# A characterization of Alternating log time by first order functional programs

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.
Document type :
Conference papers

Cited literature [32 references]

https://hal.inria.fr/inria-00110014
Contributor : Romain Péchoux <>
Submitted on : Thursday, October 26, 2006 - 12:10:28 PM
Last modification on : Tuesday, May 5, 2020 - 5:02:11 PM
Document(s) archivé(s) le : Tuesday, April 6, 2010 - 9:02:54 PM

### Identifiers

• HAL Id : inria-00110014, version 1

### Citation

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⟩

Record views