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Bounded Arithmetic and Constant Depth Frege Proofs
, 2004
"... We discuss the ParisWilkie translation from bounded arithmeticproofs to bounded depth propositional proofs in both relativized and nonrelativized forms. We describe normal forms for proofs in boundedarithmetic, and a definition of \Sigma 0depth for PKproofs that makes the translation from boun ..."
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We discuss the ParisWilkie translation from bounded arithmeticproofs to bounded depth propositional proofs in both relativized and nonrelativized forms. We describe normal forms for proofs in boundedarithmetic, and a definition of \Sigma 0depth for PKproofs that makes the translation from bounded arithmetic to propositional logic particularlytransparent. Using this, we give new proofs of the witnessing theorems for S12and T 12; namely, new proofs that the \Sigma b1definable functions of S12are polynomial time computable and that the \Sigma b1definable functions of T 12 are in Polynomial Local Search (PLS). Both proofs generalize to \Sigma
Bounded arithmetic, cryptography, and complexity
 THEORIA
, 1997
"... This survey discusses theories of bounded arithmetic, growth rates of definable functions, natural proofs, interpolation theorems, connections to cryptography, and the difficulty of obtaining independence results. ..."
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This survey discusses theories of bounded arithmetic, growth rates of definable functions, natural proofs, interpolation theorems, connections to cryptography, and the difficulty of obtaining independence results.
Ordinal Notations and WellOrderings in Bounded Arithmetic
 Annals of Pure and Applied Logic
, 2002
"... this paper. 2 General orderings This section states a couple results about general orderings. By a "general ordering" we mean any order defined by a # 1 formula; by comparison the results of sections 3 and 4 concern specific natural wellorderings based on ordinal notations ..."
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this paper. 2 General orderings This section states a couple results about general orderings. By a "general ordering" we mean any order defined by a # 1 formula; by comparison the results of sections 3 and 4 concern specific natural wellorderings based on ordinal notations