Rule Formats for Bounded Nondeterminism in Structural Operational Semantics

  • Luca Aceto
  • Álvaro García-Pérez
  • Anna Ingólfsdóttir
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9560)

Abstract

We present rule formats for structural operational semantics that guarantee that the associated labelled transition system has each of the three following finiteness properties: finite branching, initials finiteness and image finiteness.

Keywords

Structural operational semantics Labelled transition systems Rule formats Bounded nondeterminism 

Notes

Acknowledgements

We thank two anonymous referees for their careful reading of our paper and their constructive comments.

References

  1. 1.
    Abramsky, S.: Domain theory and the logic of observable properties. Ph.D. thesis, Department of Computer Science, Queen Mary College, University of London (1987)Google Scholar
  2. 2.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, Chap. 3, pp. 197–292. Elsevier, Amsterdam (2001)CrossRefGoogle Scholar
  3. 3.
    Amtoft, T., Nielson, F., Nielson, H.R.: Type and Effect Systems. Imperial College Press, London (1999)CrossRefGoogle Scholar
  4. 4.
    Apt, K.R., Plotkin, G.D.: Countable nondeterminism and random assignment. J. ACM 33(4), 724–767 (1986)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Baeten, J.C.M., Vaandrager, F.W.: An algebra for process creation. Acta Inf. 29(4), 303–334 (1992). http://dx.doi.org/10.1007/BF01178776 MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Bloom, B.: CHOCOLATE: Calculi of Higher Order COmmunication and LAmbda TErms (preliminary report). In: Boehm, H.J., Lang, B., Yellin, D.M. (eds.) Conference Record of the 21st ACM Symposium on Principles of Programming Languages, Portland, Oregon, pp. 339–347. ACM Press (1994)Google Scholar
  7. 7.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Cimini, M., Mousavi, M.R., Reniers, M.A., Gabbay, M.J.: Nominal SOS. Electron. Notes Theoret. Comput. Sci. 286, 103–116 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Fokkink, W., Vu, T.D.: Structural operational semantics and bounded nondeterminism. Acta Inf. 39(6–7), 501–516 (2003)MATHMathSciNetGoogle Scholar
  10. 10.
    Gabbay, M.J., Pitts, A.M.: A new approach to abstract syntax involving binders. In: Longo, G. (ed.) Proceedings of the 14th Symposium on Logic in Computer Science, Trento, Italy, pp. 214–224. IEEE Computer Society Press (1999)Google Scholar
  11. 11.
    van Gelder, A., Ross, K.A., Schilpf, J.S.: The well-founded semantics for general logic programs. J. ACM 38(3), 620–662 (1991)MATHGoogle Scholar
  12. 12.
    van Glabbeek, R.J.: Bounded nondeterminism and the approximation induction principle in process algebra. In: Brandenburg, F.J., Wirsing, M., Vidal-Naquet, G. (eds.) STACS 1987. LNCS, vol. 247, pp. 336–347. Springer, Heidelberg (1987) CrossRefGoogle Scholar
  13. 13.
    Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100(2), 202–260 (1992)MATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Groote, J.F.: Transition system specifications with negative premises. Theoret. Comput. Sci. 118(2), 263–299 (1993)MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    Heyting, A. (ed.): Constructivity in Mathematics. North-Holland Publishing Company, Amsterdam (1959)MATHGoogle Scholar
  16. 16.
    Keller, R.M.: Formal verification of parallel programs. Commun. ACM 19(7), 371–384 (1976)MATHCrossRefGoogle Scholar
  17. 17.
    Klusener, A.S.: Models and axioms for a fragment of real time process algebra. Ph.D. thesis, Department of Mathematics and Computing Science, Technical University of Eindhoven (1993)Google Scholar
  18. 18.
    Lévy, A.: A hierarchy of formulas in set theory. Mem. Am. Math. Soc. 57, 76 (1965)Google Scholar
  19. 19.
    Martin-Löf, P.: Intuitionistic Type Theory. Studies in Proof Theory: Lecture Notes, Bibliopolis, Napoli (1984)Google Scholar
  20. 20.
    Milner, R.: Communication and Concurrency. PHI Series in Computer Science. Prentice Hall, Upper Saddle River (1989) MATHGoogle Scholar
  21. 21.
    Mousavi, M.R., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theoret. Comput. Sci. 373(3), 238–272 (2007)MATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Nielson, F., Nielson, H.R., Hankin, C.: Principles of Program Analysis. Springer, Heidelberg (2005)MATHGoogle Scholar
  23. 23.
    Nielson, H.R., Nielson, F.: Semantics with Applications: An Appertizer. Springer, London (2007)CrossRefGoogle Scholar
  24. 24.
    Pitts, A.M.: Nominal Sets: Names and Symmetry in Computer Science. Cambridge Tracts in Theoretical Computer Science, vol. 57. Cambridge University Press, Cambridge (2013) CrossRefGoogle Scholar
  25. 25.
    Plotkin, G.D.: A structural approach to operational semantics. Technacal report. DAIMI FN-19, Department of Computer Science, Aarhus University, Denmark (1981)Google Scholar
  26. 26.
    Plotkin, G.D.: An operational semantics for CSP. In: Salwicki, A. (ed.) Logic of Programs 1980. LNCS, vol. 148, pp. 250–252. Springer, Heidelberg (1983). http://dx.doi.org/10.1007/3-540-11981-7_17 CrossRefGoogle Scholar
  27. 27.
    Plotkin, G.D.: A structural approach to operational semantics. J. Logic Algebraic Program. 60–61, 17–139 (2004)MathSciNetGoogle Scholar
  28. 28.
    Przymusinski, T.C.: The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13(4), 445–463 (1990)MATHMathSciNetGoogle Scholar
  29. 29.
    Sangiorgi, D., Walker, D.: The pi-calculus: A Theory of Mobile Processes. Cambridge Universtity Press, Cambridge (2001)Google Scholar
  30. 30.
    de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theoret. Comput. Sci. 37(3), 245–267 (1985)Google Scholar
  31. 31.
    Urban, C., Pitts, A.M., Gabbay, M.J.: Nominal unification. Theoret. Comput. Sci. 323(1–3), 473–497 (2004)MATHMathSciNetCrossRefGoogle Scholar
  32. 32.
    Vaandrager, F.W.: Expressiveness results for process algebras. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1992. LNCS, vol. 666, pp. 609–638. Springer, Heidelberg (1993) CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Luca Aceto
    • 1
  • Álvaro García-Pérez
    • 1
  • Anna Ingólfsdóttir
    • 1
  1. 1.ICE-TCS, School of Computer ScienceReykjavík UniversityReykjavíkIceland

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