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Journal Articles Theoretical Computer Science Year : 2000

A characterization of alternating log time by ramified recurrence

Abstract

We give a machine-independent characterization of the class of functions bitwise computable in alternating logarithmic time, with output of polynomial size. Recall that ALogTime is the same, for decision problems, as the $U_{E^*}$-uniform variant of ${\rm NC}^1$ \cite{Ruzzo81}. Our characterization is in terms of a weak form of ramified tree recurrence with substitutions. No initial functions other than basic tree operations are used, and no bounding conditions on the recurrence.

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Other [cs.OH]

Dates and versions

inria-00099078 , version 1 (26-09-2006)

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Daniel Leivant, Jean-Yves Marion. A characterization of alternating log time by ramified recurrence. Theoretical Computer Science, 2000, 236 (1-2), pp.192-208. ⟨10.1016/S0304-3975(99)00209-1⟩. ⟨inria-00099078⟩
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