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Exploiting Algebraic Laws to Improve Mechanized Axiomatizations

  • Luca Aceto
  • Eugen-Ioan Goriac
  • Anna Ingolfsdottir
  • Mohammad Reza Mousavi
  • Michel A. Reniers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8089)

Abstract

In the field of structural operational semantics (SOS), there have been several proposals both for syntactic rule formats guaranteeing the validity of algebraic laws, and for algorithms for automatically generating ground-complete axiomatizations. However, there has been no synergy between these two types of results. This paper takes the first steps in marrying these two areas of research in the meta-theory of SOS and shows that taking algebraic laws into account in the mechanical generation of axiomatizations results in simpler axiomatizations. The proposed theory is applied to a paradigmatic example from the literature, showing that, in this case, the generated axiomatization coincides with a classic hand-crafted one.

Keywords

Axiom System Parallel Composition Deduction Rule Closed Term Head Normal Form 
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.
    Aceto, L., Bloom, B., Vaandrager, F.W.: Turning SOS rules into equations. Information and Computation 111, 1–52 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Aceto, L., Caltais, G., Goriac, E.-I., Ingolfsdottir, A.: PREG Axiomatizer - a ground bisimilarity checker for GSOS with predicates. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 378–385. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  3. 3.
    Aceto, L., Fokkink, W., Ingólfsdóttir, A., Luttik, B.: Finite equational bases in process algebra: Results and open questions. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes... (Klop Festschrift). LNCS, vol. 3838, pp. 338–367. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Aceto, L., Fokkink, W., Verhoef, C.: Structural operational semantics. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, ch. 3, pp. 197–292. Elsevier Science, Dordrecht (2001)CrossRefGoogle Scholar
  5. 5.
    Aceto, L., Ingolfsdottir, A., Mousavi, M., Reniers, M.A.: Algebraic properties for free! Bulletin of the European Association for Theoretical Computer Science 99, 81–104 (2009)Google Scholar
  6. 6.
    Baeten, J., Basten, T., Reniers, M.: Process Algebra: Equational Theories of Communicating Processes. Cambridge Tracts in Theoretical Computer Science, vol. 50. Cambridge University Press (2009)Google Scholar
  7. 7.
    Baeten, J.J., de Vink, E.P.: Axiomatizing GSOS with termination. Journal of Logic and Algebraic Programming 60-61, 323–351 (2004)CrossRefGoogle Scholar
  8. 8.
    Bergstra, J.A., Klop, J.W.: Fixedpoint semantics in process algebra. Technical Report IW 206/82, Center for Mathematics, Amsterdam, The Netherlands (1982)Google Scholar
  9. 9.
    Bergstra, J.A., Klop, J.W.: Process algebra for synchronous communication. Information and Control 60(1-3), 109–137 (1984)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. Journal of the ACM 42(1), 232–268 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Bosscher, D.: Term rewriting properties of SOS axiomatisations. In: Hagiya, M., Mitchell, J.C. (eds.) TACS 1994. LNCS, vol. 789, pp. 425–439. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  12. 12.
    van Glabbeek, R.J.: The linear time - branching time spectrum I. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, ch. 1, pp. 3–100. Elsevier Science, Dordrecht (2001)CrossRefGoogle Scholar
  13. 13.
    Hennessy, M., Milner, A.R.: Algebraic laws for non-determinism and concurrency. Journal of the ACM 32(1), 137–161 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall (1985)Google Scholar
  15. 15.
    Milner, A.R.: Communication and Concurrency. Prentice-Hall (1989)Google Scholar
  16. 16.
    Mousavi, M., Reniers, M., Groote, J.F.: A syntactic commutativity format for SOS. Information Processing Letters 93, 217–223 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Mousavi, M., Reniers, M.A., Groote, J.F.: SOS formats and meta-theory: 20 years after. Theoretical Computer Science 373, 238–272 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Park, D.M.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  19. 19.
    Plotkin, G.D.: A structural approach to operational semantics. Journal of Logic and Algebraic Progamming 60, 17–139 (2004)MathSciNetGoogle Scholar
  20. 20.
    Ulidowski, I.: Finite axiom systems for testing preorder and De Simone process languages. Theoretical Computer Science 239(1), 97–139 (2000)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Luca Aceto
    • 1
  • Eugen-Ioan Goriac
    • 1
  • Anna Ingolfsdottir
    • 1
  • Mohammad Reza Mousavi
    • 2
  • Michel A. Reniers
    • 3
  1. 1.ICE-TCS, School of Computer ScienceReykjavik UniversityReykjavikIceland
  2. 2.Center for Research on Embedded Systems (CERES)Halmstad UniversitySweden
  3. 3.Department of Mechanical EngineeringEindhoven University of TechnologyEindhovenThe Netherlands

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