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Comparing language operations

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Abstract

A procedure for comparing language operations is formulated and used to study some general algebraic properties of such operations as well as the interrelationships of some specific well known operations. The comparison scheme is used to partition the family of all language operations into a collection of equivalence classes that forms an upper semilattice, When full semi-AFL operations are used as a basis of comparison, the Min and Max operations are shown to be in the same class as relative complementation and reside above the class containing Kleene closure. This gives the result that any complementation closed full semi-AFL is a full AFL closed under Min and Max.

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This paper was supported in part by the National Science Foundation under grant GJ-803 and in part by the U.S. Army Research Office.

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Itoga, S.Y. Comparing language operations. Math. Systems Theory 10, 305–321 (1976). https://doi.org/10.1007/BF01683281

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  • DOI: https://doi.org/10.1007/BF01683281

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