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A feasibly constructive lower bound for resolution proofs. (English) Zbl 0702.68065
Summary: We review how the counting and probabilistic methods are used to obtain superpolynomial lower bounds on resolution proofs. Then a similar lower bound using the greedy method is presented. Third, by extending the analysis of this new method to weaker forms of the pigeon-hole principle formulas, we obtain lower bounds similar to those obtained by S. R. Buss and G. Turán [Theor. Comput. Sci. 62, No.3, 311-317 (1988)]. Finally, we briefly discuss how the greedy method can be extended and shown to apply to the results of A. Urquhart [J. Assoc. Comput. Math. 34, 209-219 (1987; Zbl 0639.68093)] and V. Chvátal and E. Szemerédi [J. Assoc. Comput. Mach. 35, No.4, 759-768 (1988)].

MSC:
68Q25 Analysis of algorithms and problem complexity
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
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References:
[1] Buss, S.; Turán, G., Resolution proofs of generalized pigeonhole principles, Theoret. comput. sci., 62, 3, 311-317, (1988) · Zbl 0709.03006
[2] Chvátal, V.; Szemerédi, E., Many hard examples for resolution, J. ACM, 35, 4, 759-768, (1988) · Zbl 0712.03008
[3] Cook, S.; Urquhart, A., Functional interpretations of feasibly constructive arithmetic, (), Proc. 21st ACM symposium on theory of computing, 107-112, (1989)
[4] Haken, A., The intractability of resolution, Theoret. comput. sci., 39, 297-308, (1985) · Zbl 0586.03010
[5] Papadimitriou, C.; Steiglitz, K., Combinatorial optimization, (1982), Prentice-Hall Englewood Cliffs, NJ
[6] Urquhart, A., Hard examples for resolution, J. ACM, 34, 1, 209-219, (1987) · Zbl 0639.68093
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