Skip to main content
×
Home

Proving the validity of equations in GSOS languages using rule-matching bisimilarity

  • LUCA ACETO (a1), MATTEO CIMINI (a1) and ANNA INGOLFSDOTTIR (a1)
Abstract

This paper presents a bisimulation-based method for establishing the soundness of equations between terms constructed using operations whose semantics are specified by rules in the GSOS format of Bloom, Istrail and Meyer. The method is inspired by de Simone's FH-bisimilarity and uses transition rules as schematic transitions in a bisimulation-like relation between open terms. The soundness of the method is proved and examples showing its applicability are provided. The proposed bisimulation-based proof method is incomplete, but we do offer some completeness results for restricted classes of GSOS specifications. An extension of the proof method to the setting of GSOS languages with predicates is also offered.

Copyright
References
Hide All
Aceto L., Birgisson A., Ingolfsdottir A., Mousavi M. and Reniers M. (2010) Rule formats for determinism and idempotence. In: Arbab F. and Sirjani M. (eds.) Fundamentals of Software Engineering, Third IPM International Conference, FSEN 2009, Revised Selected Papers. Springer-Verlag Lecture Notes in Computer Science 5961 146161.
Aceto L., Bloom B. and Vaandrager F. (1994) Turning SOS rules into equations. Information and Computation 111 (1)152.
Aceto L., Cimini M. and Ingolfsdottir A. (2010a) A bisimulation-based method for proving the validity of equations in GSOS languages. In: Klin B. and Sobocinski P. (eds.) Proceedings Sixth Workshop on Structural Operational Semantics (SOS 2009). Electronic Proceedings in Theoretical Computer Science 18 116.
Aceto L., Fokkink W., Ingolfsdottir A. and Luttik B. (2005) Finite equational bases in process algebra: Results and open questions. In: Middeldorp A., van Oostrom V., van Raamsdonk F. and de Vrijer R. C. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity, Essays Dedicated to Jan Willem Klop, on the Occasion of His 60th Birthday. Springer-Verlag Lecture Notes in Computer Science 3838 338367.
Aceto L., Fokkink W., Ingolfsdottir A. and Luttik B. (2009) A finite equational base for CCS with left merge and communication merge. ACM Transactions on Compututational Logic 10 (1).
Aceto L., Fokkink W. and Verhoef C. (2001) Structural operational semantics. In: Bergstra J., Ponse A. and Smolka S. A. (eds.) Handbook of Process Algebra, Elsevier 197292.
Aceto L., Ingolfsdottir A., Luttik B. and van Tilburg P. (2008) Finite equational bases for fragments of CCS with restriction and relabelling. In: Ausiello G., Karhumäki J., Mauri G. and Ong C.-H. L. (eds.) Fifth IFIP International Conference On Theoretical Computer Science – TCS 2008. IFIP 273 317332.
Aceto L., Ingolfsdottir A., Mousavi M. and Reniers M. (2010b) A rule format for unit elements. In: van Leeuwen J., Muscholl A., Peleg D., Pokorný J. and Rumpe B. (eds.) Proceedings SOFSEM 2010: Theory and Practice of Computer Science, 36th Conference on Current Trends in Theory and Practice of Computer Science. Springer-Verlag Lecture Notes in Computer Science 5901 141152.
Baeten J. and Bergstra J. (1990) Process algebra with a zero object. In: Baeten J. C. M. and Klop J. W. (eds.) Proceedings CONCUR 90. Springer-Verlag Lecture Notes in Computer Science 458 8398.
Baeten J. and de Vink E. P. (2004) Axiomatizing GSOS with termination. Journal of Logic and Algebraic Programming 60–61 323351.
Baeten J. and Vaandrager F. (1992) An algebra for process creation. Acta Informatica 29 (4)303334.
Baeten J. and Weijland P. (1990) Process Algebra, Cambridge Tracts in Theoretical Computer Science 18, Cambridge University Press.
Bloom B., Fokkink W. and van Glabbeek R. (2004) Precongruence formats for decorated trace semantics. ACM Transactions on Computational Logic 5 (1)2678.
Bloom B., Istrail S. and Meyer A. (1995) Bisimulation can't be traced. Journal of the ACM 42 (1)232268.
Bruni R., de Frutos-Escrig D., Martí-Oliet N. and Montanari U. (2000) Bisimilarity congruences for open terms and term graphs via tile logic. In: Palamidessi C. (ed.) CONCUR 2000 – Concurrency Theory, 11th International Conference, Proceedings. Springer-Verlag Lecture Notes in Computer Science 1877 259274.
Cranen S., Mousavi M. and Reniers M. (2008) A rule format for associativity. In: van Breugel F. and Chechik M. (eds.) Proceedings of CONCUR 2008 – Concurrency Theory, 19th International Conference. Springer-Verlag Lecture Notes in Computer Science 5201 447461.
Doumenc G., Madelaine E. and de Simone R. (1990) Proving process calculi translations in ECRINS. Technical Report RR1192, INRIA.
Fokkink W., van Glabbeek R. and de Wind P. (2006) Compositionality of Hennessy–Milner logic by structural operational semantics. Theoretical Computer Science 354 (3)421440.
Fokkink W. and Verhoef C. (1998) A conservative look at operational semantics with variable binding. Information and Computation 146 (1)2454.
van Glabbeek R. (2001) The linear time–branching time spectrum. I. The semantics of concrete, sequential processes. In: Bergstra J., Ponse A. and Smolka S. A. (eds.) Handbook of Process Algebra, Elsevier 399.
Groote J. F. and Vaandrager F. (1992) Structured operational semantics and bisimulation as a congruence. Information and Computation 100 (2)202260.
Hennessy M. (1988) Algebraic Theory of Processes, MIT Press.
Hennessy M. and Milner R. (1985) Algebraic laws for nondeterminism and concurrency. Journal of the ACM 32 (1)137161.
Hoare C. A. R. (1985) Communicating Sequential Processes. Prentice-Hall International. (Available at http://www.usingcsp.com/cspbook.pdf.)
Hoare C. A. R. et al. (1987) Laws of programming. Communications of the ACM 30 (8)672686.
Larsen K. G. and Liu X. (1991) Compositionality through an operational semantics of contexts. Journal of Logic and Computation 1 (6)761795.
Madelaine E. and Vergamini D. (1991) Finiteness conditions and structural construction of automata for all process algebras. DIMACS Series in Discrete Mathematics and Theoretical Computer Science 3 275292.
Milner R. (1984) A complete inference system for a class of regular behaviours. Journal of Computer and System Sciences 28 439466.
Milner R. (1989) Communication and Concurrency, Prentice-Hall International.
Mousavi M. and Reniers M. (2005) Orthogonal extensions in structural operational semantics. In: Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP'05). Springer-Verlag Lecture Notes in Computer Science 3580 12141225.
Mousavi M., Reniers M. and Groote J. F. (2005) A syntactic commutativity format for SOS. Information Processing Letters 93 217223.
Mousavi M., Reniers M. and Groote J. F. (2007) SOS formats and meta-theory: 20 years after. Theoretical Computer Science 373 (3)238272.
Park D. (1981) Concurrency and automata on infinite sequences. In: Deussen P. (ed.) 5th GI Conference, Karlsruhe, Germany. Springer-Verlag Lecture Notes in Computer Science 104 167183.
Plotkin G. D. (1981) A structural approach to operational semantics. Report DAIMI FN-19, Computer Science Department, Aarhus University.
Plotkin G. D. (2004) A structural approach to operational semantics. Journal of Logic and Algebraic Programming 60–61 17139. (This is a revised version of Plotkin (1981).)
Rensink A. (2000) Bisimilarity of open terms. Information and Computation 156 (1-2)345385.
de Simone R. (1984) Calculabilité et Expressivité dans l'Algèbre de Processus Parallèles Meije, Thèse de 3e cycle, Univ. Paris 7.
de Simone R. (1985) Higher-level synchronising devices in Meije–SCCS. Theoretical Computer Science 37 245267.
van Weerdenburg M. (2008) Automating soundness proofs. In Hennessy M. and Klin B. (eds.) Proceedings of the Workshop on Structural Operational Semantics (SOS 2008). Electronic Notes in Theoretical Computer Science 229 (4)107118.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 5 *
Loading metrics...

Abstract views

Total abstract views: 54 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 25th November 2017. This data will be updated every 24 hours.