A third-order bounded arithmetic theory for PSPACE (2004)
| Venue: | of Lecture Notes in Computer Science |
| Citations: | 7 - 3 self |
BibTeX
@INPROCEEDINGS{Skelley04athird-order,
author = {Alan Skelley},
title = {A third-order bounded arithmetic theory for PSPACE},
booktitle = {of Lecture Notes in Computer Science},
year = {2004},
pages = {340--354},
publisher = {Springer}
}
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Abstract
Abstract. 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. Keywords: Bounded arithmetic, propositional proof complexity, PSPACE, quantified propositional calculus 1
