Logical Definability on Infinite Traces

The main results of the present paper are the equivalence of monadic second order logic and recognizability for real trace languages, and that first order definable, star-free, and aperiodic real trace languages form the same class of languages. This generalizes results on infinite words [Tho90a, for an overview] and on finite traces [Tho90b, GRS91] to infinite traces. It closes the last gap in the different characterizations of recognizable infinitary trace languages.

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