Abstract
In this paper we show that the problem of the existence of a p-optimal proof system for SAT can be characterizedin a similar manner as J. Hartmanis andL. Hemachandra characterizedthe problem of the existence of complete languages for UP. Namely, there exists a p-optimal proof system for SAT if andonly if there is a suitable recursive presentation of the class of all easy (polynomial time recognizable) subsets of SAT. Using this characterization we prove that if there does not exist a p-optimal proof system for SAT, then for every theory T there exists an easy subset of SAT which is not T-provably easy.
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References
Balcazar, J.L., Díaz, J., Gabarró, J.: Structural complexity I. 2nd edn. Springer-Verlag, Berlin Heidelberg New York (1995)
Cook, S.A., Reckhow R.A.: The relative efficiency of propositional proof systems. J. Symbolic Logic 44 (1979) 36–50
Fenner, S., Fortnow, L., Naik, A., Rogers, R.: On inverting onto functions. In: Proc. 11th Annual IEEE Conference on Computational Complexity, (1996) 213–222
Hartmanis, J., Hemachandra, L.: Complexity classes without machines: On complete languages for UP. Theoret. Comput. Sci. 58 (1988) 129–142
Kowalczyk, W.: Some connections between presentability of complexity classes and the power of formal systems of reasoning. In: Proc. Mathematical Foundations of Computer Science. Lecture Notes in Computer Science, Vol. 176. Springer-Verlag, Berlin Heidelberg New York (1988) 364–369
Köbler, J., Messner, J.: Complete problems for promise classes by optimal proof systems for test sets. In: Proc. 13th Annual IEEE Conference on Computational Complexity, (1998) 132–140
Köbler, J., Messner, J.: Is the standard proof system for SAT p-optimal? In: Proc 20th Annual Conference on the Foundations of Software Technology and Theoretical Computer Science. Lecture Notes in Computer Science, Vol. 1974. Springer-Verlag, Berlin Heidelberg New York (2000) 361–372
KrajíČek, J., Pudlák, P.: Propositional proof systems, the consistency of first order theories and the complexity of computations. J. Symbolic Logic 54 (1989) 1063–1079
Messner, J.: On optimal algorithms andoptimal proof systems. In: Proc. 16th Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, Vol. 1563. Springer-Verlag, Berlin Heidelberg New York (1999) 541–550
Messner, J., Torán, J.: Optimal proof systems for Propositional Logic and complete sets. In: Proc. 15th Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science, Vol. 1373. Springer-Verlag, Berlin Heidelberg New York (1998) 477–487
Sadowski, Z.: On an optimal deterministic algorithm for SAT. In: Proc 12th International Workshop, CSL’98. Lecture Notes in Computer Science, Vol. 1584. Springer-Verlag, Berlin Heidelberg New York (1999) 179–187
Sipser, M.: On relativization andthe existence of complete sets. In: Proc. Internat. Coll. on Automata, Languages andProgramming. Lecture Notes in Computer Science, Vol. 140. Springer-Verlag, Berlin Heidelberg New York (1982) 523–531
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Sadowski, Z. (2001). On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT). In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_21
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DOI: https://doi.org/10.1007/3-540-45132-3_21
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