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Syntactic Formats for Free

An Abstract Approach to Process Equivalence
  • Bartek Klin
  • Paweł Sobociński
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2761)

Abstract

A framework of Plotkin and Turi’s, originally aimed at providing an abstract notion of bisimulation, is modified to cover other operational equivalences and preorders. Combined with bialgebraic methods, it yields a technique for the derivation of syntactic formats for transition system specifications which guarantee operational preorders to be precongruences. The technique is applied to the trace preorder, the completed trace preorder and the failures preorder. In the latter two cases, new syntactic formats ensuring precongruence properties are introduced.

Keywords

Transition System Test Suite Natural Transformation Operational Semantic Sequential Composition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Abramsky, S., Vickers, S.: Quantales, observational logic and process semantics. Math. Struct. in Comp. Sci. 3, 161–227 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, Elsevier, Amsterdam (1999)Google Scholar
  3. 3.
    Aczel, P., Mendler, N.: A final coalgebra theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  4. 4.
    Barr, M.: Terminal coalgebras in well-founded set theory. Theoretical Computer Science 114, 299–315 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bloom, B.: When is partial trace equivalence adequate? Formal Aspects of Computing 6, 25–68 (1994)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Bloom, B., Fokkink, W., van Glabbeek, R.J.: Precongruence formats for decorated trace preorders. In: Logic in Computer Science, pp. 107–118 (2000)Google Scholar
  7. 7.
    Bloom, B., Fokkink, W.J., van Glabbeek, R.J.: Precongruence formats for decorated trace semantics. ACM Transactions on Computational Logic (to appear)Google Scholar
  8. 8.
    Bloom, B., Istrail, S., Meyer, A.: Bisimulation can’t be traced. Journal of the ACM 42, 232–268 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Fokkink, W., van Glabbeek, R.: Ntyft/ntyxt rules reduce to ntree rules. Information and Computation 126, 1–10 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    van Glabbeek, R.J.: The linear time-branching time spectrum I. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra. Elsevier, Amsterdam (1999)Google Scholar
  11. 11.
    Groote, J.F.: Transition system specifications with negative premises. Theoret. Comput. Sci. 118, 263–299 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32, 137–161 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice Hall, Englewood Cliffs (1985)zbMATHGoogle Scholar
  14. 14.
    Jacobs, B.: Categorical Logic and Type Theory. Studies in Logic and the Foundations of Mathematics, vol. 141. North Holland, Elsevier (1999)Google Scholar
  15. 15.
    Klin, B., Sobociński, P.: Syntactic formats for free: An abstract approach to process equivalence. BRICS Report RS-03-18, Aarhus University (2003), Available from http://www.brics.dk/RS/03/18/BRICS-RS-03-18.pdf
  16. 16.
    Mac Lane, S.: Categories for the Working Matematician. Springer, Heidelberg (1998)Google Scholar
  17. 17.
    Park, D.M.: Concurrency on automata and infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  18. 18.
    Plotkin, G.: A structural approach to operational semantics. DAIMI Report FN-19, Computer Science Department, Aarhus University (1981)Google Scholar
  19. 19.
    Plotkin, G.: Bialgebraic semantics and recursion (extended abstract). In: Corradini, A., Lenisa, M., Montanari, U. (eds.) Electronic Notes in Theoretical Computer Science, vol. 44. Elsevier Science Publishers, Amsterdam (2001)Google Scholar
  20. 20.
    Plotkin, G.: Bialgebraic semantics and recursion. In: Invited talk, Workshop on Coalgebraic Methods in Computer Science, Genova (2001)Google Scholar
  21. 21.
    Roscoe, A.W.: The Theory and Practice of Concurrency. Prentice Hall, Englewood Cliffs (1997)Google Scholar
  22. 22.
    Rutten, J., Turi, D.: Initial algebra and final coalgebra semantics for concurrency. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 530–582. Springer, Heidelberg (1994)Google Scholar
  23. 23.
    de Simone, R.: Higher-level synchronising devices in Meije-SCCS. Theoret. Comput. Sci. 37, 245–267 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Turi, D.: Fibrations and bisimulation (unpublished notes)Google Scholar
  25. 25.
    Turi, D.: Functorial Operational Semantics and its Denotational Dual. PhD thesis, Vrije Universiteit, Amsterdam (1996)Google Scholar
  26. 26.
    Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: Proceedings 12th Ann. IEEE Symp. on Logic in Computer Science, LICS 1997, Warsaw, Poland, June 29 – July 2, pp. 280–291. IEEE Computer Society Press, Los Alamitos (1997)CrossRefGoogle Scholar
  27. 27.
    Vaandrager, F.W.: On the relationship between process algebra and input/output automata. In: Logic in Computer Science, pp. 387–398 (1991)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Bartek Klin
    • 1
  • Paweł Sobociński
    • 1
  1. 1.BRICS University of AarhusDenmark

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