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Transitive Closures of Semi-commutation Relations on Regular omega-Languages
A semi-commutation is a relation on a finite alphabet . Given an infinite word on , we denote by and by the language . In this paper we prove that if an -language is a finite union of languages of the form , where the 's are subsets of the alphabet and the 's are letters, then is a computable regular -language accepting a similar decomposition. In addition we prove the same result holds for -languages which are finite unions of languages of the form , where the 's are accepted by diamond automata and the 's are letters. These results improve recent works by Bouajjani, Muscholl and Touili on one hand, and by Cécé, Héam and Mainier on the other hand, by extending them to infinite words
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