Abstract
In synthesis of a Σ-automaton specified in the LP language, the problem arises how to represent the set of –ω-words defined by a formula F (t ) in the form of a –ω-regular expression. Constructing this representation is based on the correspondence between structural components of formulas and –ω-regular expressions. To provide such a correspondence, two additional operations on –ω-regular sets relating to the operation of quantification in the formulas are introduced. The problem is reduced to calculating the –ω-regular expressions defined by these operations. This calculation relies on the construction of a graph of elementary extensions, in which certain set of infinite paths corresponds to all –ω-words that belong to the –ω-set to be calculated. A method for constructing a –ω-regular expression specified by such a graph is proposed in the paper. This method is based on solving a system of linear equations over –ω-regular sets.
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References
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Translated from Kibernetyka ta Systemnyi Analiz, No. 2, March–April, 2022, pp. 3–9.
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Chebotarev, A.N. Constructing a –ω-Regular Expression Specified by a Graph of Elementary Extensions. Cybern Syst Anal 58, 165–170 (2022). https://doi.org/10.1007/s10559-022-00447-0
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DOI: https://doi.org/10.1007/s10559-022-00447-0