Sparse Tiling Through Overlap Closures for Termination of String Rewriting

Authors Alfons Geser, Dieter Hofbauer, Johannes Waldmann

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Author Details

Alfons Geser
  • HTWK Leipzig, Germany
Dieter Hofbauer
  • ASW - Berufsakademie Saarland, Germany
Johannes Waldmann
  • HTWK Leipzig, Germany

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Alfons Geser, Dieter Hofbauer, and Johannes Waldmann. Sparse Tiling Through Overlap Closures for Termination of String Rewriting. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


A strictly locally testable language is characterized by its set of admissible factors, prefixes and suffixes, called tiles. We over-approximate reachability sets in string rewriting by languages defined by sparse sets of tiles, containing only those that are reachable in derivations. Using the partial algebra defined by a tiling for semantic labeling, we obtain a transformational method for proving local termination. These algebras can be represented efficiently as finite automata of a certain shape. Using a known result on forward closures, and a new characterisation of overlap closures, we can automatically prove termination and relative termination, respectively. We report on experiments showing the strength of the method.

Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • relative termination
  • semantic labeling
  • locally testable language
  • overlap closure


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