The polynomial and linear time hierarchies in V0

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Mathematical Logic Quarterly 55 (5):509-514 (2009)
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Abstract

We show that the bounded arithmetic theory V0 does not prove that the polynomial time hierarchy collapses to the linear time hierarchy . 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

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10.1002/malq.200810007

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Notes on polynomially bounded arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.
¹1-formulae on finite structures.M. Ajtai - 1983 - Annals of Pure and Applied Logic 24 (1):1.

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