An Algorithm for General Set Unification and Its Complexity

Journal of Automated Reasoning

Volumn 22, Issue 1, 1999, Pages 45-63

  Stolzenburg, Frieder ^a  

^a Institut f Informatik ^*  (Germany)

Author keywords

Complexity analysis; Finite sets; Unification algorithms

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; PROBLEM SOLVING; SET THEORY;

ASSOCIATIVE-COMMUTATIVE-IDEMPOTENT (ACI) UNIFICATION; COMPLEXITY ANALYSIS;

KNOWLEDGE BASED SYSTEMS;

EID: 0032675774     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006019227709     Document Type: Article

References (19)

1. Arenas-Sánchez, P. and Dovier, A.: Minimal set unification, in M. Hermenegildo and S. D. Swierstra (eds.), Proceedings of the 7th International Symposium on Programming Language Implementation and Logic Programming, LNCS 982, Springer, Berlin, Heidelberg, New York, 1995, pp. 397-414.
2. q, J. Automated Reasoning 8 (1992), 39-44.
3. Dovier, A., Omodeo, E. G., Pontelli, E. and Rossi, G.: {log}: A language for programming in logic with finite sets, J. Logic Programming 28(1) (1996), 1-44.
4. ECRC GmbH, München: ECLiPSe 3.5: User Manual - Extensions User Manual, 1995. Two volumes.
5. Graham, R. L., Knuth, D. E. and Patashnik, O.: Concrete Mathematics, 2nd edition, Addison-Wesley, Reading, MA, 1994.
6. Jayaraman, B. and Plaisted, D. A.: Functional programming with sets, in G. Kahn (ed.), Proceedings of the 3rd International Conference on Functional Programming Languages and Computer Architecture, LNCS 274, Springer, Berlin, Heidelberg, New York, 1987, pp. 194-211.
7. Jayaraman, B. and Plaisted, D. A.: Programming with equations, subsets, and relations, in E. L. Lusk and R. A. Overbeek (eds.), Proceedings of the North American Conference on Logic Programming, Cleveland, OH, MIT Press, Cambridge, MA, London, 1989, pp. 1051-1068.
8. Jouannaud, J.-P. and Kirchner, C.: Solving equations in abstract algebras: A rule-based survey of unification, in J.-L. Lassez and G. Plotkin (eds.), Computational Logic: Essays in Honor of Alan Robinson, MIT Press, Cambridge, MA, London, 1991, pp. 257-321.
9. Kapur, D. and Narendran, P.: NP-completeness of the set unification and matching problems, in J. H. Siekmann (ed.), Proceedings of the 8th International Conference on Automated Deduction, Oxford, LNCS 230, Springer, Berlin, Heidelberg, 1986, pp. 489-495.
10. Kapur, D. and Narendran, P.: Double-exponential complexity of computing a complete set of AC-unifiers, in Proceedings of the 7th Annual Symposium on Logic in Computer Science, Santa Cruz, CA, 1992, pp. 11-21.
11. Kapur, D. and Narendran, P.: A unification algorithm for associative-commutative-idempotent theories, preliminary report, State University of New York at Albany Department of Computer Science Institute for Programming and Logics, Albany, NY, 1993.
12. Lincoln, P. and Christian, J.: Adventures in associative-commutative unification (a summary), in E. Lusk and R. Overbeek (eds.), Proceedings of the 9th International Conference on Automated Deduction, Argonne, IL, LNCS 310, Springer, Berlin, Heidelberg, New York, 1988, pp. 358-367.
13. Pollard, C. J. and Moshier, M. D.: Unifying partial description of sets, in P. Hanson (ed.), Information, Language, and Cognition, University of British Columbia Press, Vancouver, BC, 1990, pp. 285-322.
14. Pollard, C. J. and Sag, I. A.: Head-Driven Phrase Structure Grammar, University of Chicago Press, Chicago, London, 1994. CSLI publication.
15. Shmueli, O., Tsur, S. and Zaniolo, C.: Compilation of set terms in the logic data language (LDL), J. Logic Programming 12(1-2) (1992), 89-119.
16. Siekmann, J. H.: Unification theory, J. Symbolic Comput. 7(1) (1989), 207-274.
17. Stolzenburg, F.: An algorithm for general set unification and its complexity, in E. G. Omodeo and G. Rossi (eds.), Proceedings of the Workshop on Logic Programming with Sets in Conjunction with 10th International Conference on Logic Programming, Budapest, 1993, pp. 17-22.
18. Stolzenburg, F.: Membership-constraints and complexity in logic programming with sets, in F. Baader and K. U. Schulz (eds.), Frontiers in Combining Systems, Kluwer Academic Publ., Dordrecht, The Netherlands, 1996, pp. 285-302.
19. Vitter, J. S. and Flajolet, P.: Average-case analysis of algorithms and data structures, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Elsevier Science, Amsterdam, 1990, pp. 431-524.