Abstract
We present a study of the notion of coalgebraic simulation introduced by Hughes and Jacobs. Although in their original paper they allow any functorial order in their definition of coalgebraic simulation, for the simulation relations to have good properties they focus their attention on functors with orders which are strongly stable. This guarantees a so-called “composition-preserving” property from which all the desired good properties follow. We have noticed that the notion of strong stability not only ensures such good properties but also “distinguishes the direction” of the simulation. For example, the classic notion of simulation for labeled transition systems, the relation “p is simulated by q”, can be defined as a coalgebraic simulation relation by means of a strongly stable order, whereas the opposite relation, “p simulates q”, cannot. Our study was motivated by some interesting classes of simulations that illustrate the application of these results: covariant-contravariant simulations and conformance simulations.
Research supported by the Spanish projects DESAFIOS TIN2006-15660-C02-01, WEST TIN2006-15578-C02-01, PROMESAS S-0505/TIC/0407 and UCM-BSCH GR58/08/910606.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aczel, P., Mendler, N.P.: 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)
Bloom, B., Istrail, S., Meyer, A.R.: Bisimulation can’t be traced. J. ACM 42(1), 232–268 (1995)
de Frutos-Escrig, D., Gregorio-Rodríguez, C.: Universal coinductive characterisations of process semantics. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, C.-H.L. (eds.) IFIP TCS. IFIP, vol. 273, pp. 397–412. Springer, Heidelberg (2008)
de Frutos Escrig, D., Gregorio-Rodríguez, C., Palomino, M.: On the unification of semantics for processes: observational semantics. In: Nielsen, M., Kucera, A., Miltersen, P.B., Palamidessi, C., Tuma, P., Valencia, F.D. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 279–290. Springer, Heidelberg (2009)
Groote, J.F., Vaandrager, F.W.: Structured operational semantics and bisimulation as a congruence. Inf. Comput. 100(2), 202–260 (1992)
Hughes, J., Jacobs, B.: Simulations in coalgebra. TCS 327(1-2), 71–108 (2004)
Jacobs, B., Hughes, J.: Simulations in coalgebra. In: Gumm, H.P. (ed.) CMCS 2003: 6th International Workshop on Coalgebraic Methods in Computer Science, vol. 82 (2003)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)
Leduc, G.: A framework based on implementation relations for implementing LOTOS specifications. Computer Networks and ISDN Systems 25(1), 23–41 (1992)
Lynch, N.A., Tuttle, M.R.: Hierarchical correctness proofs for distributed algorithms. In: Sixth Annual ACM Symposium on Principles of Distributed Computing, pp. 137–151 (1987)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
Tretmans, J.: Conformance testing with labelled transition systems: Implementation relations and test generation. Computer Networks and ISDN Systems 29(1), 49–79 (1996)
van Glabbeek, R.J.: The linear time-branching time spectrum I: The semantics of concrete, sequential processes. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of process algebra, pp. 3–99 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fábregas, I., de Frutos Escrig, D., Palomino, M. (2009). Non-strongly Stable Orders Also Define Interesting Simulation Relations. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-03741-2_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03740-5
Online ISBN: 978-3-642-03741-2
eBook Packages: Computer ScienceComputer Science (R0)