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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 IFIP International Federation for Information Processing
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-642-28412-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28411-3
Online ISBN: 978-3-642-28412-0
eBook Packages: Computer ScienceComputer Science (R0)