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A thirdorder bounded arithmetic theory for PSPACE
 of Lecture Notes in Computer Science
, 2004
"... Abstract. We present a novel thirdorder 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 ..."
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Cited by 7 (3 self)
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Abstract. We present a novel thirdorder 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 polynomialsize 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
Propositional PSPACE reasoning with Boolean programs versus quantified Boolean formulas
 In ICALP
, 2004
"... Abstract. We present a new propositional proof system based on a somewhat recent characterization of polynomial space (PSPACE) called Boolean programs, due to Cook and Soltys. The Boolean programs are like generalized extension atoms, providing a parallel to extended Frege. We show that this new sys ..."
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Cited by 5 (4 self)
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Abstract. We present a new propositional proof system based on a somewhat recent characterization of polynomial space (PSPACE) called Boolean programs, due to Cook and Soltys. The Boolean programs are like generalized extension atoms, providing a parallel to extended Frege. We show that this new system, BPLK, is polynomially equivalent to the system G, which is based on the familiar but very different quantified Boolean formula (QBF) characterization of PSPACE due to Stockmeyer and Meyer. This equivalence is proved by way of two translations, one of which uses an idea reminiscent of the ɛterms of Hilbert and Bernays. 1
Theories and Proof Systems for PSPACE and the EXPTime Hierarchy
, 2005
"... This document is originally a working paper recording our results in progress. It is hoped that with some reorganization, addition of basic definitions, introduction and conclusion, and of course ..."
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Cited by 2 (2 self)
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This document is originally a working paper recording our results in progress. It is hoped that with some reorganization, addition of basic definitions, introduction and conclusion, and of course
Research Statement
, 2006
"... 2 Background and Past Work The primary motivation for studying propositional proof systems is the theorem of Cook and Reckhow[8, 11] that NP=coNP iff there exists a polynomially bounded proof system for propositional tautologies. Many proof systems are studied and there are some notable successes i ..."
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2 Background and Past Work The primary motivation for studying propositional proof systems is the theorem of Cook and Reckhow[8, 11] that NP=coNP iff there exists a polynomially bounded proof system for propositional tautologies. Many proof systems are studied and there are some notable successes in the search for lower bounds, e.g.[13, 1], but this problem is very hard in general; nevertheless, there are many much more accessible problems than NP vs coNP: at one end of the scale, the detailed study of weak proof systems and their interrelations,and at the other, capturing different forms of reasoning with stronger proof systems.