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Deciding Fundamental Properties of Right-(Ground or Variable) Rewrite Systems by Rewrite Closure

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Automated Reasoning (IJCAR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3097))

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Abstract

Right-(ground or variable) rewrite systems (RGV systems for short) are term rewrite systems where all right hand sides of rules are restricted to be either ground or a variable. We define a minimal rewrite extension \(\overline{R}\) of the rewrite relation induced by a RGV system R. This extension admits a rewrite closure presentation, which can be effectively constructed from R. The rewrite closure is used to obtain decidability of the reachability, joinability, termination, and confluence properties of the RGV system R. We also show that the word problem and the unification problem are decidable for confluent RGV systems. We analyze the time complexity of the obtained procedures; for shallow RGV systems, termination and confluence are exponential, which is the best possible result since all these problems are EXPTIME-hard for shallow RGV systems.

Research of the first author was supported in part by the Spanish CICYT project MAVERISH ref. TIC2001-2476-C03-01. Research of the second author was supported in part by NSF grant CCR-0326540.

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Author information

Authors and Affiliations

  1. Technical University of Catalonia, Jordi Girona 1, Barcelona, Spain

    Guillem Godoy

  2. SRI International, Menlo Park, CA, 94025, USA

    Ashish Tiwari

Authors
  1. Guillem Godoy
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  2. Ashish Tiwari
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Editor information

Editors and Affiliations

  1. Information Security Group, Dep. of Computer Science, ETH, Zurich, Switzerland

    David Basin

  2. LORIA & INRIA Lorraine UMR 7503,  

    Michaël Rusinowitch

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Godoy, G., Tiwari, A. (2004). Deciding Fundamental Properties of Right-(Ground or Variable) Rewrite Systems by Rewrite Closure. In: Basin, D., Rusinowitch, M. (eds) Automated Reasoning. IJCAR 2004. Lecture Notes in Computer Science(), vol 3097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25984-8_5

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  • DOI: https://doi.org/10.1007/978-3-540-25984-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22345-0

  • Online ISBN: 978-3-540-25984-8

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