Termination of String Rewriting Proved Automatically
Journal of Automated Reasoning
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
On tree automata that certify termination of left-linear term rewriting systems
Information and Computation
Towards a Systematic Method for Proving Termination of Graph Transformation Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Match-Bounds with Dependency Pairs for Proving Termination of Rewrite Systems
Language and Automata Theory and Applications
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ICGT '08 Proceedings of the 4th international conference on Graph Transformations
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Automated termination proofs for logic programs by term rewriting
ACM Transactions on Computational Logic (TOCL)
Information and Computation
Bottom-up rewriting is inverse recognizability preserving
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Proving termination of rewrite systems using bounds
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
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ACM Transactions on Programming Languages and Systems (TOPLAS)
Regularity and context-freeness over word rewriting systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Weighted automata for proving termination of string rewriting
Journal of Automata, Languages and Combinatorics
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
On tree automata that certify termination of left-linear term rewriting systems
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
Finding finite automata that certify termination of string rewriting
CIAA'04 Proceedings of the 9th international conference on Implementation and Application of Automata
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Termination of string rewriting with matrix interpretations
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Efficient symbolic implementation of graph automata with applications to invariant checking
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
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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 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 criterion for the absence of a match-bound. It is still open whether match-boundedness is decidable. 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, namely the set of right hand sides of forward closures.