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105
A Unification Algorithm for the Group DiffieHellman Protocol
 IN PROC. OF WITS 2002
, 2002
"... Equational unification can be an effective tool for the analysis of cryptographic protocols. This, for example ..."
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Cited by 27 (3 self)
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Equational unification can be an effective tool for the analysis of cryptographic protocols. This, for example
Rewrite Methods for Clausal and Nonclausal Theorem Proving
 in Proceedings of the Tenth International Conference on Automata, Languages and Programming
, 1983
"... Effective theorem provers are essential for automatic verification and generation of programs. The conventional resolution strategies, albeit complete, are inefficient. On the other hand, special purpose methods, such as term rewriting systems for solving word problems, are relatively efficient but ..."
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Cited by 21 (10 self)
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Effective theorem provers are essential for automatic verification and generation of programs. The conventional resolution strategies, albeit complete, are inefficient. On the other hand, special purpose methods, such as term rewriting systems for solving word problems, are relatively efficient but applicable to only limited classes of problems. In this paper, a simple canonical set of rewrite rules for Boolean algebra is presented. Based on this set of rules, the notion of term rewriting systems is generalized to provide complete proof strategies for first order predicate calculus. The methods are conceptually simple and can frequently utilize lemmas in proofs. Moreover, when the variables of the predicates involve some domain that has a canonical system, that system can be incorporated as rewrite rules, with the algebraic simplifications being done simultaneously with the merging of clauses. This feature is particularly useful in program verification, data type specification, and programming language design, where axioms can be expressed as equations (rewrite rules). Preliminary results from our implementation indicate that the methods are spaceefficient with respect to the number of rules generated (as compared to the number of resolvents in resolution provers). 2.
Open Problems in Rewriting
 Proceeding of the Fifth International Conference on Rewriting Techniques and Application (Montreal, Canada), LNCS 690
, 1991
"... Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27 ..."
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Cited by 19 (2 self)
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Introduction Interest in the theory and applications of rewriting has been growing rapidly, as evidenced in part by four conference proceedings #including this one# #15, 26, 41,66#; three workshop proceedings #33, 47, 77#; #ve special journal issues #5,88, 24, 40, 67#; more than ten surveys #2,7,27, 28, 44, 56,57,76, 82, 81#; one edited collection of papers #1#; four monographs #3, 12,55,65#; and seven books #four of them still in progress# #8,9, 35, 54, 60,75, 84#. To encourage and stimulate continued progress in this area, wehave collected #with the help of colleagues# a number of problems that appear to us to be of interest and regarding whichwe do not know the answer. Questions on rewriting and other equational paradigms have been included; manyhave not aged su#ciently to be accorded the appellation #open problem". Wehave limited ourselves to theoretical questions, though there are certainly many additional interesting questions relating to applications and implementation
On the Unification Problem for Cartesian Closed Categories (Extended Abstract)
 IN PROCEEDINGS, EIGHTH ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 1989
"... Cartesian closed categories (CCC's) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce and Longo leads to seven e ..."
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Cited by 19 (5 self)
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Cartesian closed categories (CCC's) have played and continue to play an important role in the study of the semantics of programming languages. An axiomatization of the isomorphisms which hold in all Cartesian closed categories discovered independently by Soloviev and Bruce and Longo leads to seven equalities. We show that the unification problem for this theory is undecidable, thus settling an open question. We also show that an important subcase, namely unification modulo the linear isomorphisms, is NPcomplete. Furthermore, the problem of matching in CCC's is NPcomplete when the subject term is irreduc...
Normalised Rewriting and Normalised Completion
, 1994
"... We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algor ..."
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Cited by 19 (2 self)
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We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm, but also the wellknown Buchberger's algorithm for computing standard bases of polynomial ideals. We investigate the particular case of completion of ground equations, In this case we prove by a uniform method that completion modulo E terminates, for some interesting E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories. We give implementation results which shows the efficiency of normalised completion with respect to completion modulo AC. 1 Introduction Equational axioms are very common in most sciences, including computer science. Equations can ...
Any Ground AssociativeCommutative Theory Has a Finite Canonical System
 Proceedings 4th Conference on Rewriting Techniques and Applications
, 1991
"... We show that theories presented by a set of ground equations with several associativecommutative (AC) symbols always admit a finite canonical system. This result is obtained through the construction of a reduction ordering which is ACcompatible and total on the set of congruence classes generated ..."
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Cited by 18 (4 self)
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We show that theories presented by a set of ground equations with several associativecommutative (AC) symbols always admit a finite canonical system. This result is obtained through the construction of a reduction ordering which is ACcompatible and total on the set of congruence classes generated by the associativity and commutativity axioms. As far as we know, this is the first ordering with such properties, when several AC function symbols and free function symbols are allowed. Such an ordering is also a fundamental tool for deriving complete theorem proving strategies with builtin associative commutative unification.
External Rewriting for Skeptical Proof Assistants
, 2002
"... This paper presents the design, the implementation and experiments of the integration of syntactic, conditional possibly associativecommutative term rewriting into proof assistants based on constructive type theory. Our approach is called external since it consists in performing term rewriting in a ..."
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Cited by 18 (3 self)
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This paper presents the design, the implementation and experiments of the integration of syntactic, conditional possibly associativecommutative term rewriting into proof assistants based on constructive type theory. Our approach is called external since it consists in performing term rewriting in a speci c and ecient environment and to check the computations later in a proof assistant.
Buchberger's algorithm: A constraintbased completion procedure
, 1994
"... We present an extended completion procedure with builtin theories defined by a collection of associativity and commutativity axioms and additional ground equations, and reformulate Buchberger's algorithm for constructing Gröbner bases for polynomial ideals in this formalism. The presentation of com ..."
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Cited by 15 (2 self)
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We present an extended completion procedure with builtin theories defined by a collection of associativity and commutativity axioms and additional ground equations, and reformulate Buchberger's algorithm for constructing Gröbner bases for polynomial ideals in this formalism. The presentation of completion is at an abstract level, by transition rules, with a suitable notion of fairness used to characterize a wide class of correct completion procedures, among them Buchberger's original algorithm for polynomial rings over a field.
Dependency Pairs for Equational Rewriting
 Proc. of 12th Int. Conf. on Rewriting Techniques and Applications, RTA'01, LNCS 2051:93108
"... The dependency pair technique of Arts and Giesl [13] for termination proofs of term rewrite systems (TRSs) is extended to rewriting modulo equations. Up to now, such an extension was only known in the special case of ACrewriting [16, 18]. In contrast to that, the proposed technique works for a ..."
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Cited by 14 (3 self)
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The dependency pair technique of Arts and Giesl [13] for termination proofs of term rewrite systems (TRSs) is extended to rewriting modulo equations. Up to now, such an extension was only known in the special case of ACrewriting [16, 18]. In contrast to that, the proposed technique works for arbitrary noncollapsing equations (satisfying a certain linearity condition). With the proposed approach, it is now possible to perform automated termination proofs for many systems where this was not possible before. In other words, the power of dependency pairs can now also be used for rewriting modulo equations.