Abstract
In a previous publication, we enumerated all stuttering-insensitive linear-time (in a well-defined sense) congruences with respect to action prefix, hiding, relational renaming, and parallel composition for finite labelled transition systems. There are 20 of them. They are built from the alphabet, traces, two kinds of divergence traces, and five kinds of failures. Now we remove the finiteness assumption. To re-establish the congruence property, four kinds of infinite traces are needed. Some congruences split to two and some to three, yielding altogether 40 congruences. Like its predecessor, because of lack of space, also this publication concentrates on proving the absence of more congruences.
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.
Similar content being viewed by others
References
De Nicola, R., Vaandrager, F.: Three Logics for Branching Bisimulation. Journal of the ACM 42(2), 458–487 (1995)
Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)
Kaivola, R., Valmari, A.: The Weakest Compositional Semantic Equivalence Preserving Nexttime-less Linear Temporal Logic. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 207–221. Springer, Heidelberg (1992)
Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer, Heidelberg (1992)
Puhakka, A.: Weakest Congruence Results Concerning “Any-Lock”. In: Kobayashi, N., Pierce, B.C. (eds.) TACS 2001. LNCS, vol. 2215, pp. 400–419. Springer, Heidelberg (2001)
Puhakka, A., Valmari, A.: Weakest-Congruence Results for Livelock-Preserving Equivalences. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 510–524. Springer, Heidelberg (1999)
Roscoe, A.W.: Understanding Concurrent Systems. Springer, Heidelberg (2010)
Valmari, A.: The Weakest Deadlock-Preserving Congruence. Information Processing Letters 53(6), 341–346 (1995)
Valmari, A.: All Linear-Time Congruences for Finite LTSs and Familiar Operators. In: Brandt, J., Heljanko, K. (eds.) 12th Int. Conf. on Application of Concurrency to System Design, pp. 12–21. IEEE, USA (2012)
Valmari, A., Tienari, M.: Compositional Failure-Based Semantic Models for Basic LOTOS. Formal Aspects of Computing 7(4), 440–468 (1995)
van Glabbeek, R.J.: The Coarsest Precongruences Respecting Safety and Liveness Properties. In: Calude, C.S., Sassone, V. (eds.) TCS 2010. IFIP AICT, vol. 323, pp. 32–52. Springer, Heidelberg (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Valmari, A. (2012). All Linear-Time Congruences for Familiar Operators Part 2: Infinite LTSs. In: Koutny, M., Ulidowski, I. (eds) CONCUR 2012 – Concurrency Theory. CONCUR 2012. Lecture Notes in Computer Science, vol 7454. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32940-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-32940-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32939-5
Online ISBN: 978-3-642-32940-1
eBook Packages: Computer ScienceComputer Science (R0)