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843
The P versus NP problem
 Clay Mathematical Institute; The Millennium Prize Problem
, 2000
"... The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard comp ..."
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Cited by 18 (0 self)
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The P versus NP problem is to determine whether every language accepted by some nondeterministic algorithm in polynomial time is also accepted by some (deterministic) algorithm in polynomial time. To define the problem precisely it is necessary to give a formal model of a computer. The standard
Complexity Measures and Decision Tree Complexity: A Survey
 Theoretical Computer Science
, 2000
"... We discuss several complexity measures for Boolean functions: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial. We survey the relations and biggest gaps known between these measures, and show how they give bounds for the decision tr ..."
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Cited by 197 (17 self)
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. For example, given a computational problem it tries to establish tight upper and lower bounds on the length of the computation (or on other resources, like space). Unfortunately, for many, practically relevant, computational problems no tight bounds are known. An illustrative example is the well known P
P versus NP problem solution
, 2004
"... Contains the solution of P versus NP compexity class relation problem. As expected, P � = NP. Idea of the proof is the following: Supposing P = NP we build a problem in class P of fixed timecomplexity degree, with the following trait: every problem from P reduces to it, thus leading to contradictio ..."
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Contains the solution of P versus NP compexity class relation problem. As expected, P � = NP. Idea of the proof is the following: Supposing P = NP we build a problem in class P of fixed timecomplexity degree, with the following trait: every problem from P reduces to it, thus leading
The History and Status of the P versus NP Question
, 1992
"... this article, I have attempted to organize and describe this literature, including an occasional opinion about the most fruitful directions, but no technical details. In the first half of this century, work on the power of formal systems led to the formalization of the notion of algorithm and the re ..."
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Cited by 59 (1 self)
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and the realization that certain problems are algorithmically unsolvable. At around this time, forerunners of the programmable computing machine were beginning to appear. As mathematicians contemplated the practical capabilities and limitations of such devices, computational complexity theory emerged from the theory
The importance of the P versus NP question
 Journal ACM
"... The P versus NP problem is to determine whether every language accepted by some nondeterministic Turing machine in polynomial time is also accepted by some deterministic Turing machine in polynomial time. Unquestionably this problem has caught the interest of the mathematical community. For example ..."
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Cited by 9 (0 self)
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NP as problem number three, after Riemann and Poincaré, in “Mathematical Problems for the Next Century ” [Smale 1998]. But P versus NP is also a problem of central interest in computer science. It was posed thirty years ago [Cook 1971; Levin 1973] as a problem concerned with the fundamental limits
A personal view of averagecase complexity
 in 10th IEEE annual conference on structure in complexity theory, IEEE computer society press. Washington DC
, 1995
"... The structural theory of averagecase complexity, introduced by Levin, gives a formal setting for discussing the types of inputs for which a problem is dicult. This is vital to understanding both when a seemingly dicult (e.g. NPcomplete) problem is actually easy on almost all instances, and to d ..."
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Cited by 84 (1 self)
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The structural theory of averagecase complexity, introduced by Levin, gives a formal setting for discussing the types of inputs for which a problem is dicult. This is vital to understanding both when a seemingly dicult (e.g. NPcomplete) problem is actually easy on almost all in
An Interesting Perspective to the P versus NP Problem
"... Abstract. We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k ≤ n) polynomial functions on n always yields a polynomial function, ..."
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Abstract. We discuss the P versus NP problem from the perspective of addition operation about polynomial functions. Two contradictory propositions for the addition operation are presented. With the proposition that the sum of k (k ≤ n) polynomial functions on n always yields a polynomial function
Knowledge, Creativity and P versus NP
, 2009
"... The human quest for efficiency is ancient and universal. Computational Complexity Theory is the mathematical study of the efficiency requirements of computational problems. In this note we attempt to convey the deep implications and connections of the results and goals of computational complexity, t ..."
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Cited by 1 (0 self)
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, to the understanding of the most basic and general questions in science and technology. In particular, we will explain the P versus NP question of computer science, and explain the consequences of its possible resolution, P = NP or P ̸ = NP, to the power and security of computing, the human quest for knowledge
Cook versus KarpLevin: Separating Completeness Notions If NP Is Not Small
 Theoretical Computer Science
, 1992
"... Under the hypothesis that NP does not have pmeasure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is P T complete ("Cook complete "), but not P m complete ("KarpLevin complete"), for NP. This c ..."
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Cited by 52 (14 self)
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Under the hypothesis that NP does not have pmeasure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is P T complete ("Cook complete "), but not P m complete ("KarpLevin complete"), for NP
Cooperative Multiagent Systems: A Personal View of the State of the Art
 IEEE Transactions on Knowledge and Data Engineering
, 1999
"... Scientific research and practice in multiagent systems focuses on constructing computational frameworks, principles, and models for how both small and large societies of intelligent, semiautonomous agents can interact effectively to achieve their goals. This article provides a personal view of the ..."
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Cited by 85 (0 self)
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Scientific research and practice in multiagent systems focuses on constructing computational frameworks, principles, and models for how both small and large societies of intelligent, semiautonomous agents can interact effectively to achieve their goals. This article provides a personal view
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