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Commutation in Global Supermonoid of Free Monoids

This work is an attempt of generalization of the simple statement about the requirements of commutation of words for the case of languages. In the paper, the necessary condition for com- mutation of languages are obtained, and in the prefix case the necessary and sufficient conditions are obtained. It is important to note that the considered alphabets and languages can be infinite. The possibilities of application of the obtained results are shown in the other problems of the theory of formal languages. The boundary problems for the further solution are formulated.