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Efficient Checking of Term Ordering Constraints
, 2000
"... Simplification term orderings play a crucial role in reducing search space in paramodulationbased theorem proving. Such use of orderings requires checking simple ordering constraints on substitutions as an essential part of many operations. Due to their frequency, such checks are very costly and ..."
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Cited by 4 (0 self)
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Simplification term orderings play a crucial role in reducing search space in paramodulationbased theorem proving. Such use of orderings requires checking simple ordering constraints on substitutions as an essential part of many operations. Due to their frequency, such checks are very costly
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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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 deterministically in polynomial time provided an oracle is available for solving the second. From this notion of reducible, polynomial degrees of difficulty are defined, and it is shown that the problem of determining tautologyhood has the same polynomial degree as the problem of determining whether the first 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 alphabet Σ. This alphabet is large enough to include symbols for all sets described here. All Turing machines are deterministic recognition devices, unless the contrary is explicitly stated.
A Survey of Some Recent Trends in RewriteBased and ParamodulationBased Deduction
"... Introduction Deduction with equality is fundamental in mathematics, logics and many applications of formal methods in computer science. During the last two decades this field has importantly progressed through new KnuthBendixlike completion techniques and their extensions to ordered paramodulatio ..."
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Cited by 2 (0 self)
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to results on logicbased complexity and decidability analysis [BG01,Nie98], on deduction with constrained clauses [KKR90,NR95], on inductive theorem proving [CN00], and on many other applications like symbolic constraint solving, or equationallogic programming. In the handbook chapter [NR01
Forms of factoring in paramodulationbased calculi
"... It is a wellknown fact that some form of factoring is necessary for completeness of paramodulationbased calculi of general firstorder clauses. In this paper we give an overview of some existing formalizations of factoring, their related paramodulationbased calculi, and corresponding completeness ..."
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It is a wellknown fact that some form of factoring is necessary for completeness of paramodulationbased calculi of general firstorder clauses. In this paper we give an overview of some existing formalizations of factoring, their related paramodulationbased calculi, and corresponding
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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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
StrategyProofness and Arrow’s Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions
 J. Econ. Theory
, 1975
"... Consider a committee which must select one alternative from a set of three or more alternatives. Committee members each cast a ballot which the voting procedure counts. The voting procedure is strategyproof if it always induces every committee member to cast a ballot revealing his preference. I pro ..."
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Cited by 553 (0 self)
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prove three theorems. First, every strategyproof voting procedure is dictatorial. Second, this paper’s strategyproofness condition for voting procedures corresponds to Arrow’s rationality, independence of irrelevant alternatives, nonnegative response, and citizens ’ sovereignty conditions for social
A Separator Theorem for Planar Graphs
, 1977
"... Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which ..."
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Cited by 461 (1 self)
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Let G be any nvertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a vertex in B, neither A nor B contains more than 2n/3 vertices, and C contains no more than 2& & vertices. We exhibit an algorithm which
Properties of subsets
 Journal of Formalized Mathematics
, 1989
"... Summary. The text includes theorems concerning properties of subsets, and some operations on sets. The functions yielding improper subsets of a set, i.e. the empty set and the set itself are introduced. Functions and predicates introduced for sets are redefined. Some theorems about enumerated sets a ..."
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Cited by 1272 (0 self)
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Summary. The text includes theorems concerning properties of subsets, and some operations on sets. The functions yielding improper subsets of a set, i.e. the empty set and the set itself are introduced. Functions and predicates introduced for sets are redefined. Some theorems about enumerated sets
USER’S GUIDE TO VISCOSITY SOLUTIONS OF SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS
, 1992
"... The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking argume ..."
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Cited by 1399 (16 self)
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The notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems, existence theorems, and theorems about continuous dependence may now be proved by very efficient and striking
Results 1  10
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26,579