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International Conference on Algebraic and Logic Programming

ALP 1996: Algebraic and Logic Programming pp 194–208Cite as

A strict border for the decidability of E-unification for recursive functions

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1139))

Abstract

During the execution of functional logic programs, E-unification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability of those E-unification problems? Up to now, there does not exist a concrete answer to this question. In this paper, we answer this question by drawing and verifying a strict border between undecidability and decidability of E-unification problems for particular classes of recursive functions.

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References

  1. F. Baader and J.H. Siekmann. Unification theory. In D. M. Gabbay, C. J. Hogger, and J. A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming. Oxford Univ. Press, 1993.

    Google Scholar 

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

    Google Scholar 

  3. N. Dershowitz and J.P. Jouannaud. Rewrite systems. In Jan van Leeuwen, editor, Handbook of Theoretical Computer Science, Vol. B, chapter 6, pages 243–320. Elsevier, 1990.

    Google Scholar 

  4. R. Echahed. On completeness of narrowing strategies. Theoret. Comput. Sci., 72:133–146, 1990.

    Google Scholar 

  5. J. Engelfriet. Bottom-up and top-down tree transformations — a comparison. Math. Systems Theory, 9(3):198–231, 1975.

    Google Scholar 

  6. J. Engelfriet and H. Vogler. Modular tree transducers. Theoret. Comput. Sci., 78:267–304, 1991.

    Google Scholar 

  7. Z. Fülöp, F. Herrmann, S. Vágvölgyi, and H. Vogler. Tree transducers with external functions. Theoret. Comput. Sci., 108:185–236, 1993.

    Google Scholar 

  8. S. Ginsburg. Examples of abstract machines. IEEE Trans. on Electronic Computers, 11(2):132–135, 1962.

    Google Scholar 

  9. S. Ginsburg and G. F. Rose. Operations which preserve definability in languages. J. Assoc. Comput. Mach., 10:175–195, 1963.

    Google Scholar 

  10. J. W. Hopcroft and J. D. Ullmann. Introduction to automata theory, languages, and computation. Addison-Wesley, 1979.

    Google Scholar 

  11. G. Huet. Confluent reductions: abstract properties and applications to term rewriting systems. J. Assoc. Comput. Mach., 27:797–821, 1980.

    Google Scholar 

  12. J.M. Hullot. Canonical forms and unification. In Proceedings of the 5th conference on automated deduction, volume 87 of LNCS, pages 318–334. Springer-Verlag, 1980.

    Google Scholar 

  13. D. Kapur and P. Narendran. Matching, unification and complexity. ACM SIGSAM Bulletin, 21(4):6–9, 1987.

    Google Scholar 

  14. G. S. Makanin. The problem of solvability of equations in a free semigroup. Math. USSR Sbornik, 32(2):129–198, 1977.

    Google Scholar 

  15. Y. Matijasevič. Diophantine representation of recursively enumerable predicates. In Actes du Congrès International des Mathématiciens, volume 1, pages 235–238, Nice (France), 1970.

    Google Scholar 

  16. S. Mitra. Semantic unification for convergent systems. Technical Report CS-R-94-1855, University of Illinois at Urbana-Champaign, 1994.

    Google Scholar 

  17. A. Martelli and U. Montanari. An efficient unification algorithm. ACM Transactions on Programming Languages Systems, 4:258–282, 1982.

    Google Scholar 

  18. J.J. Moreno-Navarro and M. Rodriguez-Artalejo. Logic-programming with functions and predicates: the language BABEL. Journal Logic Programming, 12:191–223, 1992.

    Google Scholar 

  19. F. Otto, P. Narendran, and D. J. Dougherty. Some independance results for equational unification. In J. Hsiang, editor, Proceedings of the 6th International Conference on Rewriting Techniques and Applications, volume 914 of LNCS, pages 367–381, 1995.

    Google Scholar 

  20. E. Post. A variant of a recursively unsolvable problem. Bull. AMS, 52:264–268, 1946.

    Google Scholar 

  21. M. Presburger. Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen. In Comptes Rendus Premier Congrès des Mathématicienes des Pays Slaves, Warsaw, pages 92–101, 1927.

    Google Scholar 

  22. J.A. Robinson. A machine-oriented logic based on the resolution principle. J. Assoc. Comput. Mach., 20:23–41, 1965.

    Google Scholar 

  23. W.C. Rounds. Mappings and grammars on trees. Math. Systems Theory, 4:257–287, 1970.

    Google Scholar 

  24. M. E. Stickel. A complete unification algorithm for associative-commutative functions. In Proceedings of the 4th International Joint Conference on Artificial Intelligence (IJCAI), Tbilisi, pages 71–76, 1975.

    Google Scholar 

  25. J.W. Thatcher. Generalized2 sequential machine maps. J. Comput. Syst. Sci., 4:339–367, 1970.

    Google Scholar 

  26. J.H. You. Enumerating outer narrowing derivations for constructor-based term rewriting systems. J. Symbolic Computation, 7:319–341, 1989.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Deutsche Forschungsanstalt für Luft- und Raumfahrt e.V., Qualität und Sicherheit, D-51140, Köln, Germany

    Heinz Faßbender

  2. Institut für Softwaretechnik I, Fakultät Informatik, TU Dresden, D-01062, Dresden, Germany

    Sebastian Maneth

Authors
  1. Heinz Faßbender
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  2. Sebastian Maneth
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Editor information

Michael Hanus Mario Rodríguez-Artalejo

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© 1996 Springer-Verlag Berlin Heidelberg

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Faßbender, H., Maneth, S. (1996). A strict border for the decidability of E-unification for recursive functions. In: Hanus, M., Rodríguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1996. Lecture Notes in Computer Science, vol 1139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61735-3_13

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  • DOI: https://doi.org/10.1007/3-540-61735-3_13

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61735-8

  • Online ISBN: 978-3-540-70672-4

  • eBook Packages: Springer Book Archive

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