Abstract
The intention of the paper is to show the applicability of the general categorical framework of open maps to the setting of two models – higher dimensional automata (HDA) and timed higher dimensional automata (THDA) – in order to transfer general concepts of equivalences to the models. First, we define categories of the models under consideration, whose morphisms are to be thought of as simulations. Then, accompanying (sub)categories of observations are chosen relative to which the corresponding notions of open maps are developed. Finally, we use the open maps framework to obtain two abstract bisimulations which are established to coincide with hereditary history preserving bisimulations on HDA and THDA, respectively.
This work is supported in part by the DFG-RFBR (grant No 436 RUS 113/1002/01, 09-01-91334).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bednarczyk, M.A.: Hereditory history preserving bisimulation or what is the power of the future perfect in program logics. Technical Report, Polish Academy of Science (1991)
Cridlig, R.: Implementing a static analyzer of concurrent programs: Problems and perspectives. In: Dam, M. (ed.) LOMAPS-WS 1996. LNCS, vol. 1192, pp. 244–259. Springer, Heidelberg (1997)
Fajstrup, L., Goubault, E., Raussen, M.: Detecting deadlocks in concurrent systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 332–347. Springer, Heidelberg (1998)
Fahrenberg, U.: A Category of Higher-Dimensional Automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 187–201. Springer, Heidelberg (2005)
Fiore, M., Cattani, G.L., Winskel, G.: Weak bisimulation and open maps. In: 14th Annual IEEE Symposium on Logic in Computer Science, pp. 214–225. IEEE Computer Society Press, Washington (1999)
van Glabbeek, R.J.: Bisimulation semantics for higher dimensional automata, http://theory.stanford.edu/~rvg/hda
van Glabbeek, R.J.: On the Expressiveness of higher dimensional automata. Theor. Comput. Sci. 356(3), 265–290 (2006)
Goubault, E.: Domains of higher-dimensional automata. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 293–307. Springer, Heidelberg (1993)
Goubault, E.: The Geometry of Concurrency. Ph.D. thesis. Ecole Normale Superieure, Paris (1995)
Goubault, E.: A semantic view on distributed computability and complexity. In: 3rd Theory and Formal Methods Section Workshop. Imperial College Press, London (1996)
Goubault, E., Jensen, T.P.: Homology of higher-dimensional automata. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 254–268. Springer, Heidelberg (1992)
Herlihy, M., Shavit, N.: A simple constructive computability theorem for wait-free computation. In: 26th Annual ACM Symposium on Theory of Computing, pp. 243–252. ACM Press, New York (1994)
Herlihy, M., Rajsbaum, S.: New perspectives in distributed computing. In: Kutyłowski, M., Wierzbicki, T., Pacholski, L. (eds.) MFCS 1999. LNCS, vol. 1672, pp. 170–186. Springer, Heidelberg (1999)
Hune, T., Nielsen, M.: Timed bisimulation and open maps. In: Brim, L., Gruska, J., Zlatuška, J. (eds.) MFCS 1998. LNCS, vol. 1450, pp. 378–387. Springer, Heidelberg (1998)
Joyal, A., Nielsen, M., Winskel, G.: Bisimulation from open maps. Inform. Comput. 127(2), 164–185 (1996)
MacLane, S.: Categories for the working mathematician. Springer, New York (1998)
Milner, R.: Communication and concurrency. Prentice-Hall, Upper Saddle River (1989)
Nielsen, M., Cheng, A.: Observing behaviour categorically. In: Thiagarajan, P.S. (ed.) FST&TCS 1995. LNCS, vol. 1026, pp. 263–278. Springer, Heidelberg (1995)
Nielsen, M., Winskel, G.: Petri nets and bisimulation. Theor. Comput. Sci. 153(1-2), 211–244 (1996)
Oshevskaya, E.S.: A categorical account of bisimulation for timed higher dimensional automata. In: 15th International Workshop on Concurrency, Specification and Programming, pp. 174–185. Humboldt-Universitaet zu Berlin, Berlin (2006)
Oshevskaya, E.S.: Open Maps Bisimulations for Higher Dimensional Automata Models, http://www.iis.nsk.su/virb/osh09.zip
Pratt, V.R.: Modeling concurrency with geometry. In: 18th Annual ACM Symposium on Principles of Programming Languages, pp. 311–322. ACM Press, New York (1991)
Rutten, J.J.M.M.: Universal coalgebra: a theory of systems. Theor. Comput. Sci. 249, 3–80 (2000)
Sassone, V., Cattani, G.L.: Higher-dimensional transition systems. In: 11th Annual IEEE Symposium on Logic in Computer Science, pp. 55–62. IEEE Computer Society Press, Los Alamitos (1996)
Sharpe, R.W.: Differential Geometry. Springer, New York (1997)
Virbitskaite, I.B., Gribovskaya, N.S.: Open maps and observational equivalences for timed partial order models. Fundam. Inform. 60(1-4), 383–399 (2004)
Winskel, G., Nielsen, M.: Models for concurrency. In: Handbook of Logic in Computer Science, vol. 4, pp. 1–148. Oxford University Press, London (1995)
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
Oshevskaya, E.S. (2009). Open Maps Bisimulations for Higher Dimensional Automata Models. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds) Fundamentals of Computation Theory. FCT 2009. Lecture Notes in Computer Science, vol 5699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03409-1_25
Download citation
DOI: https://doi.org/10.1007/978-3-642-03409-1_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03408-4
Online ISBN: 978-3-642-03409-1
eBook Packages: Computer ScienceComputer Science (R0)