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. In this paper we relate the Rabin Index of an !-language to thecomplexity of translation amongst automata, strategies for two-person regulargames, and the complexity of controller-synthesis and verification forreal systems, via a new construction to transform Rabin automata to Chainautomata. The Rabin Index is the minimum number of pairs required torealize the language as a deterministic Rabin automaton (DRA), and is ameasure of the inherent complexity of the !-language. Chain automata...

The rabin index and chain automata, with applications to automata and games