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Process algebra for synchronous communication
 Inform. and Control
, 1984
"... Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite ..."
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Cited by 413 (57 self)
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Within the context of an algebraic theory of processes, an equational specification of process cooperation is provided. Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation. The rewrite system behind the communication algebra is shown to be confluent and terminating (modulo its permutative reductions). Further, some relationships are shown to hold between the four concepts of merging. © 1984 Academic Press, Inc.
Termination of Term Rewriting Using Dependency Pairs
 Comput. Sci
, 2000
"... We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left and righthand sides of rewrite rules, but introduce the notion of dependency pairs to compare lefthand sides with special subter ..."
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Cited by 254 (49 self)
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We present techniques to prove termination and innermost termination of term rewriting systems automatically. In contrast to previous approaches, we do not compare left and righthand sides of rewrite rules, but introduce the notion of dependency pairs to compare lefthand sides with special subterms of the righthand sides. This results in a technique which allows to apply existing methods for automated termination proofs to term rewriting systems where they failed up to now. In particular, there are numerous term rewriting systems where a direct termination proof with simplification orderings is not possible, but in combination with our technique, wellknown simplification orderings (such as the recursive path ordering, polynomial orderings, or the KnuthBendix ordering) can now be used to prove termination automatically. Unlike previous methods, our technique for proving innermost termination automatically can also be applied to prove innermost termination of term rewriting systems that are not terminating. Moreover, as innermost termination implies termination for certain classes of term rewriting systems, this technique can also be used for termination proofs of such systems.
Confluence properties of Weak and Strong Calculi of Explicit Substitutions
 JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence prope ..."
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Cited by 132 (7 self)
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Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. [12, 21, 1, 23] are the following: 1. We present a confluent weak calculus of substitutions, where no variable clashes can be feared. 2. We solve a conjecture raised in [1]: oecalculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of oecalculus, named the Envcalculus in [23], called here the confluent oecalculus.
Rewriting systems for Coxeter groups
 J. Pure Appl. Algebra
, 1994
"... A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting sys ..."
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Cited by 9 (3 self)
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A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of normal forms for the group. In this paper it is shown that the fundamental group of an orientable closed surface of genus g has a finite complete rewriting system, using the usual generators a1,.., ag, b1,.., bg along with generators representing their inverses. Constructions of finite complete rewriting systems are also given for any Coxeter group G satisfying one of the following hypotheses. 1) G has three or fewer generators. 2) G does not contain a special subgroup of the form
Normal forms for binary relations
"... We consider the representable equational theory of binary relations, in a language expressing composition, converse, and lattice operations. By working directly with a presentation of relation expressions as graphs we are able to define a notion of reduction which is confluent and strongly normalizi ..."
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We consider the representable equational theory of binary relations, in a language expressing composition, converse, and lattice operations. By working directly with a presentation of relation expressions as graphs we are able to define a notion of reduction which is confluent and strongly normalizing and induces a notion of computable normal form for terms. This notion of reduction thus leads to a computational interpretation of the representable theory. © 2006 Elsevier B.V. All rights reserved.
doi:10.1006/inco.2002.3160 A Characterisation of Multiply Recursive Functions with Higman’s Lemma
, 1999
"... We prove that string rewriting systems which reduce by Higman’s lemma exhaust the multiply recursive functions. This result provides a full characterisation of the expressiveness of Higman’s lemma when applied to rewriting theory. The underlying argument of our construction is to connect the order t ..."
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We prove that string rewriting systems which reduce by Higman’s lemma exhaust the multiply recursive functions. This result provides a full characterisation of the expressiveness of Higman’s lemma when applied to rewriting theory. The underlying argument of our construction is to connect the order type and the derivation length via the Hardy hierarchy. C ○ 2002 Elsevier Science (USA) 1.
Elsevier Semiunification*
"... Semiunification is a generalization of both matching and ordinary unification: for a given pair of terms s and r, two substitutions p and a are sought such that p(a(s)) = a(t). Semiunifiability can be used as a check for nontermination of a rewrite rule, but constructing a correct semiunificatio ..."
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Semiunification is a generalization of both matching and ordinary unification: for a given pair of terms s and r, two substitutions p and a are sought such that p(a(s)) = a(t). Semiunifiability can be used as a check for nontermination of a rewrite rule, but constructing a correct semiunification algorithm has been an elusive goal; for example, an algorithm given by Purdom in his RTA87 paper was incorrect. This paper presents a decision procedure for semiunification based on techniques similar to those used in the KnuthBendix completion procedure. When its inputs are semiunifiable, the procedure yields a canonical termrewriting system from which substitutions p and a are easily extracted. Though exponential in its computing time, the decision procedure can be improved to a polynomialtime algorithm, as will be shown. I.
Rewriting Systems and Geometric 3Manifolds
"... : The fundamental groups of most (conjecturally, all) closed 3manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting systems. The general case remains open. 1. Introduction ..."
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: The fundamental groups of most (conjecturally, all) closed 3manifolds with uniform geometries have finite complete rewriting systems. The fundamental groups of a large class of amalgams of circle bundles also have finite complete rewriting systems. The general case remains open. 1. Introduction A finite complete rewriting system for a group is a finite presentation which solves the word problem by giving a procedure for reducing each word down to a normal form. For closed irreducible 3manifolds, results of [6] show that if the fundamental group is infinite and has a finite complete rewriting system, then the group has a tame combing, so results of [12] show that the manifold has universal cover homeomorphic to RR 3 . In this paper we point out that wellknown properties of finite complete rewriting systems and wellknown facts about geometric 3manifolds combine to give the following. (See below for definitions.) Theorem 1. Suppose that M is a closed 3manifold bearing one of T...