Orienting rewrite rules with the Knuth-Bendix order

Information and Computation

Volumn 183, Issue 2, 2003, Pages 165-186

  Korovin, Konstantin ^a   Voronkov, Andrei ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Knuth Bendix orders; Ordering constraints; Orientability; Term rewriting; Termination

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY; CONSTRAINT THEORY; POLYNOMIALS; PROBLEM SOLVING;

KNUTH-BENDIX ORDERS; ORDERING CONSTRAINTS; ORIENTABILITY; TERM REWRITING; TERMINATION;

THEOREM PROVING;

EID: 0037732697     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0890-5401(03)00021-X     Document Type: Article

References (19)

1. H. Comon, Solving symbolic ordering constraints, International Journal of Foundations Computer Science 1 (4) (1990) 387-411.
2. H. Comon, R. Treinen, Ordering constraints on trees, in: S. Tison (Ed.), Trees in Algebra and Programming: CAAP'94, Vol. 787 of Lecture Notes in Computer Science, Springer Verlag, Berlin, 1994, pp. 1-14.
3. T. Cormen, C. Leiserson, R. Rives, Introduction to Algorithms, The MIT Press, Cambridge, MA, 1991.
4. N. Dershowitz, Plaisted, Rewriting, in: A Robinson, A. Voronkov (Eds.), Handbook of Automated Reasoning, vol. 1, Elsevier Science, Amsterdam, 2001, pp. 533-608 (Chapter 9).
5. D. Detlefs, R. Forgaard, A procedure for automatically proving the termination of a set of rewrite rules, in: J.-P. Jouannaud (Ed.), Rewriting Techniques and Applications, First International Conference, RTA-85, Vol. 202 of Lecture Notes in Computer Science, Springer Verlag, Dijon, France, 1985, pp. 255-270.
6. J. Dick, J. Kalmas, U. Martin, Automating the Knuth-Bendix ordering, Acta Informatica 28 (2) (1990) 95-119.
7. J.-P. Jouannaud, M. Okada, Satisfiability of systems of ordinal notations with the subterm property is decidable, in: J. Albert, B. Monien, M. Rodriguez-Artalejo (Eds.), Automata, Languages and Programming, 18th International Colloquium, ICALP'91, Vol. 510 of Lecture Notes in Computer Science, Springer Verlag, Madrid, Spain 1991, pp. 455-468.
8. D. Knuth, P. Bendix, Simple word problems in universal algebras, in: J. Leech (Ed.), Computational Problems in Abstract Algebra, Pergamon Press, Oxford, 1970, pp. 263-297.
9. K. Korovin, A. Voronkov, Knuth-Bendix ordering constraint solving is NP-complete, in: F. Orejas, P. Spirakis, J. van Leeuwen (Eds.), Automata, Languages and Programming, 28th International Colloquium, ICALP 2001, Vol. 2076 of Lecture Notes in Computer Science, Springer Verlag, Berlin, 2001, pp. 979-992.
10. K. Korovin, A. Voronkov, Knuth-Bendix constraint solving is NP-complete, Preprint CSPP-8, Department of Computer Science, University of Manchester (Nov. 2000). http://www.cs.man.ac.uk/preprints/index.html.
11. K. Korovin, A. Voronkov, A decision procedure for the existential theory of term algebras with the Knuth-Bendix ordering, in: Proc. 15th Annual IEEE Symp. on Logic in Computer Science, Santa Barbara, California, 2000, pp. 291-302.
12. M. Krishnamoorthy, P. Narendran, On recursive path ordering, Theoretical Computer Science 40 (1985) 323-328.
13. P. Lescanne, Term rewriting systems and algebra, in: R. Shostak (Ed.), 7th International Conference on Automated Deduction, CADE-7, Vol. 170 of Lecture Notes in Computer Science, 1984, pp. 166-174.
14. U. Martin, How to choose weights in the Knuth-Bendix ordering, in: Rewriting Techniques and Applications, Vol. 256 of Lecture Notes in Computer Science, 1987, pp. 42-53.
15. U. Martin, D. Shand, Invariants, patterns and weights for ordering terms, Journal of Symbolic Computations 29 (6) (2000) 921-957.
16. P. Narendran, M. Rusinowitch, R. Verma, RPO constraint solving is in NP, in: G. Gottlob, E. Grandjean, K. Seyr (Eds.). Computer Science Logic, 12th International Workshop, CSL'98, Vol. 1584 of Lecture Notes in Computer Science, Springer Verlag, Berlin, 1999, pp. 385-398.
17. R. Nieuwenhuis, Simple LPO constraint solving methods, Information Processing Letters 47 (1993) 65-69.
18. C. Papadimitriou, Computational Complexity, Addison-Wesley, Reading, MA, 1994.
19. A. Schrijver, Theory of Linear and Integer Programming, Wiley, New York, 1998.