The polynomial and linear time hierarchies in V 0 | Zendy

Kołodziejczyk Leszek A. | Zendy; Thapen Neil | Zendy

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The polynomial and linear time hierarchies in V 0

Author(s) -

Kołodziejczyk Leszek A.,

Thapen Neil

Publication year - 2009

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200810007

Subject(s) - mathematics , bounded function , prefix , hierarchy , discrete mathematics , parity (physics) , time complexity , polynomial , polynomial hierarchy , combinatorics , arithmetic , mathematical analysis , philosophy , linguistics , physics , particle physics , economics , market economy

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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