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Breaking symmetries†

Published online by Cambridge University Press:  12 November 2014

KIRSTIN PETERS  and
UWE NESTMANN
KIRSTIN PETERS
Affiliation:
Technische Universität Berlin, Germany Email: kirstin.peters@tu-berlin.de, uwe.nestmann@tu-berlin.de
UWE NESTMANN
Affiliation:
Technische Universität Berlin, Germany Email: kirstin.peters@tu-berlin.de, uwe.nestmann@tu-berlin.de
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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.

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 26 , Special Issue 6: Special Issue: Express'10 , September 2016 , pp. 1054 - 1106
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

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

References

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 1202–1213.Google Scholar
Bernstein, A. (1980) Output guards and nondeterminism in ‘communicating sequential processes’. ACM Transactions on Programming Languages and Systems 2 (2) 234–238.Google Scholar
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 527 127–141.Google Scholar
Boreale, M. and Sangiorgi, D. (1998) A fully abstract semantics for causality in the π-calculus. Acta Informatica 35 (5) 353–400.Google Scholar
Boudol, G. (1992) Asynchrony and the π-calculus (note). Note, INRIA.Google Scholar
Bougé, L. (1988) On the existence of symmetric algorithms to find leaders in networks of communicating sequential processes. Acta Informatica 25 (4) 179–201.Google Scholar
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) 223–235.Google Scholar
Bugliesi, M. and Giunti, M. (2007) Secure implementations of typed channel abstractions. In: Proceedings of POPL. SIGPLAN-SIGACT 42, ACM 251–262.Google Scholar
Busi, N., Gorrieri, R. and Zavattaro, G. (2000) On the expressiveness of linda coordination primitives. Information and Compututation 156 (1–2) 90–121.Google Scholar
Carbone, M. and Maffeis, S. (2003) On the expressive power of polyadic synchronisation in π-calculus. Nordic Journal of Computing 10 (2) 70–98.Google Scholar
Charron-Bost, B., Mattern, F. and Tel, G. (1996) Synchronous, asynchronous, and causally ordered communication. Distributed Computing 9 (4) 173–191.Google Scholar
Fu, Y. and Lu, H. (2010) On the expressiveness of interaction. Theoretical Computer Science 411 (11–13) 1387–1451.Google Scholar
Gorla, D. (2008a) Comparing communication primitives via their relative expressive power. Information and Computation 206 (8) 931–952.Google Scholar
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.)Google Scholar
Gorla, D. (2010) Towards a unified approach to encodability and separation results for process calculi. Information and Computation 208 (9) 1031–1053.Google Scholar
Hoare, C. A. R. (1978) Communicating sequential processes. Communications of the ACM 21 (8) 666–677.Google Scholar
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 537–549.Google Scholar
Honda, K. and Tokoro, M. (1991) An object calculus for asynchronous communication. In: Proceedings of ECOOP. Springer Lecture Notes in Computer Science 512 133–147.CrossRefGoogle Scholar
Johnson, R. E. and Schneider, F. B. (1985) Symmetry and similarity in distributed systems. In: Proceedings of PODC, ACM 13–22.Google Scholar
Knabe, F. (1993) A distributed protocol for channel-based communication with choice. Computers and Artificial Intelligence 12 (5) 475–490.Google Scholar
Kieburtz, R. and Silberschatz, A. (1979) Comments on ‘communicating sequential processes’. ACM Transactions on Programming Languages and Systems 1 (2) 218–225.Google Scholar
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.Google Scholar
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.Google Scholar
Milner, R., Parrow, J. and Walker, D. (1992) A calculus of mobile processes, part I and II. Information and Computation 100 (1) 1–77.Google Scholar
Milner, R. and Sangiorgi, S. (1992) Barbed sisimulation. In: Proceedings of ICALP. Springer Lecture Notes in Computer Science 623 685–695.Google Scholar
Nestmann, U. (2000) What is a ‘Good’ encoding of guarded choice? Information and Computation 156 (1–2) 287–319.Google Scholar
Nestmann, U. (2006) Welcome to jungle: A subjective guide to mobile process calculi. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 4137 52–63.Google Scholar
Nestmann, U. and Pierce, B. C. (2000) Decoding choice encodings. Information and Computation 163 (1) 1–59.Google Scholar
Palamidessi, C. (2003) Comparing the expressive power of the synchronous and the asynchronous π-calculi. Mathematical Structures in Computer Science 13 (5) 685–719.CrossRefGoogle Scholar
Parrow, J. (2008) Expressiveness of process algebras. Electronic Notes in Theoretical Computer Science 209 173–186.CrossRefGoogle Scholar
Peters, K. and Nestmann, U. (2010) Breaking symmetries. In: Proceedings of EXPRESS. Electronic Proceedings in Theoretical Computer Science 41 136–150.Google Scholar
Peters, K. and Nestmann, U. (2012a) Is it a ‘Good’ encoding of mixed choice? In: Proceedings of FoSSaCS. Lecture Notes in Computer Science 7213 210–224.Google Scholar
Peters, K and Nestmann, U. (2012b) Is it a ‘Good’ encoding of mixed choice? Technical Report, TU Berlin, Germany. http://arxiv.org/corr/home.Google Scholar
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 89–103.Google Scholar
Priami, C. (1996) Enhanced Operational Semantics for Concurrency, Ph.D. thesis, Università di Pisa-Genova-Udine.Google Scholar
Sangiorgi, D. and Walker, D. (2001) The π-Calculus: A Theory of Mobile Processes, Cambridge University Press New York, NY, USA.Google Scholar
Shapiro, E. (1989) The family of concurrent logic programming languages. ACM Computing Surveys (CSUR) 21 (3) 413–510.Google Scholar
Shapiro, E. (1991) Separating concurrent languages with categories of language embeddings. In: Proceedings of STOC, ACM 198–208.Google Scholar
Shapiro, E. (1992) Embeddings among concurrent programming languages. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 630 486–503.Google Scholar
van de Snepshout, J. (1981) Synchronous communication between asynchronous components. Information Processing Letters 13 (3) 127–130.Google Scholar
van Glabbeek, R. J. (1993) The linear time - branching time spectrum II. In: Proceedings of CONCUR. Springer Lecture Notes in Computer Science 715 66–81.Google Scholar
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. 3–99.CrossRefGoogle Scholar
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) 267–289.CrossRefGoogle Scholar