Skip to main content Accessibility help
×
Home

Breaking symmetries

  • KIRSTIN PETERS (a1) and UWE NESTMANN (a1)

Abstract

A well-known result by Palamidessi tells us that πmix (the π-calculus with mixed choice) is more expressive than πsep (its subset with only separate choice). The proof of this result analyses their different expressive power concerning leader election in symmetric networks. Later on, Gorla offered an arguably simpler proof that, instead of leader election in symmetric networks, employed the reducibility of ‘incestual’ processes (mixed choices that include both enabled senders and receivers for the same channel) when running two copies in parallel. In both proofs, the role of breaking (initial) symmetries is more or less apparent. In this paper, we shed more light on this role by re-proving the above result – based on a proper formalization of what it means to break symmetries – without referring to another problem domain like leader election.

Both Palamidessi and Gorla rephrased their results by stating that there is no uniform and reasonable encoding from πmix into πsep. We indicate how their proofs can be adapted and exhibit the consequences of varying notions of uniformity and reasonableness. In each case, the ability to break initial symmetries turns out to be essential. Moreover, by abandoning the uniformity criterion, we show that there indeed is a reasonable encoding. We emphasize its underlying principle, which highlights the difference between breaking symmetries locally instead of globally.

Copyright

Footnotes

Hide All

Supported by the DFG (German Research Foundation), grant NE-1505/2-1.

Footnotes

References

Hide All
Baldamus, M., Parrow, J. and Victor, B. (2005) A fully abstract encoding of the i-calculus with data terms. In: Proceedings of ICALP. Springer Lecture Notes in Computer Science 3580 12021213.
Bernstein, A. (1980) Output guards and nondeterminism in ‘communicating sequential processes’. ACM Transactions on Programming Languages and Systems 2 (2) 234238.
Boer, F. S. and Palamidessi, C. (1991) Embedding as a tool for Language Comparison: On the CSP hierarchy. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 527 127141.
Boreale, M. and Sangiorgi, D. (1998) A fully abstract semantics for causality in the π-calculus. Acta Informatica 35 (5) 353400.
Boudol, G. (1992) Asynchrony and the π-calculus (note). Note, INRIA.
Bougé, L. (1988) On the existence of symmetric algorithms to find leaders in networks of communicating sequential processes. Acta Informatica 25 (4) 179201.
Buckley, G. and Silberschatz, A. (1983) An effective implementation for the generalized input-output construct of CSP. ACM Transactions on Programming Languages and Systems 5 (2) 223235.
Bugliesi, M. and Giunti, M. (2007) Secure implementations of typed channel abstractions. In: Proceedings of POPL. SIGPLAN-SIGACT 42, ACM 251262.
Busi, N., Gorrieri, R. and Zavattaro, G. (2000) On the expressiveness of linda coordination primitives. Information and Compututation 156 (1–2) 90121.
Carbone, M. and Maffeis, S. (2003) On the expressive power of polyadic synchronisation in π-calculus. Nordic Journal of Computing 10 (2) 7098.
Charron-Bost, B., Mattern, F. and Tel, G. (1996) Synchronous, asynchronous, and causally ordered communication. Distributed Computing 9 (4) 173191.
Fu, Y. and Lu, H. (2010) On the expressiveness of interaction. Theoretical Computer Science 411 (11–13) 13871451.
Gorla, D. (2008a) Comparing communication primitives via their relative expressive power. Information and Computation 206 (8) 931952.
Gorla, D. (2008b) Towards a unified approach to encodability and separation results for process calculi, Technical Report, Dip. di Informatica, Univ. di Roma ‘La Sapienza’, 2008. (An extended abstract appeared in the Proceedings of CONCUR'08. Springer Lecture Notes in Computer Science 5201 492–507.)
Gorla, D. (2010) Towards a unified approach to encodability and separation results for process calculi. Information and Computation 208 (9) 10311053.
Hoare, C. A. R. (1978) Communicating sequential processes. Communications of the ACM 21 (8) 666677.
Herescu, O. M. and Palamidessi, C. (2002) A randomized distributed encoding of the pi-calculus with mixed choice. In: Baeza-Yates, R. A., Montanari, U. and Santoro, N. (eds.) IFIP TCS. IFIP Conference Proceedings, Kluwer 537549.
Honda, K. and Tokoro, M. (1991) An object calculus for asynchronous communication. In: Proceedings of ECOOP. Springer Lecture Notes in Computer Science 512 133147.
Johnson, R. E. and Schneider, F. B. (1985) Symmetry and similarity in distributed systems. In: Proceedings of PODC, ACM 1322.
Knabe, F. (1993) A distributed protocol for channel-based communication with choice. Computers and Artificial Intelligence 12 (5) 475490.
Kieburtz, R. and Silberschatz, A. (1979) Comments on ‘communicating sequential processes’. ACM Transactions on Programming Languages and Systems 1 (2) 218225.
Kumar, D. and Silberschatz, A. (1997) A counter-example to an algorithm for the generalized input-output construct of CSP. Information Processing Letters 61 287.
Lipton, R., Snyder, L. and Zalcstein, Y. (1974) A comparative study of models of parallel computation. In: 15th Annual Symposium on Switching and Automata Theory, New Orleans 145–155.
Milner, R., Parrow, J. and Walker, D. (1992) A calculus of mobile processes, part I and II. Information and Computation 100 (1) 177.
Milner, R. and Sangiorgi, S. (1992) Barbed sisimulation. In: Proceedings of ICALP. Springer Lecture Notes in Computer Science 623 685695.
Nestmann, U. (2000) What is a ‘Good’ encoding of guarded choice? Information and Computation 156 (1–2) 287319.
Nestmann, U. (2006) Welcome to jungle: A subjective guide to mobile process calculi. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 4137 5263.
Nestmann, U. and Pierce, B. C. (2000) Decoding choice encodings. Information and Computation 163 (1) 159.
Palamidessi, C. (2003) Comparing the expressive power of the synchronous and the asynchronous π-calculi. Mathematical Structures in Computer Science 13 (5) 685719.
Parrow, J. (2008) Expressiveness of process algebras. Electronic Notes in Theoretical Computer Science 209 173186.
Peters, K. and Nestmann, U. (2010) Breaking symmetries. In: Proceedings of EXPRESS. Electronic Proceedings in Theoretical Computer Science 41 136150.
Peters, K. and Nestmann, U. (2012a) Is it a ‘Good’ encoding of mixed choice? In: Proceedings of FoSSaCS. Lecture Notes in Computer Science 7213 210224.
Peters, K and Nestmann, U. (2012b) Is it a ‘Good’ encoding of mixed choice? Technical Report, TU Berlin, Germany. http://arxiv.org/corr/home.
Peters, K., Schicke-Uffmann, J.-W. and Nestmann, U. (2011) Synchrony versus causality in the asynchronous Pi-calculus. In: Proceedings of EXPRESS. Electronic Notes in Theoretical Computer Science 64 89103.
Priami, C. (1996) Enhanced Operational Semantics for Concurrency, Ph.D. thesis, Università di Pisa-Genova-Udine.
Sangiorgi, D. and Walker, D. (2001) The π-Calculus: A Theory of Mobile Processes, Cambridge University Press New York, NY, USA.
Shapiro, E. (1989) The family of concurrent logic programming languages. ACM Computing Surveys (CSUR) 21 (3) 413510.
Shapiro, E. (1991) Separating concurrent languages with categories of language embeddings. In: Proceedings of STOC, ACM 198208.
Shapiro, E. (1992) Embeddings among concurrent programming languages. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 630 486503.
van de Snepshout, J. (1981) Synchronous communication between asynchronous components. Information Processing Letters 13 (3) 127130.
van Glabbeek, R. J. (1993) The linear time - branching time spectrum II. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 715 6681.
van Glabbeek, R. J. (2001) The linear time – branching time spectrum I: The semantics of concrete, sequential processes. In: Bergstra, J. A., Ponse, A. and Smolka, S. A. (eds.) Handbook of Process Algebra, Elseveier Science B.V. 399.
Vigliotti, M. G., Phillips, I. and Palamidessi, C. (2007) Tutorial on separation results in process calculi via leader election problems. Theoretical Computer Science 388 (1–3) 267289.

Related content

Powered by UNSILO

Breaking symmetries

  • KIRSTIN PETERS (a1) and UWE NESTMANN (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.