.
L ∈ NP if, and only if, there exists a binary relation R\subset\Sigma^{*}\times\Sigma^{*} and a positive integer k such that the following two conditions are satisfied:
  1. For all x\in\Sigma^{*}, x\in L \Leftrightarrow\exists y\in\Sigma^{*} such that (x, y) ∈ R and |y|\in O(|x|^k); and
  2. the language L_{R} = \{ x\# y:(x,y)\in R\} over \Sigma\cup\{\#\} is decidable by a Turing machine in polynomial time.
A Turing machine that decides LR is called a verifier for L and a y such that (x, y) ∈ R is called a certificate of membership of x in L.
In general, a verifier does not have to be polynomial-time. However, for L to be in NP, there must be a verifier that runs in polynomial time.

Example[edit]

Let
\mathrm{COMPOSITE} = \left \{x\in\mathbb{N} \mid x=pq \text{ for integers } p, q > 1 \right \}
R = \left \{(x,y)\in\mathbb{N} \times\mathbb{N} \mid 1<y \leq \sqrt x \text{ and } y \text{ divides } x \right \}.
Clearly, the question of whether a given x is a composite is equivalent to the question of whether x is a member of COMPOSITE. It can be shown that COMPOSITE ∈ NP by verifying that it satisfies the above definition (if we identify natural numbers with their binary representations).
COMPOSITE also happens to be in P.[45][46]

NP-completeness[edit]

There are many equivalent ways of describing NP-completeness.
Let L be a language over a finite alphabet Σ.
L is NP-complete if, and only if, the following two conditions are satisfied:
  1. L ∈ NP; and
  2. any L′ in NP is polynomial-time-reducible to L (written as L' \leq_{p} L), where L' \leq_{p} L if, and only if, the following two conditions are satisfied:
    1. There exists f : Σ* → Σ* such that for all w in Σ* we have: (w\in L' \Leftrightarrow f(w)\in L); and
    2. there exists a polynomial-time Turing machine that halts with f(w) on its tape on any input w.

Popular culture[edit]

  • The film Travelling Salesman, by director Timothy Lanzone, is the story of four mathematicians hired by the US government to solve the P vs. NP problem.[47]

See also[edit]

Notes[edit]

  1. Jump up ^ Exactly how efficient a solution must be to pose a threat to cryptography depends on the details. A solution of O(N^2) or better and a reasonable constant term would be disastrous. On the other hand, a solution that is \Omega(N^4) or worse in almost all cases would not pose an immediate practical danger.

References[edit]

  1. ^ Jump up to: a b R. E. Ladner "On the structure of polynomial time reducibility," Journal of the ACM, 22, pp. 151–171, 1975. Corollary 1.1. ACM site.
  2. Jump up ^ Juris. "Gödel, von Neumann, and the P = NP problem" (PDF). Bulletin of the European Association for Theoretical Computer Science 38: 101–107. 
  3. Jump up ^ Cook, Stephen (1971). "The complexity of theorem proving procedures". Proceedings of the Third Annual ACM Symposium on Theory of Computing. pp. 151–158. 
  4. Jump up ^ Fortnow, Lance (2009). "The status of the P versus NP problem" (PDF). Communications of the ACM 52 (9): 78–86. doi:10.1145/1562164.1562186. 
  5. Jump up ^ Sipser, Michael: Introduction to the Theory of Computation, Second Edition, International Edition, page 270. Thomson Course Technology, 2006. Definition 7.19 and Theorem 7.20.
  6. ^ Jump up to: a b c William I. Gasarch (June 2002). "The P=?NP poll." (PDF). SIGACT News 33 (2): 34–47. doi:10.1145/1052796.1052804. Retrieved 29 December 2008. 
  7. Jump up ^ William I. Gasarch. "The Second P=?NP poll" (PDF). SIGACT News 74. 
  8. Jump up ^ Scott Aaronson. "PHYS771 Lecture 6: P, NP, and Friends". Retrieved 27 August 2007. 
  9. Jump up ^ Aviezri Fraenkel and D. Lichtenstein (1981). "Computing a perfect strategy for n×n chess requires time exponential in n". J. Comb. Th. A (31): 199–214. 
  10. Jump up ^ David Eppstein. "Computational Complexity of Games and Puzzles". 
  11. Jump up ^ Arvind, Vikraman; Kurur, Piyush P. (2006). "Graph isomorphism is in SPP". Information and Computation 204 (5): 835–852. doi:10.1016/j.ic.2006.02.002. 
  12. Jump up ^ Schöning, Uwe. "Graph isomorphism is in the low hierarchy". Proceedings of the 4th Annual Symposium on Theoretical Aspects of Computer Science 1987: 114–124. doi:10.1007/bfb0039599. 
  13. Jump up ^ Schöning, Uwe (1988). "Graph isomorphism is in the low hierarchy". Journal of Computer and System Sciences 37: 312–323. doi:10.1016/0022-0000(88)90010-4. 
  14. Jump up ^ Lance Fortnow. Computational Complexity Blog: Complexity Class of the Week: Factoring. 13 September 2002.
  15. Jump up ^ Pisinger, D. 2003. "Where are the hard knapsack problems?" Technical Report 2003/08, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark
  16. Jump up ^ Gondzio, Jacek; Terlaky, Tamás (1996). "3 A computational view of interior point methods". In J. E. Beasley. Advances in linear and integer programming. Oxford Lecture Series in Mathematics and its Applications 4. New York: Oxford University Press. pp. 103–144. MR 1438311. Postscript file at website of Gondzio and at McMaster University website of Terlaky. 
  17. Jump up ^ Rosenberger, Jack (May 2012). "P vs. NP poll results". Communications of the ACM 55 (5): 10. 
  18. Jump up ^ Scott Aaronson. "Reasons to believe". , point 9.
  19. Jump up ^ See Horie, S. and Watanabe, O.; Watanabe (1997). "Hard instance generation for SAT". Algorithms and Computation. Lecture Notes in Computer Science (Springer) 1350: 22–31. arXiv:cs/9809117. Bibcode:1998cs........9117H. doi:10.1007/3-540-63890-3_4. ISBN 978-3-540-63890-2.  for a reduction of factoring to SAT. A 512 bit factoring problem (8400 MIPS-years when factored) translates to a SAT problem of 63,652 variables and 406,860 clauses.
  20. Jump up ^ See, for example, Massacci, F. and Marraro, L. (2000). "Logical cryptanalysis as a SAT problem". Journal of Automated Reasoning (Springer) 24 (1): 165–203. doi:10.1023/A:1006326723002. CiteSeerX: 10.1.1.104.962.  in which an instance of DES is encoded as a SAT problem with 10336 variables and 61935 clauses. A 3DES problem instance would be about 3 times this size.
  21. Jump up ^ Find a messageM that when hashed by the function H() gives a digest h, or H(M)=h
  22. Jump up ^ De, Debapratim and Kumarasubramanian, Abishek and Venkatesan, Ramarathnam (2007). "Inversion attacks on secure hash functions using SAT solvers". Springer. pp. 377–382. 
  23. Jump up ^ Berger B, Leighton T (1998). "Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete". J. Comput. Biol. 5 (1): 27–40. doi:10.1089/cmb.1998.5.27. PMID 9541869. 
  24. Jump up ^ History of this letter and its translation from Michael Sipser. "The History and Status of the P versus NP question" (PDF). 
  25. Jump up ^ David S. Johnson. "A Brief History of NP-Completeness, 1954–2012" (PDF).  From pages 359–376 of Optimization Stories, M. Grötschel (editor), a special issue of ¨ Documenta Mathematica, published in August 2012 and distributed to attendees at the 21st International Symposium on Mathematical Programming in Berlin.
  26. Jump up ^ Cook, Stephen (April 2000). "The P versus NP Problem" (PDF). Clay Mathematics Institute. Retrieved 18 October 2006. 
  27. Jump up ^ Knuth, Donald E. (May 20, 2014). "Twenty Questions for Donald Knuth". informit.com. InformIT. Retrieved 20 July 2014. 
  28. Jump up ^ L. R. Foulds (October 1983). "The Heuristic Problem-Solving Approach". Journal of the Operational Research Society 34 (10): 927–934. doi:10.2307/2580891. JSTOR 2580891. 
  29. Jump up ^ R. Impagliazzo, "A personal view of average-case complexity," sct, pp.134, 10th Annual Structure in Complexity Theory Conference (SCT'95), 1995
  30. Jump up ^ "Tentative program for the workshop on "Complexity and Cryptography: Status of Impagliazzo's Worlds"". Archived from the original on 2013-11-15. 
  31. Jump up ^ T. P. Baker, J. Gill, R. Solovay. Relativizations of the P =? NP Question. SIAM Journal on Computing, 4(4): 431–442 (1975)
  32. Jump up ^ S. Aaronson and A. Wigderson (2008). Algebrization: A New Barrier in Complexity Theory (PDF). Proceedings of ACM STOC'2008. pp. 731–740. doi:10.1145/1374376.1374481. 
  33. Jump up ^ Aaronson, Scott. "Is P Versus NP Formally Independent?" (PDF) .
  34. Jump up ^ Ben-David, Shai; Halevi, Shai (1992). "On the independence of P versus NP". Technical Report 714. Technion .
  35. Jump up ^ John Markoff (8 October 2009). "Prizes Aside, the P-NP Puzzler Has Consequences". The New York Times. 
  36. Jump up ^ Gerhard J. Woeginger. "The P-versus-NP page". Retrieved 25 May 2014. 
  37. Jump up ^ Markoff, John (16 August 2010). "Step 1: Post Elusive Proof. Step 2: Watch Fireworks.". The New York Times. Retrieved 20 September 2010. 
  38. Jump up ^ Polymath Project wiki. "Deolalikar's P vs NP paper". 
  39. Jump up ^ Science News, "Crowdsourcing peer review"
  40. Jump up ^ Dick Lipton (12 August 2010). "Fatal Flaws in Deolalikar's Proof?". 
  41. Jump up ^ Dick Lipton (15 September 2010). "An Update on Vinay Deolalikar's Proof". Retrieved 31 December 2010. 
  42. Jump up ^ Gödel’s Lost Letter and P=NP, Update on Deolalikar’s Proof that P≠NP
  43. Jump up ^ Alexander Nazaryan (2 May 2013). "A Most Profound Math Problem". Retrieved 1 May 2014. 
  44. Jump up ^ Elvira Mayordomo. "P versus NP" Monografías de la Real Academia de Ciencias de Zaragoza 26: 57–68 (2004).
  45. Jump up ^ M. Agrawal, N. Kayal, N. Saxena. "Primes is in P" (PDF). Retrieved 29 December 2008. 
  46. Jump up ^ AKS primality test
  47. Jump up ^ Geere, Duncan. "'Travelling Salesman' movie considers the repercussions if P equals NP". Wired. Retrieved 26 April 2012. 

Further reading[edit]

External links[edit]

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Tuesday, 3 November 2015

Global data science hub launches at Imperial College London

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Unleashing the huge potential of data will be the focus of a new global institute, which is being officially launched tomorrow.
The Data Science Institute will extend our ability to address the frontiers of scientific research in the big data era.
– Professor Yike Guo
Director, Data Science Institute
In the last two years the world has produced more data than in all of human history. Developing insights from better analysis of this information will enable us to improve our predictions of diseases in people, stimulate innovation, unleash waves of productivity and create new consumer services.
The Data Science Institute (DSI) at Imperial aims to capitalise on this data revolution, by underpinning multidisciplinary collaborations between the College's academic experts and research partners in areas such as healthcare, financial services, climate science, and city infrastructure to create new solutions to complex problems.  The DSI will also foster the next generation of data scientists and engineers by developing a range of postgraduate and executive courses.
Sir Keith O’Nions, President & Rector of Imperial College London, says: “Imperial is uniquely placed to play a leading role in data science. Our critical mass of scientific, medical, engineering and business expertise puts us in a strong position to harness the power of the data generated by our research. We are defined by multidisciplinary collaboration and the large scale of our scientific and engineering collaborations at home and internationally.  Industrial partnership is a key component of our work to apply the fruits of this research for the benefit of our society and economy. I would like to thank all the corporate partners who are helping to make our vision a reality.”
The DSI is developing a range of industrial collaborations. For example, Imperial and Huawei signed an agreement last year to develop a data science lab to bring together researchers with cutting-edge facilities to build the next generation of big data applications. These partnerships build on the College’s long standing collaborations in data science with companies such as IBM and Thomson Reuters.
Professor David Gann, Vice President (Development and Innovation), says: “Data is the lifeblood of the twenty first century. Medical innovation, disease prevention, climate change research, the analysis of financial markets and consumer behaviour, and the development of cities capable of accommodating population growth, all require us to gain insights from large, complex data sets. Imperial’s Data Science Institute will act as an international hub within Imperial West, the College’s innovation and translation campus, providing an important location for researchers and industry to collaborate together in this field.”
Professor Yike Guo, Director of the DSI at Imperial, said: “From the development of large data sensor networks to mitigate the effects of flooding in the UK, to using information collected from satellites to understand how changes in the Sun may affect our climate, there is already a wealth of research, which the Data Science Institute is seeking to harness. The Data Science Institute will extend our ability to address the frontiers of scientific research in the big data era. This launch is an invitation to industry and academia to let you know that the Data Science Institute is open for business. We are looking forward to working with all of you to put data at the core of research and innovation with the aim of building a healthy and sustainable modern world.”
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Friday, 16 October 2015

Comprehension approach

 

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From Wikipedia, the free encyclopedia
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The comprehension approach is an umbrella term which refers to several methodologies of language learning that emphasise understanding of language rather than speaking.[1] This is in contrast to the better-known communicative approach, under which learning is thought to emerge through language production, i.e. a focus on speech and writing. It is known that the understanding of language often occurs before the children obtain the ability to express and speak.[2]
The comprehension approach is most strongly associated with the linguists Harris Winitz, Stephen Krashen,[3] Tracy D. Terrell and James J. Asher. The comprehension-based methodology mostly commonly found in classrooms is Asher's Total Physical Response approach;[4] Krashen and Terrell's Natural Approach[5] has not been widely applied. English as a Second Language Podcast is a more recent application of the comprehension approach grounded in Krashen's theories.
The comprehension approach is based on theories of linguistics, specifically Krashen's theories of second language acquisition,[6] and is also inspired by research on second language acquisition in children, particularly the silent period phenomenon in which many young learners initially tend towards minimal speaking.[7] In contrast, the communicative approach is largely a product of research in language education.[8]
Comprehension approach refers to a method of learning a new language through the process of understanding the meaning of words and expressions in the language as opposed to any other form of language learning. Other methods that may be used as part of the progression of language learning include the process of learning the letters, symbols and other representations of the language first before actually understanding the meaning of the words. The difference between the compression approach and the other more scientific approach to learning a new language lies in the fact that the comprehension approach is simply another dimension toward learning a new language. The comprehension approach usually involves a silent period when the learner tries to assimilate the various meanings of the words that make up the target language. How long the silent period lasts depends on the skills of the learner in terms of comprehension ability and general cognitive skills, as someone who is a quick study may be able to quickly grasp the basic concepts of a new language faster than others. During the silent period, the new language learner will try as much as possible to understand what the words mean and how to pronounce them. The disadvantage of this type of approach is that some people who are not very confident might decide to wait until they feel that they have totally grasped the concepts of the language, including the correct pronunciation, before attempting to speak that language. This may be due to a reluctance to mispronounce the words or to misapply the language while attempting to speak it.
An advantage of the comprehension approach of language learning is the fact that when the learner eventually understands the meaning and the correct application of the words, the language will sound more effortless when he or she speaks it in contrast to other forms of language learning, which may result in more stilted efforts. Since the comprehension approach requires a deliberate effort to understand the language first, it often leads to situations where the language learner might understand the general gist of the language, but lack the ability to speak it. This phenomenon may be attributed to the fact that the brain is a complex entity that allows for the resources to compartmentalize different cognitive skills, as is clearly evident in the ability to learn the meaning of a language first before speaking it.[9]
Winitz founded the International Linguistics Corporation in 1976 to supply comprehension-based materials known as The Learnables;[10] several positive articles have been published testing these picturebooks with their accompanying audio recordings, mostly with Winitz as co-author.[11]


Levels of Comprehension[edit]

  • Literal or text-explicit comprehension: Often described as “reading on the lines,” this level requires the reader to process information that is explicitly stated in the text, to understand what the author specifically reported. For example, the reader may be called on to recall or locate precisely stated main ideas, details, directions, or sequences of events. Literal comprehension requires a lower level of thinking skills than the other three levels because the reader must only recall from memory what the book said. Still it is the foundation for content-area courses and remains the most frequently tested comprehension category. It consumes the bulk of instructional time in the classroom and is the level that struggling readers and ELLs strive to attain.
  • Interpretive or text-implicit comprehension: Described frequently as “reading between the lines,” this level demands that the reader process ideas based on what was read but not explicitly stated in the text. It involves understanding what the author meant, and the reader must call on his or her intuition, personal experiences, and imagination as the foundation for making inferences. Children may be asked to predict outcomes, find main ideas, determine word meanings from context, draw conclusions, make generalizations, or infer cause-and-effect relationships. Behaviours commonly associated with critical thinking are involved in text-implicit comprehension, which is said to separate the active reader from the passive reader.
  • Critical or applied comprehension: Sometimes stated as “reading beyond the lines,” this level requires readers to integrate their own thinking with the facts from the text. Consequently, they evaluate and apply information and ideas from the printed page to their own experiences and judgment.
  • Creative comprehension: This most advanced level calls for readers to develop original ideas based on the pages read. They must use divergent thinking skills as they ponder new or alternative solutions to problems or crises presented by the writer.[12]

Factors that influence comprehension approach[edit]

There are several factors that influence comprehension approach. The first of these factors is purpose, which focuses the readers’ attention and helps them understand the text. While teachers routinely help students focus in the classroom, self-directed purpose is the better route to promote the feeling of competency that leads students to independent reading both in and out of school. In the classroom, children can make individual predictions about their reading (e.g., Do tsunamis occur in only one part of the world?), and those predictions then become purposes under the careful direction of their teacher. Outside of school, students may wish to assemble a toy for a younger sibling, and thus reading the directions for that task also has a clear purpose. In both instances, comprehension is stronger when the purpose is specific.
The second is being an active reader because active readers, according to Blachowitz and Ogle, think as they read. They use their prior knowledge (which stems from previous experiences) and their vocabulary as well as reading strategies to help them comprehend what they are reading presently.
The third factor that affects comprehension is the type of text being used. Children who have had experience with story texts may encounter difficulty with expository or informational materials. Therefore, they should be introduced to these materials early and review them often as they usually contain concepts, vocabulary, and format that are markedly different from those found in storybooks. Teachers must keep in mind that the less familiarity students have with expository texts, the harder it is for them to comprehend such books.
The fourth factor affecting comprehension is the quality of literacy instruction. They emphasize literature by reading aloud, maintaining a classroom library, and discussing books and author studies; they integrate the curriculum by making direct connections between reading/writing and the content areas. These instructors manage all aspects of classroom learning, including planning, scheduling, and student behavior, and they maintain an environment characterized by fair rules, high expectations, and a learning atmosphere. They offer supportive instructional context by monitoring student accomplishments and establishing realistic but challenging expectations. Finally, they promote self-monitored learning by teaching students how to organize their work habits and use their time productively.
The fifth factor influencing comprehension is interest. When children are curious about a subject, sometimes to the point of absorption, they will read to seek information and discover answers. Some students can even be described as hyperlexic—their interest in reading is strong enough to qualify them as avid readers.
The last and final factor is independent practice preceded by adequate instruction. Life-long readers evolve from students who are allowed to choose their own books, read them independently in class daily, and have the opportunity to discuss and share them with classmates.[13]

Footnotes[edit]

  1. Jump up ^ Winitz (1981); Gary & Gary (1981a and 1981b).
  2. Jump up ^ "Language Acquisition Methods". LTG. 15 January 2014. Retrieved 9 February 2014. 
  3. Jump up ^ See www.sdkrashen.com for some of Krashen's books and articles, available on-line.
  4. Jump up ^ Asher (1969; 1981). Further information is available at TPR-World (Sky Oaks Productions, Inc.).
  5. Jump up ^ Krashen & Terrell (1983).
  6. Jump up ^ Krashen (1982).
  7. Jump up ^ Winitz et al. (1995); cf. Gibbons (1985), whose own interpretation of the 'silent period' is that children's silence reflects lack of linguistic knowledge or bewilderment within their new language environment.
  8. Jump up ^ Acar (2005: 4).
  9. Jump up ^ "The Comprehension Approach" 54 (8 (May, 1959), pp. 344-345). May 1959. 
  10. Jump up ^ e.g. Winitz (2003); see also the International Linguistics Corporation's Learnables materials on-line.
  11. Jump up ^ e.g. McCandless & Winitz (1986).
  12. Jump up ^ "Learning from text, levels of comprehension, or: Why anyone would read a story anyway". Poetics 9 (1–3, June 1980, Pages 87–98): Pages 87–98. June 1980. 
  13. Jump up ^ "Listening techniques for a Comprehension Approach" (PDF). victoria. 

References[edit]

  • Acar, A (2005) 'The "communicative competence" controversy.' Asian EFL Journal 7(3). Retrieved 20 January 2007.
  • Asher JJ (1969) 'The total physical response approach to second language learning.' The Modern Language Journal 53: 3-17.
  • Asher JJ (1981) The total physical response: theory and practice. In H. Winitz (ed.) Native Language and Foreign Language Acquisition. New York: New York Academy of Sciences. pp. 324–331.
  • Gary JO. & Gary N (1981a) Comprehension-based language instruction: practice. In H. Winitz (ed.) Native Language and Foreign Language Acquisition. New York: New York Academy of Sciences. pp. 343–357.
  • Gary JO. & Gary N (1981b) Comprehension-based language instruction: theory. In H. Winitz (ed.) Native Language and Foreign Language Acquisition. New York: New York Academy of Sciences. pp. 332–342.
  • Gibbons J (1985) 'The silent period: an examination.' Language Learning 35: 255-267.
  • Krashen SD (1982) Principles and Practice in Second Language Acquisition. Oxford: Pergamon.
  • Krashen SD & TD Terrell (1983) The Natural Approach. New York: Pergamon.
  • McCandless P & Winitz H (1986) 'Test of pronunciation following one year of comprehension instruction in college German.' The Modern Language Journal 70: 355-362.
  • Winitz H (ed.) (1981) The Comprehension Approach to Foreign Language Instruction. Rowley, MA: Newbury House.
  • Winitz H (2003) The Learnables, Book 1. Kansas City, MO: International Linguistics Corporation. 6th edition.
  • Winitz H, Gillespie B & Starcev J (1995). 'The development of English speech patterns of a 7-year-old Polish-speaking child.' Journal of Psycholinguistic Research 24: 117-143.
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Action plan

 

The following may have direct, and indirect relevance to the Universal Debating Project. http://www.p2pfoundation.net/Universal_Debating_Project
 
 
From Wikipedia, the free encyclopedia
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An action plan is a detailed plan outlining actions needed to reach one or more goals.


Advantages of using action plans[edit]

Producing an action plan can be beneficial not only for individual basis but also for businesses. For example, it allows project managers or any member of a group to monitor their progress and take each task step-by-step, therefore allowing them to handle the project efficiently. The advantage of doing this is, it allows you to execute a structured plan for the end goal you intend to achieve. Furthermore, it provides the team with appropriate foundations, therefore prioritising the amount of time you spend on each task. This will then prevent any sidetracking that may occur. Lastly, it creates a bond within a team, as each member is aware of their individual role, as well as providing necessary information to ensure success of the project.[1][2][3]

Issues faced with action planning[edit]

When using action plans limitations will need to be considered. Firstly, each member of the team will need to be allocated individual roles and tasks which will require completion by a set date. This can be demanding for some, due to coping with the stress and distractions that may occur. Another issue is not being guided thoroughly and effectively, leading to the lack of effort and passion a member has for the project. In addition to this, if the communication throughout the team is non-existent, key information will not reach members of the group, causing lack of confidence. Lastly failing to obtain the goal you set to reach can lead to frustration and in turn the planning would have been a waste of time. There can be more addition to this article.[4][5]

Reasons for creating an action plan[edit]

An action plan is a tool in social planning. It is an organizational strategy to identify necessary steps towards a goal. It considers details, may help limit setting for an organization, and is efficient in that it is saving resources over trial and error. A written action plan also serves as a token for an organization's accountability.[6]

Guided steps to creating an action plan[edit]

When creating action plans there are guided steps that need to be followed to ensure success, however the structure can be altered in the process. Firstly, you will need to outline what you want to achieve from the project, by doing this you set yourself targets. After this the specific roles will need to be allocated ensuring sufficient amount of training, resources and issues have been considered to ensure solving any problems that may occur. The next stage allows members of the group to analyse the progress by outlining milestones, solving any issues and making any necessary changes. Lastly once the project has come to an end the final stage can be examined to ensure future success.[7]

Setting goals through action planning[edit]

A goal is the primary objective of an action plan. Setting goals gives the possibility of your dreams and prospects being brought to life. It creates motivation and provides you with a certainty that the final outcome will be worthwhile, preventing any wasted time and effort. This is achieved by being fully dedicated to the process and using the structured guide to accomplishing it. Although hard work may be produced, without a successful end goal the ideal result you set to achieve, will not prevail.[8][9][10]

Action plans - Risk Management[edit]

To benefit from risk management action plans, you need to examine certain possibilities that could affect the process, such as observing any threats and correcting them. For example, key aspects of risk management are to ensure you allocate members specific roles and monitor the risks throughout, to ensure tasks are completed with efficiency. This being a major factor, as evaluating what happens during and after the project, will allow finding the positive and negative elements of each stage in the planning, providing you the ability to develop on the risks further.[11][12]

Executing an action plan[edit]

Mike Desjardins has suggested the following[13]
  • Ownership: one person must be responsible and accountable for tracing the progress, keeping team informed, ensuring timely action steps are occurring and adjusting the actions.
  • Action steps should be clear and actionable versus vague ideas or thoughts.
  • Responsibility: each action step needs to have one person responsible.
  • Support: For each action step, determine who will support the person responsible. This can be multiple people. The key is that they’re not responsible for the action or outcome.
  • Informed: keeping the right people in the communication loop for each action is critically important. Key people might need to understand the state of progress around your actions to see how they affect other actions and objectives.
  • Metrics and budget: each action step must have a metric that tells us that the action is complete. For example, if you needed to survey your customers and don’t have the internal resources to run the survey or want to protect anonymity, using an outside resource will require money that might not be included in your current operating budget.
  • Milestone date: date the action step needs to begin
  • Completion date

Examples in the EU[edit]

Some European Union directives describe action plans in order to reach a defined target in air quality or noise reduction. If the target cannot be reached by a member state, the member needs to write a report. Sometimes action plans contain deadlines by which the plan must be ready to start the action(s) and the targets are to be reached.

References[edit]

  1. Jump up ^ "diffundo" (PDF). Retrieved 19 October 2014. 
  2. Jump up ^ Smriti Chand. "What are the Advantages and Potential Disadvantages of Planning under Management?". Retrieved 23 October 2014. 
  3. Jump up ^ Brenda Horton. "5 Reasons Why Your Business Idea Needs An Action Plan". hware. Retrieved 27 October 2014. 
  4. Jump up ^ Leigh Ann Morgan. "Advantages and Disadvantages of Goal Setting". Retrieved 23 October 2014. 
  5. Jump up ^ "The Action Plan". ITS. Retrieved 25 October 2014. 
  6. Jump up ^ "Chapter 8. Developing a Strategic Plan". Community Toolbox. University of Kansas. 2013. 
  7. Jump up ^ "Guidance to making an action plan". Retrieved 23 October 2014. 
  8. Jump up ^ "Personal Goal Setting". Retrieved 26 October 2014. 
  9. Jump up ^ Susan B. Wilson; Michael S. Pmp Dobson (12 March 2008). Goal Setting: How to Create an Action Plan and Achieve Your Goals (Second ed.). pp. 3–21. 
  10. Jump up ^ "1.4 Creating an action plan and setting achievable goals". Retrieved 26 October 2014. 
  11. Jump up ^ Jean Scheid; Marlene Gundlach. "Why You Need a Risk Management Action Plan". Bright Hub PM. Retrieved 27 October 2014. 
  12. Jump up ^ Rationality in Action. pp. 11–26. ISBN 0-521-38598-9. 
  13. Jump up ^ Mike Desjardins (13 December 2011). "How to execute corporate action plans effectively". Business In Vancouver. Retrieved 22 March 2014. 


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