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The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1048 (5 self)
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of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite
Dual polyhedra and mirror symmetry for Calabi–Yau hypersurfaces in toric varieties
 J. Alg. Geom
, 1994
"... We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined by ..."
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Cited by 467 (20 self)
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We consider families F(∆) consisting of complex (n − 1)dimensional projective algebraic compactifications of ∆regular affine hypersurfaces Zf defined by Laurent polynomials f with a fixed ndimensional Newton polyhedron ∆ in ndimensional algebraic torus T = (C ∗ ) n. If the family F(∆) defined
Practical Issues in Temporal Difference Learning
 Machine Learning
, 1992
"... This paper examines whether temporal difference methods for training connectionist networks, such as Suttons's TD(lambda) algorithm can be successfully applied to complex realworld problems. A number of important practical issues are identified and discussed from a general theoretical perspect ..."
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Cited by 415 (2 self)
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perspective. These practical issues are then examined in the context of a case study in which TD(lambda) is applied to learning the game of backgammon from the outcome of selfplay. This is apparently the first application of this algorithm to a complex nontrivial task. It is found that, with zero knowledge
Pretense and representation: The origins of a theory of mind
 Psychol. Rev
, 1987
"... One of the major developments of the second year of human life is the emergence of the ability to pretend. A child's knowledge of a real situation is apparently contradicted and distorted by pretense. If, as generally assumed, the child is just beginning to construct a system for internally rep ..."
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Cited by 411 (14 self)
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capacity for (primary) representation, creating a capacity for metarepresentation. It is this, developing toward the end of infancy, that underlies the child's new abilities to pretend and to understand pretense in others. There is a striking isomorphism between the three fundamental forms
A filtering algorithm for constraints of difference in CSPs
 Proceedings of AAAI’94, the 12th (US) National Conference on Artificial Intelligence
, 1994
"... Abstract Many reallife Constraint Satisfaction Problems (CSPs) involve some constraints similar to the alldifferent constraints. These constraints are called constraints of difference. They are defined on a subset of variables by a set of tuples for which the values occuring in the same tuple are ..."
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Cited by 378 (6 self)
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having domains of cardinality at most d, its space complexity is O(pd) and its time complexity is O(p 2 d 2 ). This filtering algorithm has been successfully used in the system RESYN, to solve the subgraph isomorphism problem.
The complexity of computing a Nash equilibrium
, 2006
"... We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability of n ..."
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Cited by 328 (23 self)
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We resolve the question of the complexity of Nash equilibrium by showing that the problem of computing a Nash equilibrium in a game with 4 or more players is complete for the complexity class PPAD. Our proof uses ideas from the recentlyestablished equivalence between polynomialtime solvability
A Graduated Assignment Algorithm for Graph Matching
, 1996
"... A graduated assignment algorithm for graph matching is presented which is fast and accurate even in the presence of high noise. By combining graduated nonconvexity, twoway (assignment) constraints, and sparsity, large improvements in accuracy and speed are achieved. Its low order computational comp ..."
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Cited by 374 (15 self)
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complexity [O(lm), where l and m are the number of links in the two graphs] and robustness in the presence of noise offer advantages over traditional combinatorial approaches. The algorithm, not restricted to any special class of graph, is applied to subgraph isomorphism, weighted graph matching
Trading Group Theory for Randomness
, 1985
"... In a previous paper [BS] we proved, using the elements of the Clwory of nilyotenf yroupu, that some of the /undamcnla1 computational problems in mat & proup, belong to NP. These problems were also ahown to belong to CONP, assuming an unproven hypofhedi.9 concerning finilc simple Q ’ oup,. The a ..."
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Cited by 353 (9 self)
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boz groupa where group operations are prrformcd by an oracle. Thcb tools we inlroduce seem interesting in their own right. \Ve define a new hierarchy of complexit)y ctesscs A.4Ak) “just above NP’, introduring Arthur ud. Merlin games, the bonndedaway version of Pnpadimitriou’s Games against Nature. We
Why functional programming matters
 The Computer Journal
, 1989
"... As software becomes more and more complex, it is more and more important to structure it well. Wellstructured software is easy to write, easy to debug, and provides a collection of modules that can be reused to reduce future programming costs. Conventional languages place conceptual limits on the ..."
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Cited by 325 (2 self)
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As software becomes more and more complex, it is more and more important to structure it well. Wellstructured software is easy to write, easy to debug, and provides a collection of modules that can be reused to reduce future programming costs. Conventional languages place conceptual limits
The Complexity of Stochastic Games
 Information and Computation
, 1992
"... We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial problem ..."
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Cited by 206 (2 self)
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We consider the complexity of stochastic games  simple games of chance played by two players. We show that the problem of deciding which player has the greatest chance of winning the game is in the class NP " coNP. 1 Introduction We consider the complexity of a natural combinatorial
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