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Regular Sets of Descendants for Constructor-Based Rewrite Systems

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Logic for Programming and Automated Reasoning (LPAR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1705))

Abstract

Starting from the regular tree language E of ground constructor-instances of any linear term, we build a finite tree automaton that recognizes the set of descendants R* (E) of E for a constructor-based term rewrite system whose right-hand-sides fulfill the following three restrictions: linearity, no nested function symbols, function arguments are variables or ground terms. Note that left-linearity is not assumed. We next present several applications.

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References

  1. H. Comon. Sequentiality, second order monadic logic and tree automata. In Proc., Tenth Annual IEEE Symposium on Logic in Computer Science, pages 508–517. IEEE Computer Society Press, 26–29 June 1995.

    Google Scholar 

  2. H. Comon, M. Dauchet, R. Gilleron, D. Lugiez, S. Tison, and M. Tommasi. Tree Automata Techniques and Applications (TATA). http://13ux02.univ-lille3.fr/tata.

  3. Hubert Comon and Florent Jacquemard. Ground reducibility is exptime-complete. In Proc. IEEE Symp. on Logic in Computer Science, Varsaw, June 1997. IEEE Comp. Soc. Press.

    Google Scholar 

  4. J. Coquidé, M. Dauchet, R. Gilleron, and S. Vagvolgyi. Bottom-up Tree Pushdown Automata and Rewrite Systems. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of LNCS, pages 287–298. Springer-Verlag, April 1991.

    Google Scholar 

  5. M. Dauchet and S. Tison. The theory of ground rewrite systems is decidable. In Proc., Fifth Annual IEEE Symposium on Logic in Computer Science, pages 242–248, Philadelphia, Pennsylvania, 1990. IEEE Computer Society Press.

    Google Scholar 

  6. N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J. Van Leuven, editor, Handbook of Theoretical Computer Science, chapter 6, pages 243–320. Elsevier Science Publishers, 1990.

    Google Scholar 

  7. T. Genet. Decidable Approximations of Sets of Descendants and Sets of Normal Forms. In Proceedings of 9th Conference on Rewriting Techniques and Applications, Tsukuba (Japan), volume 1379 of LNCS, pages 151–165. Springer-Verlag, 1998.

    Google Scholar 

  8. R. Gilleron and S. Tison. Regular Tree Languages and Rewrite Systems. Fundamenta Informaticae, 24:157–175, 1995.

    MATH  MathSciNet  Google Scholar 

  9. F. Jacquemard. Decidable Approximations of Term Rewrite Systems. In H. Ganzinger, editor, Proceedings 7th Conference RTA, New Brunswick (USA), volume 1103 of LNCS, pages 362–376. Springer-Verlag, 1996.

    Google Scholar 

  10. S. Limet and P. Réty. E-Unification by Means of Tree Tuple Synchronized Grammars. In Proceedings of 6th Colloquium on Trees in Algebra and Programming, volume 1214 of LNCS, pages 429–440. Springer-Verlag, 1997.

    Google Scholar 

  11. S. Limet and P. Réty. E-Unification by Means of Tree Tuple Synchronized Grammars. Discrete Mathematics and Theoritical Computer Science, 1:69–98, 1997. (http://dmtcs.loria.fr/).

    MATH  Google Scholar 

  12. P. Réty. Méthodes d’Unification par Surréduction. Thèse de Doctorat d’Université, Université de Nancy I, March 1988. In french.

    Google Scholar 

  13. K. Salomaa. Deterministic Tree Pushdown Automata and Monadic Tree Rewriting Systems. The Journal of Computer and System Sciences, 37:367–394, 1988.

    Article  MATH  MathSciNet  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Réty, P. (1999). Regular Sets of Descendants for Constructor-Based Rewrite Systems. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_10

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  • DOI: https://doi.org/10.1007/3-540-48242-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66492-5

  • Online ISBN: 978-3-540-48242-0

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