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Confluence of Shallow Right-Linear Rewrite Systems

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Computer Science Logic (CSL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3634))

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Abstract

We show that confluence of shallow and right-linear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving, which implies that its reachability and joinability problems are decidable. The new decidability result is obtained by building upon our prior work for the class of ground term rewriting systems and shallow linear term rewriting systems. The proof relies on the concept of extracting more general rewrite derivations from a given rewrite derivation.

The first author was partially supported by Spanish Min. of Educ. and Science by the LogicTools project (TIN2004-03382). The second author was supported in part by the National Science Foundation under grants ITR-CCR-0326540 and CCR-0311348.

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References

  1. Bachmair, L., Ganzinger, H.: Rewrite-based equational theorem proving with selection and simplification. J. of Logic and Computation 4, 217–247 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bouajjani, A.: Languages, rewriting systems, and verification of infinite-state systems. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 24–39. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree automata techniques and applications (1997), Available on http://www.grappa.univ-lille3.fr/tata

  4. Comon, H., Haberstrau, M., Jouannaud, J.-P.: Syntacticness, cyclesyntacticness, and shallow theories. Information and Computation 111(1), 154–191 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dershowitz, N., Jouannaud, J.P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Amsterdam. Formal Models and Semantics, vol. B, pp. 243–320. North-Holland, Amsterdam (1990)

    Google Scholar 

  6. Giesl, J., Zantema, H.: Liveness in rewriting. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 321–336. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Godoy, G., Tiwari, A.: Deciding fundamental properties of right-(ground or variable) rewrite systems by rewrite closure. In: Basin, D., Rusinowitch, M. (eds.) IJCAR 2004. LNCS (LNAI), vol. 3097, pp. 91–106. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  8. Godoy, G., Tiwari, A., Verma, R.: On the confluence of linear shallow term rewrite systems. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 85–96. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Godoy, G., Tiwari, A., Verma, R.: Deciding confluence of certain term rewriting systems in polynomial time. Annals of Pure and Applied Logic 130(1-3), 33–59 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  10. Jacquemard, F.: Reachability and confluence are undecidable for flat term rewriting systems. Inf. Process. Lett. 87(5), 265–270 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  11. Martí-Oliet, N., Meseguer, J.: Rewriting logic: roadmap and bibliography. Theor. Comput. Sci. 285(2), 121–154 (2002)

    Article  MATH  Google Scholar 

  12. Nieuwenhuis, R.: Basic paramodulation and decidable theories. In: Proc. 11th IEEE Symp. on Logic In Comp. Sc. LICS, pp. 473–483. IEEE Computer Society, Los Alamitos (1996)

    Chapter  Google Scholar 

  13. Takai, T., Kaji, Y., Seki, H.: Right-linear finite path overlapping term rewriting systems effectively preserve recognizability. In: Bachmair, L. (ed.) RTA 2000. LNCS, vol. 1833, pp. 246–260. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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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. Oxford University Computing Laboratory, Wolfson Building, Parks Road, OX1 3QD, Oxford, United Kingdom

    Luke Ong

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© 2005 Springer-Verlag Berlin Heidelberg

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Godoy, G., Tiwari, A. (2005). Confluence of Shallow Right-Linear Rewrite Systems. In: Ong, L. (eds) Computer Science Logic. CSL 2005. Lecture Notes in Computer Science, vol 3634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538363_37

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  • DOI: https://doi.org/10.1007/11538363_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28231-0

  • Online ISBN: 978-3-540-31897-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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