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International Conference on Rewriting Techniques and Applications

RTA 1998: Rewriting Techniques and Applications pp 211–225Cite as

Co-definite set constraints

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1379))

Abstract

In this paper, we introduce the class of co-definite set constraints. This is a natural subclass of set constraints which, when satisfiable, have a greatest solution. It is practically motivated by the set-based analysis of logic programs with the greatest-model semantics. We present an algorithm solving co-definite set constraints and show that their satisfiability problem is DEXPTIME-complete.

On leave from Wroclaw University. Partially supported by Polish KBN grant 8T11C02913.

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References

  1. A. Aiken. Set constraints: Results, applications and future directions. In Proceedings of the Workshop on Principles and Practice of Constraint Programming, LNCS 874, pages 326–335. Springer-Verlag, 1994.

    Google Scholar 

  2. A. Arnold and M. Nivat. Formal computations of non deterministic recursive program schemes. Mathematical Systems Theory, 13:219–236, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Arnold and D. Niwinski. Fixed point characterization of weak monadic logic definable sets of trees. In M. Nivat and A. Podelski, editors, Tree Automata and Languages, pages 159–188. North Holland, 1992.

    Google Scholar 

  4. L. Bachmair, H. Ganzinger, and U. Waldmann. Set constraints are the monadic class. In Eighth Annual IEEE Symposium on Logic in Computer Science, pages 75–83, 1993.

    Google Scholar 

  5. W. Charatonik and L. Pacholski. Set constraints with projections are in NEXPTIME. In Proceedings of the 35th Symposium on Foundations of Computer Science, pages 642–653, 1994.

    Google Scholar 

  6. W. Charatonik and A. Podelski. Set constraints for greatest models. Technical Report MPI-I-97-2-004, Max-Planck-Institut für Informatik, April 1997. www.mpisb.mpg.de/~podelski/papers/greatest.html.

    Google Scholar 

  7. W. Charatonik and A. Podelski. Set constraints with intersection. In G. Winskel, editor, Twelfth Annual IEEE Symposium on Logic in Computer Science (LICS), pages 362–372. IEEE, June 1997.

    Google Scholar 

  8. P. Devienne, J.-M. Talbot, and S. Tison. Solving classes of set constraints with tree automata. Technical Report IT-303, Laboratoire d'Informatique Fondamentale de Lille, May 1997.

    Google Scholar 

  9. T. Friihwirth, E. Shapiro, M. Vardi, and E. Yardeni. Logic programs as types for logic programs. In Sixth Annual IEEE Symposium on Logic in Computer Science, pages 300–309, July 1991.

    Google Scholar 

  10. F. Gécseg and M. Steinby. Tree Automata. Akademiai Kiado, 1984.

    Google Scholar 

  11. N. Heintze and J. Jaffar. A decision procedure for a class of set constraints (extended abstract). In Fifth Annual IEEE Symposium on Logic in Computer Science, pages 42–51, 1990.

    Google Scholar 

  12. N. Heintze and J. Jaffar. A finite presentation theorem for approximating logic programs. In Seventeenth Annual ACM Symposium on Principles of Programming Languages, pages 197–209, January 1990.

    Google Scholar 

  13. N. Heintze and J. Jaffar. Semantic types for logic programs. In F. Pfenning, editor, Types in Logic Programming, pages 141–156. MIT Press, 1992.

    Google Scholar 

  14. N. Heintze and J. Jaffar. Set constraints and set-based analysis. In Proceedings of the Workshop on Principles and Practice of Constraint Programming, LNCS 874, pages 281–298. Springer-Verlag, 1994.

    Google Scholar 

  15. D. Kozen. Logical aspects of set constraints. In 1993 Conference on Computer Science Logic, LNCS 832, pages 175–188. Springer-Verlag, Sept. 1993.

    Google Scholar 

  16. J. W. Lloyd. Foundations of Logic Programming. Symbolic Computation. Springer-Verlag, Berlin, Germany, second, extended edition, 1987.

    Google Scholar 

  17. D. A. McAllester, R. Givan, C. Witty, and D. Kozen. Tarskian set constraints. In Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pages 138–147, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.

    Google Scholar 

  18. P. Mishra. Towards a theory of types in Prolog. In IEEE International Symposium on Logic Programming, pages 289–298, 1984.

    Google Scholar 

  19. D. Niwinski. On fixed-point clones. In L. Kott, editor, Proceedings of the 13th International Conference on Automata, Languages and Programming, volume 226 of Lecture Notes in Computer Science, pages 464–473. Springer-Verlag, 1986.

    Google Scholar 

  20. L. Pacholski and A. Podelski. Set constraints —a pearl in research on constraints. In G. Smolka, editor, Proceedings of the Third International Conference on Principles and Practice of Constraint Programming —CP97, volume 1330 of Springer LNCS, Berlin, Germany, October 1997. Springer-Verlag.

    Google Scholar 

  21. A. Podelski, W. Charatonik, and M. Müller. Set-based error diagnosis of concurrent constraint programs. submitted for publication, 1997.

    Google Scholar 

  22. H. Seidl. Haskell overloading is DEXPTIME-complete. Information Processing Letters, 52:57–60, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  23. W. Thomas. Handbook of Theoretical Computer Science, volume B, chapter Automata on Infinite Objects, pages 134–191. Elsevier, 1990.

    Google Scholar 

  24. M. Vardi and P. Wolper. Automata-theoretic techniques for modal logics of programs. Journal of Computer and System Sciences, 32, 1986.

    Google Scholar 

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Authors and Affiliations

  1. Max-Planck-Institut für Informatik, Im Stadtwald, D-66123, Saarbrücken, Germany

    Witold Charatonik & Andreas Podelski

Authors
  1. Witold Charatonik
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  2. Andreas Podelski
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Tobias Nipkow

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© 1998 Springer-Verlag

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Charatonik, W., Podelski, A. (1998). Co-definite set constraints. In: Nipkow, T. (eds) Rewriting Techniques and Applications. RTA 1998. Lecture Notes in Computer Science, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052372

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  • DOI: https://doi.org/10.1007/BFb0052372

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64301-2

  • Online ISBN: 978-3-540-69721-3

  • eBook Packages: Springer Book Archive

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