Abstract
A method is proposed to construct the -ω-regular expression that specifies the intersection of sets of -ω-words represented by -ω-regular expressions R1 and R2. The sought-for expression is constructed without passing to ω-automata, i.e., by directly transforming the expression R = R1 ∩ R2. The process of constructing the -ω-regular expression specifying the intersection R1 ∩ R2 is represented in the form of a tree of intersections whose vertices correspond to intersections of simple -ω-regular expressions obtained during transforming the intersection R1 ∩ R2 . The constructed tree of intersections defines a system of linear equations with variables whose values are sets of -ω-words. One of these variables R corresponds to the set of -ω-words specified by the intersection R1 ∩ R2,i.e., the expression specifying the intersection of -ω-regular expressions R1 and R2 is the value of the variable R in the solution of this system of linear equations.
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Translated from Kibernetyka ta Systemnyi Analiz, No. 5, September–October, 2021, pp. 12–21.
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Chebotarev, A.N. Intersection of -ω-Regular Expressions. Cybern Syst Anal 57, 676–684 (2021). https://doi.org/10.1007/s10559-021-00393-3
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DOI: https://doi.org/10.1007/s10559-021-00393-3