Computing Simulations over Tree Automata: Efficient Techniques for Reducing Tree Automata

We address the problem of computing simulation relations over treeautomata. In particular, we consider downward and upward simulations ontree automata, which are, loosely speaking, analogous to forward andbackward relations over word automata. We provide simple and efficientalgorithms for computing these relations based on a reduction to theproblem of computing simulations on labelled transition systems.Furthermore, we show that downward and upward relations can be combinedto get relations compatible with the tree language equivalence, whichcan subsequently be used for an efficient size reduction ofnondeterministic tree automata. This is of a very high interest, forinstance, for symbolic verification methods such as regular modelchecking, which use tree automata to represent infinite sets ofreachable configurations. We provide experimental results showing the efficiency of our algorithms on examples of tree automata taken fromregular model checking computations.