A characterization of Alternating log time by first order functional programs

Romain Péchoux 1 Jean-Yves Marion 1 Guillaume Bonfante 1
1 CALLIGRAMME - Linear logic, proof networks and categorial grammars
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We a give an intrinsic characterization of the class of functions which are computable in $\NCUN$ that is by a uniform, logarithmic depth and polynomial size family circuit. Recall that the class of functions in \Alogtime, that is in logarithmic time on an Alternating Turing Machine, is $\NCUN$. Our characterization is in terms of first order functional programming languages. We define measure-tools called Sup-interpretations, which allow to give space and time bounds and allow also to capture a lot of program schemas. This study is part of a research on static analysis in order to predict program resources. It is related to the notion of Quasi-interpretations and belongs to the implicit computational complexity line of research.
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Submitted on : Thursday, October 26, 2006 - 12:10:28 PM
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Romain Péchoux, Jean-Yves Marion, Guillaume Bonfante. A characterization of Alternating log time by first order functional programs. 13th International Conference on Logic for Programming Artificial Intelligence and Reasoning - LPAR-13, Nov 2006, Phnom Penh/Cambodia. ⟨inria-00110014⟩

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