Abstract
Although Knowledge Representation is full of reasoning problems that have been formally proved to be both NP-hard and coNP-hard, the experimental analysis has largely focused on problems belonging to either NP or coNP. We still do not know, for example, whether well studied phenomena such as “phase transition”, which show up for many NP-complete problems (e.g., sat) happen for Σ p 2-complete problems, and whether they are related to an “easy-hard-easy” pattern or not. The goal of this paper is to show some results of an ongoing experimental analysis that aims to provide reasonable answers to such questions. We analyze the problem of evaluating Quantified Boolean Formulae, which is the prototypical complete problem for all levels of the Polynomial Hierarchy, the computationally simplest hierarchy of complexity classes above NP of great interest to KR.
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References
J. M. Crawford and L. D. Auton. Experimental results on the crossover point in satisfiability problems. In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-93), pages 21–27, 1993.
M. Cadoli, A. Giovanardi, E. Giunchiglia, F. Giunchiglia, M. Schaerf, and R. Sebastiani. Experimental analysis of the computational cost of satisfiability checking in logics for commonsense reasoning. Technical Report MRG/DIST 96-0040, Dipartimento di Informatica, Sistemistica e Telematica, Universitá di Genova, July 1996.
P. Cheeseman, B. Kanefski, and W. M. Taylor. Where the really hard problem are. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence (IJCAI-91), pages 163–169, 1991.
M. R. Garey and D. S. Johnson. Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, San Francisco, Ca, 1979.
G. Gottlob. Complexity results for nonmonotonic logics. Journal of Logic and Computation, 2:397–425, 1992.
F. Giunchiglia and R. Sebastiani. A SAT-based decision procedure for ALC. In Proceedings of the Fifth International Conference on the Principles of Knowledge Representation and Reasoning (KR-96), pages 304–314, 1996.
T. Hogg, B. A. Hubermann, and C. P. Williams (eds.). Special volume on frontiers of problem solving: Phase transitions and complexity. Artificial Intelligence Journal, 81, 1996.
T. Larrabee and Y. Tsuji. Evidence threshold for random 3CNF formulas. In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI-93), pages 112–118, 1993.
D. Mitchell, B. Selman, and H. Levesque. Hard and easy distributions for SAT problems. In Proceedings of the Tenth National Conference on Artificial Intelligence (AAAI-92), pages 459–465, 1992.
L. J. Stockmeyer. The polynomial-time hierarchy. Theoretical Computer Science, 3:1–22, 1976.
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© 1997 Springer-Verlag Berlin Heidelberg
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Cadoli, M., Giovanardi, A., Schaerf, M. (1997). Experimental analysis of the computational cost of evaluating Quantified Boolean Formulae. In: Lenzerini, M. (eds) AI*IA 97: Advances in Artificial Intelligence. AI*IA 1997. Lecture Notes in Computer Science, vol 1321. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63576-9_109
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DOI: https://doi.org/10.1007/3-540-63576-9_109
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