The paper deals with star-free languages in trace monoids. We define a constrained star operation, named star-free star, and show a new characterisation of star-free trace languages, using this operation instead of complement. We obtain this characterisation combining a star-free star characterisation for word languages and logical characterisation of trace languages (Ebinger/Muscholl). Moreover, some new, simple proofs of known results are presented in the paper.
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