Using groups for investigating rewrite systems

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Using groups for investigating rewrite systems

We describe several technical tools that prove to be efficient for investigating the rewrite systems associated with a family of algebraic laws, and might be useful for more general rewrite systems. These tools consist in introducing a monoid of partial operators, listing the monoid relations expressing the possible local confluence of the rewrite system, then introducing the group presented by...

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The use of automata techniques to prove the termination of string rewrite systems and left-linear term rewrite systems is advocated by Geser et al. in a recent sequence of papers. We extend their work to non-left-linear rewrite systems. The key to this extension is the introduction of so-called raise rules and the use of tree automata that are not quite deterministic. Furthermore, we present ne...

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Rewrite Systems for Integer Arithmetic

H.Zantema Utrecht University, Compo Sc. Dept. P.O. Box 80.089, 3508 TB Utrecht [email protected] We present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground confluent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by successor and prede...

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ژورنال

عنوان ژورنال: Mathematical Structures in Computer Science

سال: 2008

ISSN: 0960-1295,1469-8072

DOI: 10.1017/s0960129508007160