We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages. To this end, letters are annotated with natural numbers, called match heights. If the minimal height of all positions in a redex is h+1 then every position in the reduct will get height h+1. In a match-bounded system, match heights are globally bounded. Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages. Hence it is decidable whether a given rewriting system has a given match bound. We also provide a sufficient criterion for the abence of a match-bound. The problem of existence of a match-bound is still open. Match-boundedness for all strings can be used as an automated criterion for termination, for match-bounded systems are terminating. This criterion can be strengthened by requiring match-boundedness only for a restricted set of strings, for instance the set of right hand sides of forward closures.
We introduce a new class of automated proof methods for the termination of rewriting systems on strings. The basis of all these methods is to show that rewriting preserves regular languages. To this end, letters are annotated with natural numbers, called match heights. If the minimal height of all positions in a redex is h+1 then every position in the reduct will get height h+1. In a match-bounded system, match heights are globally bounded. Using recent results on deleting systems, we prove that rewriting by a match-bounded system preserves regular languages. Hence it is decidable whether a given rewriting system has a given match bound. We also provide a sufficient criterion for the abence of a match-bound. The problem of existence of a match-bound is still open. Match-boundedness for all strings can be used as an automated criterion for termination, for match-bounded systems are terminating. This criterion can be strengthened by requiring match-boundedness only for a restricted set of strings, for instance the set of right hand sides of forward closures.
The subject of this book is string-rewriting systems. It is generally accepted that string-rewriting was first introduced by Axel Thue in the early part of this century. In the 1960's and early...
Replacement systems, such as term rewriting systems, tree manipulat ing systems, and graph grammars, have been used in Computer Science in the context of theorem proving, program optimization,...
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