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Theories for Complexity Classes and their Propositional Translations
 Complexity of computations and proofs
, 2004
"... We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus. ..."
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We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC and P. We present simple translations between these theories and systems of the quanti ed propositional calculus.
Theories for Complexity Classes and their Propositional Translations
, 2004
"... Abstract We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC0 and P. We present simple translations between these theories and systems of the quantified propositional calculus. 1 Introduction An important part of bounded arithmetic i ..."
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Abstract We present in a uniform manner simple twosorted theories corresponding to each of eight complexity classes between AC0 and P. We present simple translations between these theories and systems of the quantified propositional calculus. 1 Introduction An important part of bounded arithmetic is associating logical theories with various complexity classes, and then translating proofs in these theories to families of proofs in appropriate propositional (or quantified propositional) proof systems. Our purpose here is to give a unified treatment of this threeway association, as it applies to the sequence of complexity classes