# A characterization of alternating log time by ramified recurrence

2 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Journal articles
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https://hal.inria.fr/inria-00099078
Contributor : Publications Loria <>
Submitted on : Tuesday, September 26, 2006 - 8:50:47 AM
Last modification on : Tuesday, April 13, 2021 - 2:43:43 PM

### Citation

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

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