A Unified Approch for Showing Language Inclusion and Equivalence Between Various Types of omega-Automata

We consider the language containment and equivalence problems for six different types of ω-automata: Buchi, Muller, Rabin, Streett, the L-automata of Kurshan, and the ∀-automata of Manna and Pnueli. We give a six by six matrix in which each row and column is associated with one of these types of automata. The entry in the i th row and j th column is the complexity of showing containment between the i th type of automaton and the j th . Thus, for example, we give the complexity of showing language containment and equivalence between a Buchi automaton and a Muller or Streett automaton. Our results are obtained by a uniform method that associates a formula of the logic CTL* with each type of automaton. Our algorithms use a model checking procedure for the logic with the formulas obtained from the automata. The results of our paper are important for verification of finite state concurrent systems with fairness constraints. A natural way of reasoning about such systems is to model the finite state program by one ω-automaton and its specification by another.