Distributed ω-Automata

In this paper, we introduce the notion of distributed ω-automata. Distributed ω-automata are a group of automata working in unison to accept an ω-language. We build the theory of distributed ω-automata for finite state automata and pushdown automata in different modes of cooperation like the t-mode, *-mode, = k-mode, ≤ k-mode and ≥ k-mode along with different acceptance criteria i.e. Büchi-, Muller-, Rabin- and Streett- acceptance criteria. We then analyze the acceptance power of such automata in all the above modes of cooperation and acceptance criteria. We present proofs that distributed ω-finite state automata do not have any additional power over ω-finite state automata in any of the modes of cooperation or acceptance criteria, while distributed ω-pushdown automata can accept languages not in CFLω. We give proofs for the equivalence of all modes of cooperation and acceptance criteria in the case of distributed ω-pushdown automata. We show that the power of distributed ω-pushdown automata is equal to that of ω-Turing Machines. We also study the deterministic version of distributed ω-pushdown automata. Deterministic ω-pushdown automata accept only languages contained in CFLω but distributed deterministic ω-pushdown automata can accept languages not in CFLω and have the same power as their nondeterministic counterparts. We also define distributed completely deterministic ω-pushdown automata and analyze their power. © 2003 World Scientific Publishing Company.