Abstract

Over the last decades the theory of finite automata on infinite objects has been an important source of tools for the specification and the verification of computer programs. Trees are more suitable than words to model nondeterminism and thus concurrency. In the literature, there are several examples of acceptance conditions that have been proposed for automata on infinite words and then have been fruitfully extended to infinite trees (Büchi, Rabin, and Muller conditions). The type of acceptance condition can influence both the succinctness of the corresponding class of automata and the complexity of the related decision problems. Here we consider, for automata on infinite trees, two acceptance conditions that are obtained by a relaxation of the Muller acceptance condition: the Landweber and the Muller-Superset conditions. We prove that Muller-Superset tree automata accept the same class of languages as Büchi tree automata, but using more succinct automata. Landweber tree automata, instead, define a class of languages which is not comparable with the one defined by Büchi tree automata. We prove that, for this class of automata, the emptiness problem is decidable in polynomial time, and thus we expand the class of automata with a tractable emptiness problem.

Citations