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The polynomial and linear time hierarchies in V0

✍ Scribed by Leszek A. Kołodziejczyk; Neil Thapen

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 203 KB
Volume: 55
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200810007

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We show that the bounded arithmetic theory V^0^ does not prove that the polynomial time hierarchy collapses to the linear time hierarchy (without parameters). The result follows from a lower bound for bounded depth circuits computing prefix parity, where the circuits are allowed some auxiliary input; we derive this from a theorem of Ajtai (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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