Set constraints and automata

Rémi Gilleron (1) , Sophie Tison (2) , Marc Tommasi (1)

1 GRAppA - LIFL - Groupe de Recherche en Apprentissage Automatique
2 LIFL - Laboratoire d'Informatique Fondamentale de Lille

We define a new class of automata which is an acceptor model for mappings from the set of terms T? over a ranked alphabet ? into a set E of labels. When E is a set of tuples of binary values, an automaton can be viewed as an acceptor model for n-tuples of tree languages. We prove decidability of emptiness and closure properties for this class of automata. As a consequence of these results, we prove decidability of satisfiability of systems of positive and negative set constraints without projection symbols. We prove the decidability of the satisfiability problem for systems of positive and negative set constraints without projection symbols. Moreover we prove that a non-empty set of solutions always contain a regular solution (i.e., a n-tuple of regular tree languages). We also deduce decidability results for properties of sets of solutions of systems of set constraints.

Domaines: Langage de programmation [cs.PL]

Rémi Gilleron, Sophie Tison, Marc Tommasi. Set constraints and automata. Information and Computation, 1999, 149 (1), pp.1--41. ⟨inria-00538886⟩