Set Constraints and Automata

Abstract

We define a new class of automata which is an acceptor model for mappings from the set of terms TΣ over a ranked alphabet Σ into a set E of labels. When E = {0, 1}n 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. © 1999 Academic Press.