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Réécriture d’arbres de piles et traces de systèmes à compteurs

Abstract : In this thesis, we study classes of infinite graphs and their properties,especially the model-checking problem, the accessibility problem and therecognised languages.We define a notion of stack trees, and a related notionof ground rewriting, which is an extension of both higher-order pushdownautomata and ground tree rewriting systems. We also define a notion ofrecognisability on the sets of ground rewriting operations through operationautomata. This notion induces a notion of recognisability over sets of stacktrees and a normalisation of recognisable sets of operations, similar to theknown notions over higher-order pushdown automata. We show that the graphsdefined by these ground stack tree rewriting systems have a decidableFO-theory, by exhibiting a finite set interpretation from a graph defined bya higher-order automaton to a graph defined by a ground stack tree rewritingsystem.We also consider the context-freeness problem for counter systems, andthe related problem of stratifiability of semi-linear sets. We prove thedecidability of the stratifiability problem for integral polyhedra and that itis coNP-complete. We use this result to show that the context-freeness problemfor flat counter systems is as well coNP-complete. Finally, we give a new proofof the decidability of the context-freeness problem for vector additionsystems, previously studied by Schwer
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Submitted on : Thursday, March 10, 2016 - 4:15:38 PM
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Vincent Penelle. Réécriture d’arbres de piles et traces de systèmes à compteurs. Informatique et langage [cs.CL]. Université Paris-Est, 2015. Français. ⟨NNT : 2015PESC1122⟩. ⟨tel-01286343⟩



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