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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. ..."
Abstract

Cited by 30 (7 self)
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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.
Provably Total Functions in
"... This paper investigates the provably total functions of fragments of first and secondorder Bounded Arithmetic. The (strongly) 3 are precisely the (strong) ] functions. The # and U are the EXPTIME [wit, poly] functions and the # definable functions of V 2 are the EXPTI ..."
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This paper investigates the provably total functions of fragments of first and secondorder Bounded Arithmetic. The (strongly) 3 are precisely the (strong) ] functions. The # and U are the EXPTIME [wit, poly] functions and the # definable functions of V 2 are the EXPTIME functions. We give witnessing theorems for these theories and prove conservation results 3 over S 3 and for U 2 over V 2 .