Skip to main content
SpringerLink
Log in

Constraint Solving on Terms

  • Chapter
  • First Online:
Constraints in Computational Logics (CCL 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2002))

Included in the following conference series:

Abstract

In this chapter, we focus on constraint solving on terms, also called Herbrand constraints in the introductory chapter, and we follow the main concepts introduced in that chapter.

Both authors supported by the ESPRIT working group CCL-II, ref.WG # 22457.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Adi and Claude Kirchner. Associative commutative matching based on the syntacticity of the ac theory. In Franz Baader, J. Siekmann, and W. Snyder, editors, Proceedings 6th International Workshop on Unification, Dagstuhl (Germany). Dagstuhl seminar, 1992.

    Google Scholar 

  2. F. Baader. Unification, weak unification, upper bound, lower bound, and generalization problems. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of Lecture Notes in Computer Science, pages 86–97. Springer-Verlag, April 1991.

    Google Scholar 

  3. J.R. Büchi. On a decision method in restricted second-order arithmetic. In E. Nagel et al., editor, Proc. Int. Congr. on logic, methodology and philosophy of science, Standford, 1960. Stanford Univ. Press.

    Google Scholar 

  4. Alexandre Boudet and Hubert Comon. Diophantine equations, Presburger arithmetic and finite automata. In H. Kirchner, editor, Proc. Coll. on Trees in Algebra and Programming (CAAP’96), Lecture Notes in Computer Science, 1996.

    Google Scholar 

  5. Peter Borovanský, Horatiu Cirstea, Hubert Dubois, Claude Kirchner, Hélène Kirchner, Pierre-Etienne Moreau, Christophe Ringeissen, and Marian Vittek. ELAN V 3.3 User Manual. LORIA, Nancy (France), third edition, December 1998.

    Google Scholar 

  6. L. Bachmair, H. Ganzinger, C. Lynch, and W. Snyder. Basic paramodulation. Information and Computation, 121(2):172–192, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  7. Leo Bachmair, Harald Ganzinger, and Uwe Waldmann. Set constraints are the monadic class. In Proc. 8th IEEE Symp. Logic in Computer Science, Montréal, 1993.

    Google Scholar 

  8. H.-J. Bürckert, A. Herold, and M. Schmidt-Schauß. On equational theories, unification and decidability. Journal of Symbolic Computation, 8(1 & 2):3–50, 1989. Special issue on unification. Part two.

    Article  MATH  MathSciNet  Google Scholar 

  9. Peter Borovanský, Claude Kirchner, Hélène Kirchner, Pierre-Etienne Moreau, and Christophe Ringeissen. An overview of ELAN. In Claude Kirchner and Hélène Kirchner, editors, Proceedings of the second International Workshop on Rewriting Logic and Applications, http://volume15,http://www.elsevier.nl/locate/entcs/volume16.html,Pont-à-Mousson (France), September 1998. Electronic Notes in Theoretical Computer Science.

  10. Franz Baader and Tobias Nipkow. Term Rewriting and all That. Cambridge University Press, 1998.

    Google Scholar 

  11. A. Bockmayr. A note on a canonical theory with undecidable unification and matching problem. Journal of Automated Reasoning, 3(1):379–381, 1987.

    MATH  MathSciNet  Google Scholar 

  12. R. V. Book and J. Siekmann. On unification: Equational theories are not bounded. Journal of Symbolic Computation, 2:317–324, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  13. F. Baader and W. Snyder. Unification theory. In J.A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning. Elsevier Science Publishers, 1999. To appear.

    Google Scholar 

  14. B. Bogaert and Sophie Tison. Equality and disequality constraints on brother terms in tree automata. In A. Finkel, editor, Proc. 9th Symp. on Theoretical Aspects of Computer Science, Paris, 1992. Springer-Verlag.

    Google Scholar 

  15. H.-J. Bürckert. Matching-A special case of unification? Journal of Symbolic Computation, 8(5):523–536, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  16. O. Bernholtz, M. Vardi, and P. Wolper. Au automata-theoretic approach to branching-time model checking. In Proc. 6th Int. Conf. on Computer Aided verification, volume 818 of Lecture Notes in Computer Science. Springer Verlag, 1994.

    Google Scholar 

  17. Carlos Castro. Building Constraint Satisfaction Problem Solvers Using Rewrite Rules and Strategies. Fundamenta Informaticae, 34:263–293, September 1998.

    Google Scholar 

  18. A.-C. Caron, H. Comon, J.-L. Coquidé, M. Dauchet, and F. Jacquemard. Pumping, cleaning and symbolic constraints solving. In Proc. Int. Conference on Algorithms, Languages and Programming, Lecture Notes in Computer Science, vol. 820, Jerusalem, July 1994. Springer-Verlag.

    Google Scholar 

  19. Anne-Cécile Caron, Jean-Luc Coquide, and Max Dauchet. Encompassment properties and automata with constraints. In Claude Kirchner, editor, Rewriting Techniques and Applications, 5th International Conference, RTA-93, LNCS 690, pages 328–342, Montreal, Canada, June 16–18, 1993. Springer-Verlag.

    Google Scholar 

  20. Hubert Comon and Catherine Delor. Equational formulae with membership constraints. Information and Computation, 112(2):167–216, August 1994.

    Article  MATH  MathSciNet  Google Scholar 

  21. H. Comon, M. Dauchet, R. Gilleron, D. Lugiez, S. Tison, and M. Tommasi. Tree automata techniques and applications. A preliminary version of this unpublished book is available on http://l3ux02.univ-lille3.fr/tata, 1997.

  22. Hubert Comon, Mehmet Dincbas, Jean-Pierre Jouannaud, and Claude Kirchner. A methodological view of constraint solving. Constraints, 4(4):337–361, December 1999.

    Article  MATH  MathSciNet  Google Scholar 

  23. H. Comon and M. Fernández. Negation elimination in equational formulae. In Proc. 17th International Symposium on Mathematical Foundations of Computer Science (Praha), Lecture Notes in Computer Science, 1992.

    Google Scholar 

  24. V. Cortier, H. Ganzinger, F. Jacquemard, and V Veanes. Decidable fragments of simultaneous rigid reachability. In Proc. ICALP’99, 1999. To appear in ICALP’99.

    Google Scholar 

  25. Jacques Chabin. Unification Générale par Surréduction Ordonnée Contrainte et Surréduction Dirigée. Thése de Doctorat d’Université, Universit é d’Orléans, January 1994.

    Google Scholar 

  26. Hubert Comon, Marianne Haberstrau, and Jean-Pierre Jouannaud. Syntacticness, cycle-syntacticness and shallow theories. Information and Computation, 111(1):154–191, May 1994.

    Article  MATH  MathSciNet  Google Scholar 

  27. A. Church. Logic, arithmetic, automata. In Proc. International Mathematical Congress, 1962.

    Google Scholar 

  28. H. Comon and F. Jacquemard. Ground reducibility and automata with disequality constraints. In P. Enjalbert, E. W. Mayr, and K. W. Wagner, editors, Proceedings 11th Annual Symposium on Theoretical Aspects of Computer Science, Caen (France), volume 775 of Lecture Notes in Computer Science, pages 151–162. Springer-Verlag, February 1994.

    Google Scholar 

  29. 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 

  30. Hubert Comon and Yan Jurski. Higher-order matching and tree automata. In M. Nielsen and W. Thomas, editors, Proc. Conf. on Computer Science Logic, volume 1414 of LNCS, pages 157–176, Aarhus, August 1997. Springer-Verlag.

    Google Scholar 

  31. H. Comon and P. Lescanne. Equational problems and disunification. Journal of Symbolic Computation, 7(3 & 4):371–426, 1989. Special issue on unification. Part one.

    Article  MATH  MathSciNet  Google Scholar 

  32. A. Colmerauer. PROLOG II, manuel de référence et modèle théorique. Technical report, GIA, Université Aix-Marseille II, 1982.

    Google Scholar 

  33. H. Comon. Sufficient completeness, term rewriting system and antiuni fication. In J. Siekmann, editor, Proceedings 8th International Conference on Automated Deduction, Oxford (UK), volume 230 of Lecture Notes in Computer Science, pages 128–140. Springer-Verlag, 1986.

    Google Scholar 

  34. H. Comon. Unification et disunification. Théories et applications. Thése de Doctorat d’Université, Institut Polytechnique de Grenoble (France), 1988.

    Google Scholar 

  35. Hubert Comon. Inductive proofs by specification transformations. In Nachum Dershowitz, editor, Proceedings of the Third International Conference on Rewriting Techniques and Applications, pages 76–91, Chapel Hill, NC, April 1989. Vol. 355 of Lecture Notes in Computer Science, Springer, Berlin.

    Google Scholar 

  36. H. Comon. Solving symbolic ordering constraints. International Journal of Foundations of Computer Sciences, 1(4):387–411, 1990.

    Article  MATH  MathSciNet  Google Scholar 

  37. H. Comon. Disunification: a survey. In Jean-Louis Lassez and G. Plotkin, editors, Computational Logic. Essays in honor of Alan Robinson, chapter 9, pages 322–359. The MIT press, Cambridge (MA, USA), 1991.

    Google Scholar 

  38. Hubert Comon. Complete axiomatizations of some quotient term algebras. Theoretical Computer Science, 118(2):167–191, September 1993.

    Article  MATH  MathSciNet  Google Scholar 

  39. H. Comon. Completion of rewrite systems with membership constraints. Part II: Constraint solving. Journal of Symb. Computation, 25:421–453, 1998. This is the second part of a paper whose abstract appeared in Proc. ICALP 92, Vienna.

    Article  MATH  MathSciNet  Google Scholar 

  40. Hubert Comon and Ralf Treinen. Ordering constraints on trees. In Sophie Tison, editor, Colloquium on Trees in Algebra and Programming, volume 787 of Lecture Notes in Computer Science, pages 1–14, Edinburgh, Scotland, April 1994. Springer Verlag.

    Chapter  Google Scholar 

  41. M. Dauchet. Symbolic constraints and tree automata. In Jouannaud [Jou94], pages 217–218.

    Google Scholar 

  42. Dauchet, Caron, and Coquidé. Automata for reduction properties solving. JSCOMP: Journal of Symbolic Computation, 20, 1995.

    Google Scholar 

  43. N. Dershowitz and C. Hoot. Natural termination. Theoretical Computer Science, 142(2):179–207, May 1995.

    Article  MATH  MathSciNet  Google Scholar 

  44. Gilles Dowek, Thérèse Hardin, and Claude Kirchner. Theorem proving modulo. Rapport de Recherche 3400, Institut National de Recherche en Informatique et en Automatique, April 1998. ftp://ftp.inria.fr/INRIA/publication/RR/RR-3400.ps.gz.

  45. Max Dauchet, Thierry Heuillard, Pierre Lescanne, and Sophie Tison. The confluence of ground term rewriting systems is decidable. In Proc. 3rd IEEE Symp. Logic in Computer Science, Edinburgh, 1988.

    Google Scholar 

  46. N. Dershowitz and J.-P. Jouannaud. Rewrite Systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, chapter 6, pages 244–320. Elsevier Science Publishers B. V. (North-Holland), 1990.

    Google Scholar 

  47. D. Dougherty and P. Johann. An improved general E-unification method. In M. E. Stickel, editor, Proceedings 10th International Conference on Automated Deduction, Kaiserslautern (Germany), volume 449 of Lecture Notes in Computer Science, pages 261–275. Springer-Verlag, July 1990.

    Google Scholar 

  48. C. Dwork, P. Kanellakis, and J. C. Mitchell. On the sequential nature of unification. Journal of Logic Programming, 1(1):35–50, 1984.

    Article  MATH  MathSciNet  Google Scholar 

  49. M. Davis, Y. Matijasevič, and J. A. Robinson. Hilbert’s tenth problem: Positive aspects of a negative solution. In F. E. Browder, Editor, Mathematical Developments Arising from Hilbert Problems, American Mathematical Society, pages 323–378, 1976.

    Google Scholar 

  50. Anatoli Degtyarev, Yuri Matiyasevich, and Andrei Voronkov. Simultaneous reigid e-unification and related algorithmic problems. In Proc. IEEE Symp. on Logic in Computer Science, pages 494–502. IEEE Comp. Soc. Press, 1996.

    Google Scholar 

  51. Gilles Dowek. Third order matching is decidable. Annals of Pure and Applied Logic, 1993.

    Google Scholar 

  52. Max Dauchet and Sophie Tison. The theory of ground rewrite systems is decidable. In Proc. 5th IEEE Symp. Logic in Computer Science, Philadelphia, 1990.

    Google Scholar 

  53. Steven Eker. Associative-commutative matching via bipartite graph matching. Computer Journal, 38(5):381–399, 1995.

    Article  Google Scholar 

  54. C.C. Elgot. Decision problems of finite automata design and related arithmetics. Trans. Amer. Math. Soc., 98:21–52, 1961.

    Article  MathSciNet  Google Scholar 

  55. M. Fay. First order unification in equational theories. In Proceedings 4th Workshop on Automated Deduction, Austin (Tex., USA), pages 161–167, 1979.

    Google Scholar 

  56. M. Fernández. Narrowing based procedures for equational disunification. Applicable Algebra in Engineering, Communication and Computation, 3:1–26, 1992.

    Article  MATH  Google Scholar 

  57. M. Fernández. Negation elimination in empty or permutative theories. J. Symbolic Computation, 26(1):97–133, July 1998.

    Article  MATH  Google Scholar 

  58. F. Fages and G. Huet. Complete sets of unifiers and matchers in equational theories. Theoretical Computer Science, 43(1):189–200, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  59. Jeanne Ferrante and Charles W. Rackoff. The computational complexity of logical theories. Number 718 in Lecture Notes in Mathematics. Springer Verlag, 1979.

    Google Scholar 

  60. L. Fribourg. SLOG: A logic programming language interpreter based on clausal superposition and rewriting. In IEEE Symposium on Logic Programming, Boston (MA), 1985.

    Google Scholar 

  61. J. A. Goguen and J. Meseguer. EQLOG: Equality, types, and generic modules for logic programming. In Douglas De Groot and Gary Lindstrom, editors, Functional and Logic Programming, pages 295–363. Prentice Hall, Inc., 1986. An earlier version appears in Journal of Logic Programming, Volume 1, Number 2, pages 179–10, September 1984.

    Google Scholar 

  62. H. Ganzinger, C. Meyer, and C. Weidenbach. Soft typing for ordered resolution. In W. McCune, editor, Proc. 14th Conference on Automated Deduction, volume 1249 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1997.

    Google Scholar 

  63. Jean Gallier, S. Raatz, and Wayne Snyder. Theorem proving using rigid E-unification: Equational matings. In Proc. 2nd IEEE Symp. Logic in Computer Science, Ithaca, NY, June 1987.

    Google Scholar 

  64. J. Gallier and W. Snyder. A general complete E-unification procedure. In P. Lescanne, editor, Proceedings 2nd Conference on Rewriting Techniques and Applications, Bordeaux (France), volume 256 of Lecture Notes in Computer Science, pages 216–227, Bordeaux (France), 1987. Springer-Verlag.

    Google Scholar 

  65. J. Gallier and W. Snyder. Complete sets of transformations for general E-unification. Theoretical Computer Science, 67(2–3):203–260, October 1989.

    Article  MATH  MathSciNet  Google Scholar 

  66. R. Gilleron, S. Tison, and M. Tommasi. Solving systems of set constraints with negated subset relationships. In Proc. 34th Symposium on Foundations of Computer Science, pages 372–380, Palo Alto, CA, November 1993. IEEE Computer society press.

    Google Scholar 

  67. Rémy Gilleron, Sophie Tison, and Marc Tommasi. Solving systems of set constraints using tree automata. In Proc. 10th Symposium on Theoretical Aspects of Computer Science, Würzburg, LNCS, 1993.

    Google Scholar 

  68. R. Gilleron, S. Tison, and M. Tommasi. Some new decidability results on positive and negative set constraints. In Jouannaud [Jou94], pages 336–351.

    Google Scholar 

  69. Claus Hintermeier, Claude Kirchner, and Hélène Kirchner. Dynamically-typed computations for order-sorted equational presentations. Journal of Symbolic Computation, 25(4):455–526, 98. Also report LORIA 98-R-157.

    Article  MathSciNet  Google Scholar 

  70. S. Hölldobler. Foundations of Equational Logic Programming, volume 353 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 1989.

    Google Scholar 

  71. J. Hsiang and M. Rusinowitch. Proving refutational completeness of theorem proving strategies: The transfinite semantic tree method. Journal of the ACM, 38(3):559–587, July 1991.

    Article  MATH  MathSciNet  Google Scholar 

  72. G. Huet. Résolution d’equations dans les langages d’ordre 1,2,...,ω. Thése de Doctorat d’Etat, Université de Paris 7 (France), 1976

    Google Scholar 

  73. J.-M. Hullot. Associative-commutative pattern matching. In Proceedings 9th International Joint Conference on Artificial Intelligence, 1979.

    Google Scholar 

  74. J.-M. Hullot. Canonical forms and unification. In W. Bibel and R. Kowalski, editors, Proceedings 5th International Conference on Automated Deduction, Les Arcs (France), volume 87 of Lecture Notes in Computer Science, pages 318–334. Springer-Verlag, July 1980.

    Google Scholar 

  75. J.-M. Hullot. Compilation de Formes Canoniques dans les Théories équationelles. Thèse de Doctorat de Troisième Cycle, Université de Paris Sud, Orsay (France), 1980.

    Google Scholar 

  76. J.-P. Jouannaud and Claude Kirchner. Solving equations in abstract algebras: a rule-based survey of unification. In Jean-Louis Lassez and G. Plotkin, editors, Computational Logic. Essays in honor of Alan Robinson, chapter 8, pages 257–321. The MIT press, Cambridge (MA, USA), 1991.

    Google Scholar 

  77. J.-P. Jouannaud, Claude Kirchner, and Hélène Kirchner. Incremental construction of unification algorithms in equational theories. In Proceedings International Colloquium on Automata, Languages and Programming, Barcelona (Spain), volume 154 of Lecture Notes in Computer Science, pages 361–373. Springer-Verlag, 1983.

    Google Scholar 

  78. Florent Jacquemard, Christoph Meyer, and Christoph Weidenbach. Unification in extensions of shallow equational theories. In T. Nipkow, editor, Porceedings of the 9th International Conference on Rewriting Techniques and Applications, volume 1379 of Lecture Notes in Computer Science, pages 76–90, Tsukuba, Japan, 1998. Springer-Verlag.

    Google Scholar 

  79. J.-P. Jouannaud and M. Okada. Satisfiability of systems of ordinal notations with the subterm property is decidable. In J. Leach Albert, B. Monien, and M. Rodríguez Artalejo, editors, Proceedings 18th ICALP Conference, Madrid (Spain), volume 510 of Lecture Notes in Computer Science. Springer Verlag, 1991.

    Google Scholar 

  80. Jean-Pierre Jouannaud, editor. First International Conference on Constraints in Computational Logics, volume 845 of Lecture Notes in Computer Science, München, Germany, September 1994. Springer Verlag.

    MATH  Google Scholar 

  81. Claude Kirchner. Méthodes et outils de conception systématique d’algorithmes d’uniéation dans les théories _equationnelles. Thèse de Doctorat d’Etat, Université Henri Poincaré-Nancy 1, 1985.

    Google Scholar 

  82. Claude Kirchner and Hélène Kirchner. Constrained equational reasoning. In Proceedings of the ACM-SIGSAM 1989 International Symposium on Symbolic and Algebraic Computation, Portland (Oregon), pages 382–389. ACM Press, July 1989. Report CRIN 89-R-220.

    Google Scholar 

  83. Claude Kirchner and F. Klay. Syntactic theories and unification. In Proceedings 5th IEEE Symposium on Logic in Computer Science, Philadelphia (Pa., USA), pages 270–277, June 1990.

    Google Scholar 

  84. Claude Kirchner and Hélène Kirchner. Rewriting, solving, proving. A preliminary version of a book available at http://www.loria.fr/~ckirchne/rsp.ps.gz, 1999.

  85. Claude Kirchner, Hélène Kirchner, and M. Rusinowitch. Deduction with symbolic constraints. Revue d’Intelligence Artificielle, 4(3):9–52, 1990. Special issue on Automatic Deduction.

    Google Scholar 

  86. Claude Kirchner, Hélène Kirchner, and Marian Vittek. Designing constraint logic programming languages using computational systems. In P. Van Hentenryck and V. Saraswat, editors, Principles and Practice of Constraint Programming. The Newport Papers., chapter 8, pages 131–158. The MIT press, 1995.

    Google Scholar 

  87. Claude Kirchner and P. Lescanne. Solving disequations. In D. Gries, editor, Proceedings 2nd IEEE Symposium on Logic in Computer Science, Ithaca (N.Y., USA), pages 347–352. IEEE, 1987.

    Google Scholar 

  88. Nils Klarlund. A theory of restrictions for logics and automata. In Proc. Computer Aided Verification (CAV), volume 1633 of Lecture Notes in Computer Science, pages 406–417, 1999.

    Google Scholar 

  89. D. Kozen. Set constraints and logic programming. In Jouannaud [Jou94]. To appear in Information and Computation.

    Google Scholar 

  90. Claude Kirchner and Christophe Ringeissen. Rule-Based Constraint Programming. Fundamenta Informaticae, 34(3):225–262, September 1998.

    MATH  MathSciNet  Google Scholar 

  91. Jean-Louis Lassez and K. Marriot. Explicit representation of terms defined by counter examples. Journal of Automated Reasoning, 3(3):301–318, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  92. D. Lugiez and J.L. Moysset. Tree automata help one to solve equational formulae in ac-theories. Journal of symbolic computation, 11(1), 1994.

    Google Scholar 

  93. Jean-Louis Lassez, M. J. Maher, and K. Marriot. Unification revisited. In J. Minker, editor, Foundations of Deductive Databases and Logic Programming. Morgan-Kaufman, 1988.

    Google Scholar 

  94. S. Limet and P. Réty. E-unification by means of tree tuple synchronized grammars:. Discrete Mathematics and Theoretical Computer Science, 1(1):69–98, 1997.

    MATH  MathSciNet  Google Scholar 

  95. M. J. Maher. Complete axiomatization of the algebra of finite, rational trees and infinite trees. In Proceedings 3rd IEEE Symposium on Logic in Computer Science, Edinburgh (UK). COMPUTER SOCIETY PRESS, 1988.

    Google Scholar 

  96. 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 

  97. J. Meseguer, J. A. Goguen, and G. Smolka. Order-sorted unification. In Claude Kirchner, editor, Unification, pages 457–488. Academic Press, London, 1990.

    Google Scholar 

  98. U. Martin and T. Nipkow. Boolean unification-the story so far. Journal of Symbolic Computation, 7(3 & 4):275–294, 1989. Special issue on unification. Part one.

    Article  MATH  MathSciNet  Google Scholar 

  99. Martin Müller and Joachim Niehren. Ordering constraints over feature trees expressed in second-order monadic logic. In Proc. Int. Conf. on Rewriting Techniques and Applications, volume 1379 of Lecture Notes in Computer Science, pages 196–210, Tsukuba, Japan, 1998.

    Google Scholar 

  100. J. Moreno-Navarro and M. Rodriguez-Artalejo. Logic programming with functions and predicates: the language BABEL. Journal of Logic Programming, 12(3):191–223, February 1992.

    Article  MATH  Google Scholar 

  101. Michael J. Maher and Peter J. Stuckey. On inductive inference of cyclic structures. In F. Hoffman, editor, Annals of Mathematics and Artificial Intelligence, volume F. J.C. Baltzer Scientific Pub. Company, 1990. To appear.

    Google Scholar 

  102. J. Mzali. Méthodes de filtrage équationnel et de preuve automatique de théorèmes. Thèse de Doctorat d’Université, Université Henri Poincaré-Nancy 1, 1986.

    Google Scholar 

  103. R. Nieuwenhuis. Simple lpo constraint solving methods. Information Processing Letters, 47(2), 1993.

    Google Scholar 

  104. Robert Nieuwenhuis. On narrowing, refutation proofs and constraints. In Jieh Hsiang, editor, Rewriting Techniques and Applications, 6th International Conference, RTA-95, LNCS 914, pages 56–70, Kaiserslautern, Germany, April 5–7, 1995. Springer-Verlag.

    Google Scholar 

  105. Roberto Nieuwenhuis. Solved forms for path ordering constraints. In Paliath Narendran and Michael Rusinowitch, editors, Porceedings of RTA’99, volume 1631 of Lecture Notes in Computer Science, pages 1–15. Springer Verlag, July 1999.

    Google Scholar 

  106. P. Narendran and F. Otto. Some results on equational unification. In M. E. Stickel, editor, Proceedings 10th International Conference on Automated Deduction, Kaiserslautern (Germany), volume 449 of Lecture Notes in Computer Science, pages 276–291, July 1990.

    Google Scholar 

  107. R. Nieuwenhuis and A. Rubio. Theorem Proving with Ordering and Equality Constrained Clauses. J. Symbolic Computation, 19(4):321–352, April 1995.

    Article  MATH  MathSciNet  Google Scholar 

  108. W. Nutt, P. Réty, and G. Smolka. Basic narrowing revisited. Journal of Symbolic Computation, 7(3 & 4):295–318, 1989. Special issue on unification. Part one.

    Article  MATH  MathSciNet  Google Scholar 

  109. P. Narendran, M. Rusinowitch, and R. Verma. RPO constraint solving is in NP. In Annual Conference of the European Association for Computer Science Logic, Brno (Czech Republic), August 1998. Available as Technical Report 98-R-023, LORIA, Nancy (France).

    Google Scholar 

  110. W. Nutt. The unification hierarchy is undecidable. In H.-J. Bürckert and W. Nutt, editors, Proceedings 3rd International Workshop on Unification, Lambrecht (Germany), June 1989.

    Google Scholar 

  111. Vincent Padovani. Filtrage d’ordre supérieur. PhD thesis, Université de Paris VII, 1996.

    Google Scholar 

  112. Dominique Perrin. Finite automata. In Handbook of Theoretical Computer Science, volume Formal Models and Semantics, pages 1–58. Elsevier, 1990.

    Google Scholar 

  113. Reinhard Pichler. Solving equational problems efficiently. In Harald Ganzinger, editor, Automated Deduction-CADE-16, 16th International Conference on Automated Deduction, LNAI 1632, pages 97–111, Trento, Italy, July 7–10, 1999. Springer-Verlag.

    Google Scholar 

  114. G. Plotkin. Building-in equational theories. Machine Intelligence, 7:73–90, 1972.

    MATH  MathSciNet  Google Scholar 

  115. L. Pacholski and A. Podelski. Set constraints-a pearl in research on constraints. In Gert Smolka, editor, Proc. 3rd Conference on Principles and Practice of Constraint Programming-CP97, volume 1330 of Lecture Notes in Computer Science, pages 549–561, Linz, Austria, 1997. Springer Verlag. Invited Tutorial.

    Google Scholar 

  116. M. S. Paterson and M. N. Wegman. Linear unification. Journal of Computer and System Sciences, 16:158–167, 1978.

    Article  MATH  MathSciNet  Google Scholar 

  117. M.O. Rabin. Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc., 141:1–35, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  118. M. Rabin. Decidable theories. In J. Barwise, editor, Handbook of Mathematical Logic, pages 595–629. North-Holland, 1977.

    Google Scholar 

  119. Christophe Ringeissen. Prototyping Combination of Unification Algorithms with the ELAN Rule-Based Programming Language. In Proceedings 8th Conference on Rewriting Techniques and Applications, Sitges (Spain), volume 1232 of Lecture Notes in Computer Science, pages 323–326. Springer-Verlag, 1997.

    Google Scholar 

  120. T. Shiple, J. Kukula, and R. Ranjan. A comparison of presburger engines for EFSM reachability. In Proc. Computer Aided verification (CAV), volume 1427 of Lecture Notes in Computer Science, pages 280–292, 1998.

    Google Scholar 

  121. W. Snyder. Complete sets of transformations for general unification. PhD thesis, University of Pennsylvania, 1988.

    Google Scholar 

  122. J. Siekmann and P. Szabó. Universal unification and classification of equational theories. In Proceedings 6th International Conference on Automated Deduction, New York (N.Y., USA), volume 138 of Lecture Notes in Computer Science. Springer-Verlag, 1982.

    Google Scholar 

  123. J. Siekmann and P. Szabó. Universal unification. In R. Shostak, editor, Proceedings 7th International Conference on Automated Deduction, Napa Valley (Calif., USA), volume 170 of Lecture Notes in Computer Science, pages 1–42, Napa Valley (California, USA), 1984. Springer-Verlag.

    Google Scholar 

  124. M. Schmidt-Schauß. Unification in permutative equational theories is undecidable. In Claude Kirchner, editor, Unification, pages 117–124. Academic Press inc., London, 1990.

    Google Scholar 

  125. Gert Smolka and Ralf Treinen. Records for logic programming. Journal of Logic Programming, 18(3):229–258, April 1994.

    Article  MATH  MathSciNet  Google Scholar 

  126. P. Szabó. Unifikationstheorie erster Ordnung. PhD thesis, Universität Karlsruhe, 1982.

    Google Scholar 

  127. E. Tiden and S. Arnborg. Unification problems with one-sided distributivity. Journal of Symbolic Computation, 3(1 & 2):183–202, April 1987.

    Article  MATH  MathSciNet  Google Scholar 

  128. W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 134–191. Elsevier, 1990.

    Google Scholar 

  129. Wolfgang Thomas. Languages, automata and logic. In G. Rozenberg and A. Salomaa, editors, Handbook of Formal Languages, volume 3, pages 389–456. Springer-Verlag, 1997.

    Google Scholar 

  130. Marc Tommasi. Automates et contraintes ensemblistes. Thèse de l’Univ. de Lille, February 1994.

    Google Scholar 

  131. R. Treinen. A new method for undecidability proofs of first order theories. J. Symbolic Computation, 14(5):437–458, November 1992.

    Article  MATH  MathSciNet  Google Scholar 

  132. Ralf Treinen. Feature trees over arbitrary structures. In Patrick Blackburn and Maarten de Rijke, editors, Specifying Syntactic Structures, chapter 7, pages 185–211. CSLI Publications and FoLLI, 1997.

    Google Scholar 

  133. J.W. Thatcher and J.B. Wright. Generalized finite automata with an application to a decision problem of second-order logic. Math. Systems Theory, 2:57–82, 1968.

    Article  MathSciNet  Google Scholar 

  134. Jerzy Tiuryn and Mitchell Wand. Type reconstruction with recursive types and atomic subtyping. In CAAP’ 93: 18th Colloquium on Trees in Algebra and Programming, July 1993.

    Google Scholar 

  135. M. Vardi. An automata-theoretic approach to linear time logic. In Logic for concurrency: structure versus automata, volume 1043 of Lecture Notes in Comp. Science. Springer Verlag, 1996.

    Google Scholar 

  136. Margus Veanes. On simultaneous rigid E-unification. PhD thesis, Computing Science Department, Uppsala University, Uppsala, Sweden, 1997.

    Google Scholar 

  137. K. N. Venkataraman. Decidability of the purely existential fragment of the theory of term algebras. Journal of the ACM, 34(2):492–510, 1987.

    Article  MathSciNet  Google Scholar 

  138. A. Werner, A. Bockmayr, and S. Krischer. How to realize LSE narrowing. In Proceedings Fourth International Conference on Algebraic and Logic Programming, Madrid (Spain), Lecture Notes in Computer Science. Springer-Verlag, September 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LSV, Ecole Normale Supérieure de Cachan, Cachan, France

    Hubert Comon

  2. LORIA and INRIA, Villers-lés-Nancy, France

    Claude Kirchner

Authors
  1. Hubert Comon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Claude Kirchner
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Karlsruhe University, Germany

    Gerhard Goos

  2. Cornell University, NY, USA

    Juris Hartmanis

  3. Utrecht University, The Netherlands

    Jan van Leeuwen

  4. Laboratoire Spécification et Vérification, École Normale Supérieure de Cachan, 61, avenue du Président Wilson, 94234, Cachan Cedex, France

    Hubert Comon

  5. Laboratoire de Recherche en Informatique, Université Paris-Sud, Bâtiment 490, 91405, Orsay Cedex, France

    Claude Marché  & Ralf Treinen  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Comon, H., Kirchner, C. (2001). Constraint Solving on Terms. In: Goos, G., Hartmanis, J., van Leeuwen, J., Comon, H., Marché, C., Treinen, R. (eds) Constraints in Computational Logics. CCL 1999. Lecture Notes in Computer Science, vol 2002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45406-3_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-45406-3_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41950-1

  • Online ISBN: 978-3-540-45406-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation