Skip to main content
SpringerLink
Log in

Problems of Synthesis of Σ-Automata Specified in Languages LP and LF of First Order Logic

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

For two fragments LP and LF of monadic first-order logic with bounded quantifiers, the corresponding versions of the proposed specification theorem are formulated and proved that allow one to reduce the procedure for synthesizing Σ-automata specified by formulas of these logics to an equivalent transformation of formulas.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Abadi, L. Lamport, and P. Wolper, “Realizable and unrealizable specifications of reactive systems,” in: Lecture Notes in Computer Science, Vol. 372, Springer, Berlin-Heidelberg (1989), pp. 1–17.

  2. A. Pnueli and R. Rosner, “On the synthesis of a reactive module,” in: Proc. 16th ACM Symp. on Principles of Programming Languages, Austin (1989), pp. 179–190.

  3. R. Alur and S. La Torre, “Deterministic generators and games for LTL fragments,” ACM Transactions on Computational Logic, Vol. 5, No 1, 1–25 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. Harding, M. Ryan, and P.-J. Schobbens, “A new algorithm for strategy synthesis in LTL games,” in: Lecture Notes in Computer Science, Vol. 3440, Springer, Berlin-Heidelberg (2005), pp. 477–492.

  5. N. Piterman, A. Pnueli, and Y. Sa’ar, “Synthesis of reactive(1) designs” in: Lecture Notes in Computer Science, Vol. 3855, Springer, Berlin-Heidelberg (2006), pp. 364–380.

    MATH  Google Scholar 

  6. A. N. Chebotarev, “Harmonization of automata specifications represented in the language L,” Cybernetics and Systems Analysis, Vol. 52, No. 3, 341–350 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  7. B. Alpern and F. Schneider, “Recognizing safety and liveness,” Distributed Computing, No. 2, 117–126 (1987).

    Article  MATH  Google Scholar 

  8. A. N. Chebotarev, “Harmonization of interacting automata,” Cybernetics and Systems Analysis, Vol. 51, No. 5, 676–686 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  9. A. N. Chebotarev, “Regular form of deterministic FSMs specification in the language L,” Applied Discrete Mathematics, No. 4, 64–72 (2010).

    Google Scholar 

  10. A. N. Chebotarev, “Extension of the automaton specification logical language and the synthesis problem,” Cybernetics and Systems Analysis, Vol. 32, No. 6, 756-765 (1996).

    Article  MathSciNet  MATH  Google Scholar 

  11. A. N. Chebotarev, “Synthesis of a procedural representation of an automaton specified in the logical language L*. I,” Cybernetics and Systems Analysis, Vol. 33, No. 4, 505–515 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  12. A. N. Chebotarev, “Some subsets of monadic first-order logic (MFO) used for the specification and synthesis of Σ-automata,” Cybernetics and Systems Analysis, Vol. 53, No. 4, 512–523 (2017).

    Article  Google Scholar 

  13. O. Finkel, “Topological properties of omega context free languages,” Theoretical Computer Science, Vol. 262 (1–2), 669–697 (2001).

Download references

Author information

Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    A. N. Chebotarev

Authors
  1. A. N. Chebotarev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Chebotarev.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2017, pp. 22–33.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chebotarev, A.N. Problems of Synthesis of Σ-Automata Specified in Languages LP and LF of First Order Logic. Cybern Syst Anal 53, 675–683 (2017). https://doi.org/10.1007/s10559-017-9969-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-017-9969-8

Keywords

Search

Navigation