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SIAM Journal on Computing
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ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
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STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
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FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
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LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
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COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
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STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT)
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
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Theoretical Computer Science
Optimal Proof Systems, Optimal Acceptors and Recursive Presentability
Fundamenta Informaticae
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We investigate the question whether there is a (p-)optimal proof system for SAT or for TAUT and its relation to completeness and collapse results for nondeterministic function classes. A p-optimal proof system for SAT is shown to imply (1) that there exists a complete function for the class of all total nondeterministic multi-valued functions and (2) that any set with an optimal proof system has a p-optimal proof system. By replacingthe assumption of the mere existence of a (p-) optimal proof system by the assumption that certain proof systems are (p-)optimal we obtain stronger consequences, namely collapse results for various function classes. Especially we investigate the question whether the standard proof system for SAT is p-optimal. We show that this assumption is equivalent to a variety of complexity theoretical assertions studied before, and to the assumption that every optimal proof system is p-optimal. Finally, we investigate whether there is an optimal proof system for TAUT that admits an effective interpolation, and show some relations between various completeness assumptions.