Abstract
This paper shows that the \(\pi \)-calculus with implicit matching is no more expressive than \(\mathrm {CCS}_{\gamma }\), a variant of CCS in which the result of a synchronisation of two actions is itself an action subject to relabelling or restriction, rather than the silent action \(\tau \). This is done by exhibiting a compositional translation from the \(\pi \)-calculus with implicit matching to \(\mathrm {CCS}_{\gamma }\) that is valid up to strong barbed bisimilarity.
The full \(\pi \)-calculus can be similarly expressed in \(\mathrm {CCS}_{\gamma }\) enriched with the triggering operation of Meije.
I also show that these results cannot be recreated with CCS in the rĂ´le of \(\mathrm {CCS}_{\gamma }\), not even up to reduction equivalence, and not even for the asynchronous \(\pi \)-calculus without restriction or replication.
Finally I observe that CCS cannot be encoded in the \(\pi \)-calculus.
Chapter PDF
Similar content being viewed by others
References
Austry, D., Boudol, G.: Algèbre de processus et synchronisations. TCS 30(1), 91–131 (1984). https://doi.org/10.1016/0304-3975(84)90067-7
Baeten, J.C.M., Weijland, W.P.: Process Algebra. Cambridge Tracts in Theoretical Computer Science 18, Cambridge University Press (1990). https://doi.org/10.1017/CBO9780511624193
Banach, R., van Breugel, F.: Mobility and modularity: expressing \(\pi \)-calculus in CCS. Preprint (1998), http://www.cs.man.ac.uk/~banach/some.pubs/Pi.CCS.ext.abs.pdf
Bergstra, J.A., Klop, J.W.: Algebra of communicating processes. In: Mathematics and Computer Science, pp. 89–138. CWI Monograph 1, North-Holland (1986)
Boudol, G.: Asynchrony and the \(\pi \)-calculus (note). Tech. Rep. 1702, INRIA (1992)
Brookes, S.D., Hoare, C.A.R., Roscoe, A.W.: A theory of communicating sequential processes. J. ACM 31(3), 560–599 (1984). https://doi.org/10.1145/828.833
Ferrari, G.L., Montanari, U., Quaglia, P.: A pi-calculus with explicit substitutions. Theoretical Computer Science 168(1), 53–103 (1996). https://doi.org/10.1016/S0304-3975(96)00063-1
Glabbeek, R.J. van: On the expressiveness of ACP (extended abstract). In: Proc. ACP’94. pp. 188–217. Workshops in Computing, Springer (1994). https://doi.org/10.1007/978-1-4471-2120-6_8
Glabbeek, R.J. van: On cool congruence formats for weak bisimulations. Theoretical Computer Science 412(28), 3283–3302 (2011). https://doi.org/10.1016/j.tcs.2011.02.036
Glabbeek, R.J. van: Musings on encodings and expressiveness. In: Proc. EXPRESS/SOS’12. EPTCS, vol. 89, pp. 81–98. Open Publishing Association (2012). https://doi.org/10.4204/EPTCS.89.7
Glabbeek, R.J. van: A theory of encodings and expressiveness. In: Proc. FoSSaCS’18. LNCS, vol. 10803, pp. 183–202. Springer (2018). https://doi.org/10.1007/978-3-319-89366-2_10
Glabbeek, R.J. van, Weijland, W.P.: Branching time and abstraction in bisimulation semantics. Journal of the ACM 43(3), 555–600 (1996). https://doi.org/10.1145/233551.233556
Gorla, D.: Towards a unified approach to encodability and separation results for process calculi. Information and Computation 208(9), 1031–1053 (2010). https://doi.org/10.1016/j.ic.2010.05.002
Gorla, D., Nestmann, U.: Full abstraction for expressiveness: history, myths and facts. Mathematical Structures in Computer Science 26(4), 639–654 (2016). https://doi.org/10.1017/S0960129514000279
Groote, J.F., Mousavi, M.R.: Modeling and Analysis of Communicating Systems. MIT Press (2014)
Hennessy, M., Lin, H.: Symbolic bisimulations. Theoretical Comp. Sc. 138(2), 353–389 (1995). https://doi.org/10.1016/0304-3975(94)00172-F
Luttik, B.: On the expressiveness of choice quantification. Ann. Pure Appl. Logic 121, 39–87 (2003). https://doi.org/10.1016/S0168-0072(02)00082-9
Milner, R.: Calculi for synchrony and asynchrony. Theoretical Comp. Sc. 25, 267–310 (1983). https://doi.org/10.1016/0304-3975(83)90114-7
Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)
Milner, R.: Operational and algebraic semantics of concurrent processes. In: Handbook of Theoretical Computer Science, chap. 19, pp. 1201–1242. Elsevier Science Publishers B.V. (North-Holland) (1990)
Milner, R.: Functions as processes. Mathematical Structures in Computer Science 2(2), 119–141 (1992). https://doi.org/10.1017/S0960129500001407
Milner, R.: Communicating and Mobile Systems: the \(\pi \)-Calculus. Cambridge University Press (1999)
Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, I. I&C 100, 1–40 (1992). https://doi.org/10.1016/0890-5401(92)90008-4
Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes, II. I&C 100, 41–77 (1992). https://doi.org/10.1016/0890-5401(92)90009-5
Milner, R., Parrow, J., Walker, D.: Modal logics for mobile processes. TCS 114, 149–171 (1993). https://doi.org/10.1016/0304-3975(93)90156-N
Milner, R., Sangiorgi, D.: Barbed bisimulation. In: Proc. ICALP’92. LNCS, vol. 623, pp. 685–695. Springer (1992). https://doi.org/10.1007/3-540-55719-9_114
Nestmann, U.: Welcome to the jungle: A subjective guide to mobile process calculi. In: Proc. CONCUR’06. LNCS, vol. 4137, pp. 52–63. Springer (2006). https://doi.org/10.1007/11817949_4
Palamidessi, C.: Comparing the expressive power of the synchronous and asynchronous pi-calculi. Mathematical Structures in Comp. Science 13(5), 685–719 (2003). https://doi.org/10.1017/S0960129503004043
Parrow, J.: General conditions for full abstraction. Math. Struct. in Comp. Sc. 26(4), 655–657 (2016). https://doi.org/10.1017/S0960129514000280
Peters, K., Nestmann, U., Goltz, U.: On distributability in process calculi. In: Proc. ESOP’13. LNCS, vol. 7792, pp. 310–329. Springer (2013). https://doi.org/10.1007/978-3-642-37036-6_18
Roscoe, A.W.: CSP is expressive enough for \(\pi \). In: Reflections on the Work of C.A.R. Hoare, pp. 371–404. Springer (2010). https://doi.org/10.1007/978-1-84882-912-1_16
Sangiorgi, D.: A theory of bisimulation for the pi-calculus. Acta Inf. 33(1), 69–97 (1996). https://doi.org/10.1007/s002360050036
Sangiorgi, D., Walker, D.: The \(\pi \)-calculus: A Theory of Mobile Processes. Cambridge University Press (2001)
Simone, R. de: Higher-level synchronising devices in Meije-SCCS. TCS 37, 245–267 (1985). https://doi.org/10.1016/0304-3975(85)90093-3
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2022 The Author(s)
About this paper
Cite this paper
van Glabbeek, R. (2022). Comparing the expressiveness of the \(\pi \)-calculus and CCS. In: Sergey, I. (eds) Programming Languages and Systems. ESOP 2022. Lecture Notes in Computer Science, vol 13240. Springer, Cham. https://doi.org/10.1007/978-3-030-99336-8_20
Download citation
DOI: https://doi.org/10.1007/978-3-030-99336-8_20
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-99335-1
Online ISBN: 978-3-030-99336-8
eBook Packages: Computer ScienceComputer Science (R0)