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APAL
2011

The provably total NP search problems of weak second order bounded arithmetic

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The provably total NP search problems of weak second order bounded arithmetic
We define a new NP search problem, the “local improvement” principle, about labellings of an acyclic, bounded-degree graph. We show that, provably in PV, it characterizes the ∀Σb 1 consequences of V 1 2 and that natural restrictions of it characterize the ∀Σb 1 consequences of U1 2 and of the bounded arithmetic hierarchy. We also show that over V 0 it characterizes the ∀ΣB 0 consequences of V 1 and hence that, in some sense, a miniaturized version of the principle gives a new characterization of the ∀Πb 1 consequences of S1 2 . Throughout our search problems are “type-2” NP search problems, which take second-order objects as parameters.
Leszek Aleksander Kolodziejczyk, Phuong Nguyen, Ne
Added 12 May 2011
Updated 12 May 2011
Type Journal
Year 2011
Where APAL
Authors Leszek Aleksander Kolodziejczyk, Phuong Nguyen, Neil Thapen
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