A Third-Order Bounded Arithmetic Theory for PSPACE
نویسنده
چکیده
We present a novel third-order theory W 1 1 of bounded arithmetic suitable for reasoning about PSPACE functions. This theory has the advantages of avoiding the smash function symbol and is otherwise much simpler than previous PSPACE theories. As an example we outline a proof in W 1 1 that from any configuration in the game of Hex, at least one player has a winning strategy. We then exhibit a translation of theorems of W 1 1 into families of propositional tautologies with polynomial-size proofs in BPLK (a recent propositional proof system for PSPACE and an alternative to G). This translation is clearer and more natural in several respects than the analogous ones for previous PSPACE theories.
منابع مشابه
Theories and Proof Systems for PSPACE and the EXP - Time Hierarchy
Theories and Proof Systems for PSPACE and the EXP-Time Hierarchy Alan Ramsay Skelley Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2006 This dissertation concerns theories of bounded arithmetic and propositional proof systems associated with PSPACE and classes from the exponential-time hierarchy. The second-order viewpoint of Zambella and Cook associates sec...
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