Abstract
We investigate rewriting systems on strings by annotating letters with natural numbers, so called match heights. A position in a reduct will get height h+1 if the minimal height of all positions in the redex is h. In a match-bounded system, match heights are globally bounded. Exploiting recent results on deleting systems, we prove that it is decidable whether a given rewriting system has a given match bound. Further, we show that match-bounded systems preserve regularity of languages. Our main focus, however, is on termination of rewriting. Match-bounded systems are shown to be linearly terminating, and–more interestingly–for inverses of match-bounded systems, termination is decidable. These results provide new techniques for automated proofs of termination.
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Geser, A., Hofbauer, D., Waldmann, J. (2003). Match-Bounded String Rewriting Systems. In: Rovan, B., Vojtáš, P. (eds) Mathematical Foundations of Computer Science 2003. MFCS 2003. Lecture Notes in Computer Science, vol 2747. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45138-9_39
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DOI: https://doi.org/10.1007/978-3-540-45138-9_39
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