Walking automata in free inverse monoids

David Janin 1, 2
1 PoSET - Models for a Structured Programming of Space and Time
Inria Bordeaux - Sud-Ouest, SCRIME - Studio de Création et de Recherche en Informatique et Musique Électroacoustique, LaBRI - Laboratoire Bordelais de Recherche en Informatique
Abstract : Walking automata, be they running over words, trees or even graphs, possibly extended with pebbles that can be dropped and lifted on vertices, have long been defined and studied in Computer Science. However, questions concerning walking automata are surprisingly complex to solve. In this paper, we study a generic notion of walking automata over graphs whose semantics naturally lays within inverse semigroup theory. Then, from the simplest notion of walking automata on birooted trees, that is, elements of free inverse monoids, to the more general cases of walking automata on birooted finite subgraphs of Cayley's graphs of groups, that is, elements of free E-unitary inverse monoids, we provide a robust algebraic framework in which various classes of recognizable or regular languages of birooted graphs can uniformly be defined and related one with the other.
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David Janin. Walking automata in free inverse monoids. 42nd International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM), Jan 2016, Harrachov, Czech Republic. ⟨hal-00738793v4⟩

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