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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 1050 (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
How To Prove Yourself: Practical Solutions to Identification and Signature Problems
, 1987
"... In this paper we describe simple identification and signature schemes which enable any user to prove his identity and the authenticity of his messages to any other user without shared or public keys. The schemes are provably secure against any known or chosen message attack ff factoring is difficult ..."
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Cited by 1028 (1 self)
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In this paper we describe simple identification and signature schemes which enable any user to prove his identity and the authenticity of his messages to any other user without shared or public keys. The schemes are provably secure against any known or chosen message attack ff factoring
A solution to the simultaneous localization and map building (SLAM) problem
 IEEE Transactions on Robotics and Automation
, 2001
"... Abstract—The simultaneous localization and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle ..."
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Cited by 505 (30 self)
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location. Starting from the estimationtheoretic foundations of this problem developed in [1]–[3], this paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative
Computational LambdaCalculus and Monads
, 1988
"... The λcalculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with λterms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification is introduced, that may jeopardise the ap ..."
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Cited by 501 (6 self)
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the applicability of theoretical results to real situations. In this paper we introduce a new calculus based on a categorical semantics for computations. This calculus provides a correct basis for proving equivalence of programs, independent from any specific computational model.
Notions of Computation and Monads
, 1991
"... The i.calculus is considered a useful mathematical tool in the study of programming languages, since programs can be identified with Iterms. However, if one goes further and uses bnconversion to prove equivalence of programs, then a gross simplification is introduced (programs are identified with ..."
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Cited by 867 (15 self)
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with total functions from calues to values) that may jeopardise the applicability of theoretical results, In this paper we introduce calculi. based on a categorical semantics for computations, that provide a correct basis for proving equivalence of programs for a wide range of notions of computation.
Modular elliptic curves and Fermat’s Last Theorem
 ANNALS OF MATH
, 1995
"... When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n> 2 such that a n + b n = c n ..."
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Cited by 617 (2 self)
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n. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet.
Learning logical definitions from relations
 MACHINE LEARNING
, 1990
"... This paper describes FOIL, a system that learns Horn clauses from data expressed as relations. FOIL is based on ideas that have proved effective in attributevalue learning systems, but extends them to a firstorder formalism. This new system has been applied successfully to several tasks taken fro ..."
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Cited by 935 (8 self)
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This paper describes FOIL, a system that learns Horn clauses from data expressed as relations. FOIL is based on ideas that have proved effective in attributevalue learning systems, but extends them to a firstorder formalism. This new system has been applied successfully to several tasks taken
Fair endtoend windowbased congestion control
 IEEE/ACM TRANS. ON NETWORKING
, 2000
"... In this paper, we demonstrate the existence of fair endtoend windowbased congestion control protocols for packetswitched networks with first comefirst served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of maxmin fairness. T ..."
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Cited by 676 (3 self)
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In this paper, we demonstrate the existence of fair endtoend windowbased congestion control protocols for packetswitched networks with first comefirst served routers. Our definition of fairness generalizes proportional fairness and includes arbitrarily close approximations of maxmin fairness
AgentSpeak(L): BDI Agents speak out in a logical computable language
, 1996
"... BeliefDesireIntention (BDI) agents have been investigated by many researchers from both a theoretical specification perspective and a practical design perspective. However, there still remains a large gap between theory and practice. The main reason for this has been the complexity of theoremprov ..."
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Cited by 514 (2 self)
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BeliefDesireIntention (BDI) agents have been investigated by many researchers from both a theoretical specification perspective and a practical design perspective. However, there still remains a large gap between theory and practice. The main reason for this has been the complexity of theoremproving
Convergence Properties of the NelderMead Simplex Method in Low Dimensions
 SIAM Journal of Optimization
, 1998
"... Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper pr ..."
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Cited by 598 (3 self)
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Abstract. The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper
Results 1  10
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