Abstract
In this paper closure properties and decision problems for families of languages accepted by deterministic and nondeterministic systolic binary Y-tree automata are studied. Non closure results under basic language operations are stated by means of new nonacceptability criteria for these classes of automata. Necessary and sufficient conditions are given in terms of the shape of the underlying Y-tree, for the closure under ?-free regular substitution, concatenation, inverse homomorfism and for the closure under right concatenation with and quotient by finite sets. Moreover in the nondeterministic case necessary and sufficient conditions are given again in terms of the shape of the underlying Y-tree for the closure under right concatenation with regular sets and for the decidability of the problems of emptiness, finiteness, equivalence and co-emptiness. A sufficient condition is given for the decidability of the stability problem, in the deterministic case, while some undecidability results are proved in the nondeterministic case.
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