Abstract
Process algebra, e.g. CSP, offers different semantical observations (e.g. traces, failures, divergences) on a single syntactical system description. These observations are either computed algebraically from the process syntax, or “extracted” from a single operational model. Bialgebras capture both approaches in one framework and characterize their equivalence; however, due to use of finality, lack the capability to simultaneously cater for various semantics. We suggest to relax finality to quasi-finality. This allows for several semantics, which also can be coarser than bisimulation. As a case study, we show that our approach works out in the case of the CSP failures model.
This research was supported in part by Grid-Tools Ltd, UK.
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References
Plotkin, G.D.: A structural approach to operational semantics. Technical Report DAIMI FN-19, University of Aarhus (1981)
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)
Turi, D., Plotkin, G.: Towards a mathematical operational semantics. In: Proc. 12th LICS Conference, pp. 280–291. IEEE, Computer Society Press (1997)
Hoare, C.A.R.: Communicating Sequencial Processes. Series in Computer Science. Prentice-Hall International (1985)
Roscoe, A.: The Theory and Practice of Concurrency. Prentice-Hall, Englewood Cliffs (1998)
van Glabbeek, R.: The linear time–branching time spectrum I: the semantics of concrete, sequential processes. In: Bergstra, J., Ponse, A., Smolka, S. (eds.) Handbook of Process Algebra, pp. 3–99. Elsevier (2001)
Monteiro, L.: A Coalgebraic Characterization of Behaviours in the Linear Time – Branching Time Spectrum. In: Corradini, A., Montanari, U. (eds.) WADT 2008. LNCS, vol. 5486, pp. 251–265. Springer, Heidelberg (2009)
Freire, E., Monteiro, L.: Defining Behaviours by Quasi-finality. In: Oliveira, M.V.M., Woodcock, J. (eds.) SBMF 2009. LNCS, vol. 5902, pp. 290–305. Springer, Heidelberg (2009)
Aczel, P.: Final Universes of Processes. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 1–28. Springer, Heidelberg (1994)
Wolter, U.: CSP, partial automata, and coalgebras. Theoretical Computer Science 280, 3–34 (2002)
Boreale, M., Gadducci, F.: Processes as formal power series: A coinductive approach to denotational semantics. Theoretical Computer Science 360, 440–458 (2006)
Power, J., Turi, D.: A coalgebraic foundation for linear time semantics. In: Hofmann, M., Rosolini, G., Pavlovic, D. (eds.) Conference on Category Theory and Computer Science, CTCS 1999. Electronic Notes in Theoretical Computer Science, vol. 29, pp. 259–274. Elsevier (1999)
Jacobs, B.: Trace semantics for coalgebras. In: Adamek, J., Milius, S. (eds.) Coalgebraic Methods in Computer Science. Electronic Notes in Theoretical Computer Science, vol. 106, pp. 167–184. Elsevier (2004)
Hasuo, I., Jacobs, B., Sokolova, A.: Generic trace semantics via coinduction. Logical Methods in Computer Science 3(4:11), 1–36 (2007)
Jacobs, B., Sokolova, A.: Exemplaric expressivity of modal logic. Journal of Logica and Computation 5(20), 1041–1068 (2010)
Klin, B.: Bialgebraic methods and modal logic in structural operational semantics. Inf. Comput. 207(2), 237–257 (2009)
Klin, B.: Structural operational semantics and modal logic, revisited. In: Jacobs, B., Niqui, M., Rutten, J., Silva, A. (eds.) Coalgebraic Methods in Computer Science. Electronic Notes in Theoretical Computer Science, vol. 264, pp. 155–175. Elsevier (2010)
Groote, J.F., Vaandrager, F.W.: Structural operational semantics and bisimulations as a congruence. Information and Computation 100(2), 202–260 (1992)
Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)
Monteiro, L., Maldonado, A.P.: Towards bialgebraic semantics based on quasi-final coalgebras. Technical Report FCT/UNL-DI 1-2011, CITI and DI, Faculdade de Ciências e Tecnologia, UNL (2011), http://ctp.di.fct.unl.pt/~lm/publications/MM-TR-1-2011.pdf
Maldonado, A.P., Monteiro, L., Roggenbach, M.: Towards bialgebraic semantics for CSP. Technical Report FCT/UNL-DI 3-2010, CITI and DI, Faculdade de Ciências e Tecnologia, UNL (2010), http://ctp.di.fct.unl.pt/~apm/publications/MMR-TR-3-2010.pdf
Roggenbach, M.: CSP-CASL—A new integration of process algebra and algebraic specification. Theoretical Computer Science 354, 42–71 (2006)
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Maldonado, A.P., Monteiro, L., Roggenbach, M. (2012). Towards Bialgebraic Semantics for the Linear Time – Branching Time Spectrum. In: Mossakowski, T., Kreowski, HJ. (eds) Recent Trends in Algebraic Development Techniques. WADT 2010. Lecture Notes in Computer Science, vol 7137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28412-0_14
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DOI: https://doi.org/10.1007/978-3-642-28412-0_14
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