Skip to main content
SpringerLink
Log in

Synthesis algorithm for recursive processes by μ-calculus

Extended abstract

  • Selected Papers
  • Conference paper
  • First Online:
Book cover Algorithmic Learning Theory (AII 1994, ALT 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 872))

Abstract

This paper proposes an inductive synthesis algorithm for a recursive process from the enumeration of facts, which must be satisfied by the target process. We adopt a subcalculus of μ-calculus to represent facts of a process. First, a new preorder ≤ d on recursive processes is introduced in such a way that p≤d q means that p ⊨ f implies q ⊨ f, for all formulae f in the subcalculus. Then, we present the synthesis algorithm. The correctness of the algorithm consists in that it only produces processes that satisfy the given facts. By adding more and more facts, the algorithm will eventually produce the target process. It will be shown that the algorithm is complete for the subcalculus.

A part of this study is supported by Grants from the Asahi Glass Foundation and Research Funds from Japanese Ministry of Education

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Angluin, D.: “Learning Regular Sets from Queries and Counterexamples”, Inf. and Comput, 75, pp. 87–106 (1987).

    Google Scholar 

  2. Brookes, S.D., C.A.R Hoare and A.W. Roscoe: “A Theory of Communicating Sequential Processes”, J. ACM., 31, 3, pp. 560–599 (1984).

    Google Scholar 

  3. Clocksin, W.F. and C.S. Mellish: “Programming in Prolog”, Springer-Verlag(1981).

    Google Scholar 

  4. Fantechi, A., S. Gnesi S. and G. Ristori: “Compositional Logic Semantics and LOTOS”, Protocol Specification, Testing and Verification, XL., IFIP, pp. 365–378

    Google Scholar 

  5. Graf, S. and J. Sifakis: “A Logic for the Description of Non-deterministic Programs and Their Properties”, Inf. and contr., 68, pp. 254–270 (1986)

    Google Scholar 

  6. Hennessy, M. and R. Milner: “Algebraic Laws for Nondeterminism and Concurrency”, J. ACM., 32, 1, pp. 137–161 (1985).

    Google Scholar 

  7. Hennessy, M.: “Algebraic Theory of Processes”, The MIT Press(1988).

    Google Scholar 

  8. Hindley, J.R. and J.P. Seldin: “Introduction to Combinators and λ-Calculus”, London Mathematical Society Student Texts 1, Cambridge Univ. Press(1986).

    Google Scholar 

  9. Hoare, C.A.R.: “Communicating Sequential Process”, Prentice Hall(1985).

    Google Scholar 

  10. Kimura, S., A. Togashi and S. Noguchi: “A Synthesis Algorithm of Basic Processes by Modal Formulas” (in Japanese), Trans. IEICE, J75-D-I, pp. 1048–1061 (1992).

    Google Scholar 

  11. Kimura, S., A. Togashi and N. Shiratori: “Synthesis Algorithm for Recursive Processes by μ-calculus”, preprint.

    Google Scholar 

  12. Kozen, D.: “Results on the Propositional μ-calculus”, Theoret. Comput. Sci., 27, pp. 333–354 (1983).

    Google Scholar 

  13. Manna, Z. and P. Wolper: “Synthesis of Communicating Processes from Temporal Logic Specifications”, ACM Trans. on Programming Languages and Systems, 6, 1, pp. 68–93 (1984).

    Google Scholar 

  14. Milner, R.: “Communication and Concurrency”, Prentice-Hall(1989).

    Google Scholar 

  15. Park, D.: “Concurrency and automata on infinite sequences”, Lecture Notes in Comput. Sci. 104, pp. 167–183, Springer-Verlag(1981).

    Google Scholar 

  16. Gotzhein, R.: “Specifying Communication Services With Temporal Logic”, Protocol Specification, Testing and Verification, XL, pp. 295–309 (1990).

    Google Scholar 

  17. van Glabbeek, R.J.: “The Linear Time — Branching Time Spectrum”, Lecture Notes in Comput. Sci. 458, Springer-Verlag(1990).

    Google Scholar 

  18. Shapiro, E.Y.: “Inductive Inference of Theories From Facts”, Technical Report 192, Yale Univ(1981).

    Google Scholar 

  19. Stirling, C.: “A Proof-Theoretic Characterization of Observational Equivalence”, Theoretical Computer Science, 39, pp. 27–45 (1985).

    Google Scholar 

  20. Stirling, C.: “Modal Logics For Communicating Systems”, Theoretical Computer Science, 49, pp. 311–347 (1987).

    Google Scholar 

  21. Stirling, C.: “An Introduction to Modal and Temporal Logics for CCS”, Lecture Notes in Comput. Sci. 491, Springer-Verlag, pp. 2–20 (1991).

    Google Scholar 

  22. Streett, R.S. and E.A. Emerson: “An Automata Theoretic Decision Procedure for the Propositional Mu-Calculus”, Info. and Comput. 81, Academic Press, pp. 249–264 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, 980-77, Sendai, Japan

    Shigetomo Kimura, Atsushi Togashi & Norio Shiratori

Authors
  1. Shigetomo Kimura
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atsushi Togashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Norio Shiratori
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Setsuo Arikawa Klaus P. Jantke

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kimura, S., Togashi, A., Shiratori, N. (1994). Synthesis algorithm for recursive processes by μ-calculus. In: Arikawa, S., Jantke, K.P. (eds) Algorithmic Learning Theory. AII ALT 1994 1994. Lecture Notes in Computer Science, vol 872. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58520-6_78

Download citation

  • DOI: https://doi.org/10.1007/3-540-58520-6_78

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58520-6

  • Online ISBN: 978-3-540-49030-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation