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On the Confluence of Linear Shallow Term Rewrite Systems

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STACS 2003 (STACS 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2607))

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Abstract

We show that the confluence of shallow linear term rewrite systems is decidable. The decision procedure is a nontrivial generalization of the polynomial time algorithms for deciding confluence of ground and restricted non-ground term rewrite systems presented in [13]

Partially supported by the Spanish CICYT project MAVERISH ref. TIC2001-2476-C03-01.

Research supported in part by DARPA under the MoBIES and SEC programs administered by AFRL under contracts F33615-00-C-1700 and F33615-00-C-3043, and NSF CCR-0082560.

Research supported in part by NSF grant CCR-9732186.

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References

  1. L. Bachmair. Canonical Equational Proofs. Birkhäuser, Boston, 1991.

    Google Scholar 

  2. H. Comon, G. Godoy, and R. Nieuwenhuis. The confluence of ground term rewrite systems is decidable in polynomial time. In 42nd Annual IEEE Symposium on Foundations of Computer Science (FOCS), Las Vegas, Nevada, USA, 2001.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Dauchet, T. Heuillard, P. Lescanne, and S. Tison. Decidability of the confluence of finite ground term rewrite systems and of other related term rewrite systems. Information and Computation, 88(2):187–201, October 1990.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Ganzinger, F. Jacquemard, and M. Veanes. Rigid reachability: The non-symmetric form of rigid E-unification. Intl. Journal of Foundations of Computer Science, 11(1):3–27, 2000.

    Article  MathSciNet  Google Scholar 

  6. Guillem Godoy, Robert Nieuwenhuis, and Ashish Tiwari. Classes of Term Rewrite Systems with Polynomial Confluence Problems. ACMTransactions on Computational Logic (TOCL), 2002. To appear.

    Google Scholar 

  7. A. Hayrapetyan and R.M. Verma. On the complexity of confluence for ground rewrite systems. In Bar-Ilan International Symposium On The Foundations Of Artificial Intelligence, 2001. Proceedings on the web at http://www.math.tau.ac.il/~nachumd/bisfai-pgm.html

  8. D. E. Knuth and P. B. Bendix. Simpleword problems in universal algebras. In J. Leech, editor, Computational Problems in Abstract Algebra, pages 263–297. Pergamon Press, Oxford, 1970.

    Google Scholar 

  9. A. Levy and J. Agusti. Bi-rewriting, a term rewriting technique for monotone order relations. In C. Kirchner, editor, Rewriting Techniques and Applications RTA-93, pages 17–31, 1993. LNCS 690.

    Google Scholar 

  10. R. Nieuwenhuis. Basic paramodulation and decidable theories. In 11th IEEE Symposium on Logic in Computer Science, LICS 1996, pages 473–482. IEEE Computer Society, 1996.

    Google Scholar 

  11. M. Oyamaguchi. The Church-Rosser property for ground term-rewriting systems is decidable. Theoretical Computer Science, 49(1):43–79, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Tiwari. Rewrite closure for ground and cancellative AC theories. In R. Hariharan and V. Vinay, editors, Conference on Foundations of Software Technology and Theoretical Computer Science, FST&TCS’ 2001, pages 334–346. Springer-Verlag, 2001. LNCS 2245.

    Google Scholar 

  13. A. Tiwari. Deciding confluence of certain term rewriting systems in polynomial time. In Gordon Plotkin, editor, IEEE Symposium on Logic in Computer Science, LICS 2002, pages 447–456. IEEE Society, 2002.

    Google Scholar 

  14. A. Tiwari. On the combination of equational and rewrite theories induced by certain term rewrite systems. Menlo Park, CA 94025, 2002. Available at: http://www.csl.sri.com/~tiwari/combinationER.ps

  15. R. Verma, M. Rusinowitch, and D. Lugiez. Algorithms and reductions for rewriting problems. Fundamenta Informaticae, 43(3):257–276, 2001. Also in Proc. of Int’l Conf. on Rewriting Techniques and Applications 1998.

    MathSciNet  Google Scholar 

  16. H. Zantema. Termination of term rewriting: interpretation and type elimination. Journal of Symbolic Computation, 17:23–50, 1994.

    Article  MATH  MathSciNet  Google Scholar 

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Godoy, G., Tiwari, A., Verma, R. (2003). On the Confluence of Linear Shallow Term Rewrite Systems. In: Alt, H., Habib, M. (eds) STACS 2003. STACS 2003. Lecture Notes in Computer Science, vol 2607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36494-3_9

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  • DOI: https://doi.org/10.1007/3-540-36494-3_9

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  • Print ISBN: 978-3-540-00623-7

  • Online ISBN: 978-3-540-36494-8

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