Abstract
We show that the bounded arithmetic theory V0 does not prove that the polynomial time hierarchy collapses to the linear time hierarchy (without parameters). This result follows from a lower bound for bounded depth circuits computing prefix parity, where the circuits are allowed some auxiliary input.
This is a continuation of earlier work by the authors which showed that this collapse is not provable in \({\mbox{\rm{PV}}}\) under a cryptographic assumption.
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Kołodziejczyk, L.A., Thapen, N. (2007). The Polynomial and Linear Hierarchies in V0 . In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_42
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DOI: https://doi.org/10.1007/978-3-540-73001-9_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73000-2
Online ISBN: 978-3-540-73001-9
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