Article

# Set Constraints and Automata.

Inf. Comput 01/1999; 149:1-41. DOI:10.1006/inco.1998.2747
Source: DBLP

ABSTRACT We define a new class of automata which is an acceptor model for mappings from the set of terms T Sigma over a ranked alphabet Sigma into a set E of labels. When E = f0; 1g 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. 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. Keywords : Automata, Set Constraints, Undecidability, Automata with equality tests. R'esum'e Nous d'efinissons une nouvelle classe d'automates capables de reconna itre des applications de T Sigma dans E o`u T Sigma est l'ensemble des termes construits sur un al...

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01/1968
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##### Article: Rational spaces and set constraints
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ABSTRACT: Set constraints are inclusions between expressions denoting sets of ground terms. They have been used extensively in program analysis and type inference. In this paper we investigate the topological structure of the spaces of solutions to systems of set constraints. We identify a family of topological spaces called rational spaces, which formalize the notion of a topological space with a regular or self-similar structure, such as the Cantor discontinuum or the space of runs of a finite automaton. We develop the basic theory of rational spaces and derive generalizations and proofs from topological principles of some results in the literature on set constraints.
Theoretical Computer Science. 01/1995;
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##### Conference Proceeding: Systems of set constraints with negative constraints are NEXPTIME-complete
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ABSTRACT: A system of set constraints is a system of expressions E⊆F where E and F describe sets of ground terms over a ranked alphabet. Aiken et al. (1993) classified the complexity of such systems. In A. aiken et al. (1993), it was shown that if negative constraints Enot⊆F were allowed, then the problem as decidable. This was done by reduction to a Diophantine problem, the nonlinear reachability problem, which was shown to be decidable. We show that nonlinear reachability is NP-complete. By bounding the reduction of A. aiken et al. (1993), we conclude that systems of set constraints allowing negative constraints are NEXPTIME-complete
Logic in Computer Science, 1994. LICS '94. Proceedings., Symposium on; 08/1994