Recognizable and rational languages of finite an infinite traces

Trace languages are used in computer science to provide a description of the behaviours of concurrent systems. If we are interested in systems which never stop then we have to consider languages of infinite traces. In this paper, we introduce and study recognizable and rational languages of finite and infinite traces. We characterize recognizable languages by means of a syntactic congruence. We prove that the family of recognizable languages is strictly included in the family of rational languages. Next, we study the closure properties of the family of recognizable languages. We prove that this family is closed under the Boolean operations and under concatenation. Contrary to the (finite) iteration, the infinite iteration of a finite trace is proved to be recognizable. We conclude this paper with some open problems.

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