Graphes infinis de présentation finie

Antoine Meyer 1
1 GALION - Graphs, Automata, Logics, Languages and vErificatiON
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, UR1 - Université de Rennes 1, INSA Rennes - Institut National des Sciences Appliquées - Rennes, CNRS - Centre National de la Recherche Scientifique : UMR6074
Abstract : This thesis contributes to the study of families of finitely presented infinite graphs, their structural properties and their relations to each other. Given a finite alphabet Σ, a Σ-labeled infinite graph can be characterized as a finite set of binary relations (Ra)a∈Σ over an arbitrary countable domain V . There are many ways to finitely characterize such sets of relations, either explicitly using rewriting systems or formalisms from automata theory, either externally. After giving an overview of the main results in this domain, we focus on three specific problems. In a first time, we define several families of term-rewriting systems whose derivation relation can be finitely represented. These results raise interesting questions concerning the corresponding families of infinite graphs. In a second time, we study two families of infinite graphs whose sets of traces (or languages) coincide with the well-known family of context-sensitive languages. They are the rational graphs and the linearly bounded graphs. We investigate the case of deterministic context-sensitive languages, and establish a structural comparison between these two families of graphs. Finally, in an approach closer to the concerns of the verification community, we propose a symbolic reachability algorithm for a class of higher-order pushdown automata.
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https://tel.archives-ouvertes.fr/tel-00325707
Contributor : Antoine Meyer <>
Submitted on : Tuesday, September 30, 2008 - 10:12:27 AM
Last modification on : Friday, November 16, 2018 - 1:27:06 AM
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  • HAL Id : tel-00325707, version 1

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Antoine Meyer. Graphes infinis de présentation finie. Informatique [cs]. Université Rennes 1, 2005. Français. ⟨tel-00325707⟩

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