Finitely Presented Infinite Graphs

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 alpha-bet Σ, a Σ-labeled infinite graph can be characterized as a finite set of binaryrelations (Ra)a∈Σ over an arbitrary countable domain V . There are many ways tofinitely characterize such sets of relations, either explicitly using rewriting systemsor formalisms from automata theory, either externally.After giving an overview of the main results in this domain, we focus on threespecific problems. In a first time, we define several families of term-rewritingsystems whose derivation relation can be finitely represented. These results raiseinteresting questions concerning the corresponding families of infinite graphs. Ina second time, we study two families of infinite graphs whose sets of traces (orlanguages) coincide with the well-known family of context-sensitive languages.They are the rational graphs and the linearly bounded graphs. We investigatethe case of deterministic context-sensitive languages, and establish a structuralcomparison between these two families of graphs. Finally, in an approach closerto the concerns of the verification community, we propose a symbolic reachabilityalgorithm for a class of higher-order pushdown automata.tel-00325707,version1-30Sep2008