Extended Tree Automata Models for the Verification of Infinite State Systems

Florent Jacquemard 1, 2
1 DAHU - Verification in databases
CNRS - Centre National de la Recherche Scientifique : UMR8643, Inria Saclay - Ile de France, ENS Cachan - École normale supérieure - Cachan, LSV - Laboratoire Spécification et Vérification [Cachan]
Abstract : This document presents the study of several models of state machines, all of them extending the same formalism: the classical tree automata, and their application in various reasoning tasks, such as static analysis of programs or systems, typing, verification of the consistency of specifications, model checking... Trees are a natural data structure, widespread in computer science, for instance for the representation of hierarchical or nested data structures, e.g. filesystems, for specific algorithms (binary search trees, distributed algorithms), for an abstract model for semi-structured data used for information exchange in the Web, for an algebraic presentation of recursive processes, as terms in logic... When it comes to reasoning on systems manipulating trees, or modeled by trees, it is crucial to have finite representation of infinite sets of trees. Tree automata are finite state machines providing such a representation, acknowledged as suitable for a use in reasoning tasks: they are a well established theoretical model, in close relationship with logic, they enjoy good compositional properties and efficient decision algorithms. In particular, tree automata are used at the core of systems for software and hardware verification and theorem proving. However, tree automata have also some severe limitations in expressiveness. For instance, they are unable of non-linear pattern matching or of expressing integrity constraints such as keys. Some extensions have been proposed in order to improve the model while trying to preserve good properties. We present in this document several such extensions, their properties and the advents of their use in symbolic verification of systems and programs.
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Florent Jacquemard. Extended Tree Automata Models for the Verification of Infinite State Systems. Formal Languages and Automata Theory [cs.FL]. École normale supérieure de Cachan - ENS Cachan, 2011. ⟨tel-00643595⟩

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