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Axiomatizations and Conservation Results for Fragments of Bounded Arithmetic
, 1990
"... This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author's dissertation. It is shown that (# i+1 )PIND and strong # i replacement are consequences of S 2 . Also # i+1 IND is a consequence of T 2 . The latter result is proved by ..."
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Cited by 27 (3 self)
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This paper presents new results on axiomatizations for fragments of Bounded Arithmetic which improve upon the author's dissertation. It is shown that (# i+1 )PIND and strong # i replacement are consequences of S 2 . Also # i+1 IND is a consequence of T 2 . The latter result is proved by showing that S i+1 conservative over 2 . Furthermore, S i+1 replacement with respect to Boolean combinations of # i+1 formulas. 1
Generalized Theorems on the Relationships among Reducibility Notions to Certain Complexity Classes
 Mathematical Systems Theory
, 1994
"... In this paper, we give several generalized theorems concerning reducibility notions to certain complexity classes. We study classes that are either (I) closed under NP manyone reductions and polynomial time conjunctive reductions or (II) closed under coNP manyone reductions and polynomial time dis ..."
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Cited by 5 (1 self)
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In this paper, we give several generalized theorems concerning reducibility notions to certain complexity classes. We study classes that are either (I) closed under NP manyone reductions and polynomial time conjunctive reductions or (II) closed under coNP manyone reductions and polynomial time disjunctive reductions. We prove that for such a class K, reducibility notions of sets to K under polynomial time constantround truthtable reducibility, polynomial time logTuring reducibility, logspace constantround truthtable reducibility, logspace logTuring reducibility and logspace Turing reducibility are all equivalent and (2) every set that is polynomial time positive Turing reducible to a set in K is already in K. From these results, we derive some observations on the reducibility notions to C=P and NP.
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 .