Investigations on autark assignments

Discrete Applied Mathematics

Volumn 107, Issue 1-3, 2000, Pages 99-137

  Kullmann, Oliver ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Autark assignment; Conjunctive normal form; Deficiency; Linear autarky; Linear programming; Matched formulas; Minimally unsatisfiable clause sets; Polynomial time; Propositional logic; q Horn formulas; Resolution; Satisfiability

Indexed keywords

EID: 0002209170     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(00)00262-6     Document Type: Article

References (38)

1. Aharoni R., Linial N. Minimal non-two-colorable hyper-graphs and minimal unsatisfiable formulas. J. Combin. Theory A. 43:1986;196-204.
2. Bachem A., Kern W. Linear Programming Duality: An Introduction to Oriented Matroids. 1992;Universitext, Springer, Berlin.
3. Boros E., Crama Y., Hammer P.L. Polynomial-time inference of all valid implications for Horn and related formulae. Ann. Math. Artificial Intelligence. 1:1990;21-32.
4. Boros E., Crama Y., Hammer P.L., Saks M. A complexity index for satisfiability problems. SIAM J. Comput. 23(1):1994;45-49.
5. Boros E., Hammer P.L., Sun X. Recognition of. q -Horn formulae in linear time Discrete Appl. Math. 55:1994;1-13.
6. N. Bourbaki, Algebra I; Elements of Mathematics, Springer, Berlin, 1989 (Chapters 1-3).
7. H.K. Büning, On the minimal unsatisfiability problem for some subclasses of CNF, Abstracts of the 16th International Symposium on Mathematical Programming, Lausanne, 1997.
8. Büning H.K. An upper bound for minimal resolution refutations. Gottlob G., Grandjean E., Seyr K. Computer Science Logic 12th International Workshop, CSL'98. Lecture Notes in Computer Science. Vol. 1584:1999;171-178 Springer, Berlin.
9. Cook S.A., Reckhow R.A. The relative efficiency of propositional proof systems. J. Symbolic Logic. 44(1):1979;36-50.
10. Davydov G., Davydova I. Tautologies and positive solvability of linear homogeneous systems. Ann. Pure Appl. Logic. 57:1992;27-43.
11. Eiter T., Kilpeläinen P., Mannila H. Recognizing renamable generalized propositional Horn formulas is NP-complete. Discrete Appl. Math. 59:1995;23-31.
12. T. Fliti, G. Reynaud, Sizes of minimally unsatisfiable conjunctive normal forms, Faculté des Sciences de Luminy, Department of Mathematique-Informatique, 13288 Marseille, France, November 1994.
13. J. Franco, Relative size of certain polynomial time solvable subclasses of satisfiability, in: D. Du, J. Gu, P.M. Pardalos (Eds.), Satisfiability Problem: Theory and Applications, DIMACS Workshop March 11-13, 1996, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 35, American Mathematical Society, 1997, pp. 211-223.
14. J. Franco, A. van Gelder, A perspective on certain polynomial time solvable classes of satisfiability, Discrete Appl. Math. (2000), to appear.
15. van Gelder A. Autarky pruning in propositional model elimination reduces failure redundancy. J. Automat. Reasoning. 23(2):1999;137-193.
16. G. Huet, Confluent reductions: abstract properties and applications to term rewriting systems, 18th Annual Symposium on Foundations of Computer Science, IEEE, New York, 1977, pp. 30-45.
17. O. Kullmann, Worst-case analysis, 3-SAT decision and lower bounds: approaches for improved SAT algorithms, in: D. Du, J. Gu, P.M. Pardalos (Eds.), Satisfiability Problem: Theory and Applications, DIMACS Workshop March 11-13, 1996, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 35, American Mathematical Society, 1997, pp. 261-313.
18. O. Kullmann, Heuristics for SAT algorithms: searching for some foundations, Discrete Appl. Math. (1998) 23, submitted for publication.
19. O. Kullmann, Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs, Technical Report TR99-041, Electronic Colloquium on Computational Complexity (ECCC), October 1999.
20. Kullmann O. New methods for 3-SAT decision and worst-case analysis. Theoret. Comput. Sci. 223(1-2):1999;1-72.
21. Kullmann O. On a generalization of extended resolution. Discrete Appl. Math. 96-97(1-3):1999;149-176.
22. O. Kullmann, An application of matroid theory to the SAT problem, In: Fifteenth Annual IEEE Conference of Computational Complexity, pp. 116-124, IEEE Computer Society, July 2000. See also TR00-018, Electronic Colloquium on Computational Complexity (ECCC), March 2000.
23. O. Kullmann, An application of matroid theory to the SAT problem, In: Fifteenth Annual IEEE Conference of Computational Complexity, pp. 116-124, IEEE Computer Society, July 2000. See also TR00-018, Electronic Colloquium on Computational Complexity (ECCC), March 2000.
24. O. Kullmann, Lean clause-sets: Generalizations of minimally unsatisfiable clause-sets, submitted to Disc. Appl. Math. (2000).
25. O. Kullmann, H. Luckhardt, Algorithms for SAT / TAUT decision based on various measures, preprint, the ps-file can be obtained from http: // www.cs.utoronto.ca/ ~ kullmann / , December 1998, 71pp.
26. Lovász L., Plummer M.D. Matching Theory of Mathematics Studies, Vol. 121. 1986;North-Holland, Amsterdam.
27. n steps Discrete Appl. Math. 10:1985;287-295.
28. Newman M.H.A. On theories with a combinatorial definition of "equivalence" Ann. Math. 43:1942;223-243.
29. F. Okushi, Parallel cooperative propositional theorem proving, Ann. Math. Artificial Intelligence 26 (2000) , 59-85.
30. T.J. Schaefer, The complexity of statisfiability problems, Proceedings of the 10th Annual ACM Symposium on Theory of Computing (STOC), 1978, pp. 216-226.
31. Schrijver A. Theory of Linear and Integer Programming. 1986;Wiley, New York.
32. Shaohan Ma, Dongmin L. A polynomial-time algorithm for reducing the number of variables in MAX SAT problem. Sci. China (Ser. E). 40(3):1997;301-311.
33. G.S. Tseitin, On the complexity of derivation in propositional calculus, in: A.O. Slisenko (Ed.), Seminars in Mathematics, Vol. 8, V.A. Steklov Mathematical Institute, Leningrad, 1968 (English translation: Studies in mathematics and mathematical logic), Part II, 1970, pp. 115-125.
34. G.S. Tseitin, On the complexity of derivation in propositional calculus, in: A.O. Slisenko (Ed.), Seminars in Mathematics, Vol. 8, V.A. Steklov Mathematical Institute, Leningrad, 1968 (English translation: Studies in mathematics and mathematical logic), Part II, 1970, pp. 115-125.
35. H. van Maaren, A short note on linear autarkies, q-Horn formulas and the complexity index, Technical Report 99-26, DIMACS, May 1999. Can be obtained from http: // dimacs.rutgers.edu / Technical Reports / .
36. H. van Maaren, On some tractable cases of satisfiability problems, Inform. Comput. (2000), to appear; journal version of [35].
37. H. van Maaren, J. Warners, Solving satisfiability problems using elliptic approximations - effective branching rules, Technical Report 98-18, Delft University of Technology, 1998. Journal version to appear in Discrete Appl. Math.
38. Whitney H. On the abstract properties of linear dependence. Amer. J. Math. 57:1935;509-533.