Abstract
When synthesizing a Σ-automaton specified in the language LP, the problem arises of representing the set of left-infinite words given by a formula F(t) in the form of a –ω-regular expression. Construction of this expression is based on the correspondence between structural elements of formulas and –ω-regular expressions. To ensure this correspondence, two additional operations that correspond to the quantification operations in formulas are introduced over –ω-regular sets. Methods of representation of these operations in terms of the language of –ω-regular expressions are considered. The results obtained allow to construct –ω-regular expressions for a rather wide class of LP formulas of the form F(t).
Similar content being viewed by others
References
A. N. Chebotarev, “Synthesis of Σ-automata specified in the first order logical languages LP and LF,” Cybern. Syst. Analysis, Vol. 54, No. 4, 527–540 (2018). https://doi.org/10.1007/s10559-018-0054-8.
A. N. Chebotarev, “Detecting fictitious states in a Σ-automaton synthesized from its specification in the language LP,” Cybern. Syst. Analysis, Vol. 55, No. 5, 742–751 (2019). https://doi.org/10.1007/s10559-019-00184-x.
K. Schneider, Verification of Reactive Systems, Springer, Berlin–Heidelberg (2004).
D. Bresolin, A. Montanari, and G. Puppis, “A theory of ultimately periodic languages and automata with an application to time granularity,” Acta Informatica, Vol. 46, 331–360 (2009).
J. Cohen-Chesnot, “On the expressive power of temporal logic for infinite words,” Theoretical Computer Science, Vol. 83, Iss. 2, 301–312 (1991).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2020, pp. 3–17.
Rights and permissions
About this article
Cite this article
Chebotarev, A.N. From LP Formulas of the Form F(t) to –ω-Regular Expressions. Cybern Syst Anal 56, 689–700 (2020). https://doi.org/10.1007/s10559-020-00286-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10559-020-00286-x