Witnessing Functions in Bounded Arithmetic and Search Problems

Witnessing Functions in Bounded Arithmetic and Search Problems (1994)

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by Mario Chiari , Jan Krajicek

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Datum	Value	Source
TITLE	Witnessing Functions in Bounded Arithmetic and Search Problems	user correction - Legacy Corrections
AUTHOR NAME	Mario Chiari	user correction - Legacy Corrections
AUTHOR AFFIL	; 1; Mathematical Institute; 1; and Institute of Computer Science; b	user correction - Legacy Corrections
AUTHOR ADDR	; 1- and \Sigma	user correction - Legacy Corrections
AUTHOR NAME	Jan Krajicek	user correction - Legacy Corrections
ABSTRACT	We investigate the possibility to characterize (multi)functions that are \Sigma b i -definable with small i (i = 1; 2; 3) in fragments of bounded arithmetic T2 in terms of natural search problems defined over polynomial-time structures. We obtain the following results: 1. A reformulation of known characterizations of (multi)functions that are \Sigma b 1 - and \Sigma b 2 -definable in the theories S 1 2 and T 1 2 . 2. New characterizations of (multi)functions that are \Sigma b 2 - and \Sigma b 3 - definable in the theory T 2 2 . 3. A new non-conservation result: the theory T 2 2 (ff) is not 8\Sigma b 1 (ff)- conservative over the theory S 2 2 (ff). To prove that the theory T 2 2 (ff) is not 8\Sigma b 1 (ff)-conservative over the theory S 2 2 (ff), we present two examples of a \Sigma b 1 (ff)-principle separating the two theories: (a) the weak pigeonhole principle WPHP (a 2 ; f; g) formalizing that no function f is a bijection between a 2 and a with the inverse...	user correction - Legacy Corrections
YEAR	1994	user correction - Legacy Corrections
CITATIONS	30 found	ParsCit 1.0