Abstract
We show that a slightly extended version of asynchronous cellular automata, relative to any class of pomsets and dags without autoconcurrency, has the same expressive power as the existential fragment of monadic second-order logic. In doing so, we provide a framework that unifies many approaches to modeling distributed systems such as the models of asynchronous trace automata and communicating finite-state machines. As a byproduct, we exhibit classes of pomsets and dags for which the radius of graph acceptors can be reduced to 1.
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
Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. In: Proceedings of LICS 1993. IEEE Computer Society Press, Los Alamitos (1993)
Bollig, B., Leucker, M.: Message-Passing Automata are expressively equivalent to EMSO Logic. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 146–160. Springer, Heidelberg (2004)
Brand, D., Zafiropulo, P.: On communicating finite-state machines. Journal of the ACM 30(2) (1983)
Cécé, G., Finkel, A., Purushothaman Iyer, S.: Unreliable channels are easier to verify than perfect channels. Information and Computation 124(1) (1996)
Diekert, V., Rozenberg, G. (eds.): The Book of Traces. World Scientific, Singapore (1995)
Droste, M., Gastin, P., Kuske, D.: Asynchronous cellular automata for pomsets. Theoretical Computer Science 247(1-2) (2000)
Finkel, A.: Decidability of the termination problem for completely specified protocols. Distributed Computing 7(3) (1994)
Genest, B., Muscholl, A., Kuske, D.: A Kleene theorem for a class of communicating automata with effective algorithms. In: Calude, C.S., Calude, E., Dinneen, M.J. (eds.) DLT 2004. LNCS, vol. 3340, pp. 30–48. Springer, Heidelberg (2004)
Hanf, W.P.: Model-theoretic methods in the study of elementary logic. In: The Theory of Models. North-Holland, Amsterdam (1965)
Henriksen, J.G., Mukund, M., Narayan Kumar, K., Thiagarajan, P.S.: Regular collections of message sequence charts. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, p. 405. Springer, Heidelberg (2000)
Kuske, D.: Emptiness is decidable for asynchronous cellular machines. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, p. 536. Springer, Heidelberg (2000)
Matz, O., Schweikardt, N., Thomas, W.: The monadic quantifier alternation hierarchy over grids and graphs. Information and Computation 179(2) (2002)
Potthoff, A., Seibert, S., Thomas, W.: Nondeterminism versus determinism of finite automata over directed acyclic graphs. Bulletin of the Belgian Mathematical Society 1 (1994)
Thomas, W.: On Logics, Tilings, and Automata. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510. Springer, Heidelberg (1991)
Thomas, W.: Elements of an automata theory over partial orders. In: Proceedings of POMIV 1996. DIMACS, vol. 29, AMS (1996)
Thomas, W.: Automata theory on trees and partial orders. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214. Springer, Heidelberg (1997)
Wiesław Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. — Informatique Théorique et Applications, 21 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bollig, B. (2005). On the Expressiveness of Asynchronous Cellular Automata. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_46
Download citation
DOI: https://doi.org/10.1007/11537311_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28193-1
Online ISBN: 978-3-540-31873-6
eBook Packages: Computer ScienceComputer Science (R0)