Skip to main content
×
×
Home

The true concurrency of differential interaction nets

  • DAMIANO MAZZA (a1)
Abstract

We analyse the reduction of differential interaction nets from the point of view of so-called ‘true concurrency,’ that is, employing a non-interleaving model of parallelism. More precisely, we associate with each differential interaction net an event structure describing its reduction. We show how differential interaction nets are only able to generate confusion-free event structures, and we argue that this is a serious limitation in terms of the concurrent behaviours they may express. In fact, confusion is an extremely elementary phenomenon in concurrency (for example, it already appears in CCS with just prefixing and parallel composition) and we show how its presence is preserved by any encoding respecting the degree of distribution and the reduction semantics. We thus infer that no reasonably expressive process calculus may be satisfactorily encoded in differential interaction nets. We conclude with an analysis of one such encoding proposed by Ehrhard and Laurent, and argue that it does not contradict our claims, but rather supports them.

Copyright
References
Hide All
Abramsky, S. (1993). Computational interpretations of linear logic. Theoretical Computer Science 111 (1–2) 357.
Abramsky, S. (1994). Proofs as processes. Theoretical Computer Science 135 (1) 59.
Alexiev, V. (1999). Non-deterministic Interaction Nets. Ph.D. Thesis, University of Alberta.
Baldan, P., Corradini, A., Montanari, U. and Ribeiro, L. (2007). Unfolding semantics of graph transformation. Information Computation 205 (5) 733782.
Bellin, G. and Scott, P.J. (1994). On the pi-calculus and linear logic. Theoretical Computer Science 135 (1) 1165.
Boldi, P., Cardone, F. and Sabadini, N. (1993). Concurrent automata, prime event structures and universal domains. In: Droste, M. and Gurevich, Y. (eds.) Semantics of Programming Languages and Model Theory, Algebra, Logic and Applications, vol. 5, Gordon and Breach, 89108.
Caires, L. and Pfenning, F. (2010). Session types as intuitionistic linear propositions. In: Gastin, P. and Laroussinie, F. (eds.) Proceedings of CONCUR 2010, Lecture Notes in Computer Science, vol. 6269, Springer, 222236.
Clark, D. and Kennaway, R. (1996). Event structures and non-orthogonal term graph rewriting. Mathematical Structures in Computer Science 6 (6) 545578.
Crafa, S., Varacca, D. and Yoshida, N. (2012). Event structure semantics of parallel extrusion in the pi-calculus. In: Birkedal, L. (ed.) Proceedings of FoSSaCS 2012, Lecture Notes in Computer Science, vol. 7213, Springer, 225239.
Dorman, A. (2013). Concurrency in Interaction Nets and Graph Rewriting. Ph.D. Thesis, Università degli Studi Roma Tre / Université Paris Nord-Sorbonne Paris Cité.
Ehrhard, T. (2005). Finiteness spaces. Mathematical Structures in Computer Science 15 (4) 615646.
Ehrhard, T. and Laurent, O. (2010a). Acyclic solos and differential interaction nets. Logical Methods in Computer Science 6 (3).
Ehrhard, T. and Laurent, O. (2010b). Interpreting a finitary Pi-calculus in differential interaction nets. Information and Computation 208 (6) 606633.
Ehrhard, T. and Regnier, L. (2006). Differential interaction nets. Theoretical Computer Science 364 (2) 166195.
Girard, J.-Y. (1987). Linear logic. Theoretical Computer Science 50 (1) 1102.
Girard, J.-Y. (1996). Proof-nets: The parallel syntax for proof-theory. In: Ursini and Agliano (eds.), Logic and Algebra. Marcel Dekker, Inc.
Gorla, D. (2010). Towards a unified approach to encodability and separation results for process calculi. Information and Computation 208 (9) 10311053.
Honda, K. and Laurent, O. (2010). An exact correspondence between a typed pi-calculus and polarised proof-nets. Theoretical Computer Science 411 (22–24) 22232238.
Khasidashvili, Z. and Glauert, J.R.W. (2005). The conflict-free reduction geometry. Theoretical Computer Science 347 (3) 465497.
Kobayashi, N., Pierce, B.C. and Turner, D.N. (1999). Linearity and the Pi-Calculus. ACM Transactions on Programming Languages and Systems 21 (5) 914947.
Lafont, Y. (1990). Interaction nets. In: Conference Record of POPL'90, ACM Press, 95108.
Lafont, Y. (1997). Interaction combinators. Information and Computation 137 (1) 69101.
Laneve, C., Parrow, J. and Victor, B. (2001). Solo diagrams. In: Kobayashi, N. and Pierce, B.C. (eds.) Proceedings of TACS 2001, Lecture Notes in Computer Science, vol. 2215, Springer, 127144.
Laneve, C. and Victor, B. (2003). Solos in concert. Mathematical Structures in Computer Science 13 (5) 657683.
Mazurkiewicz, A.W. (1986). Trace theory. In: Brauer, W., Reisig, W. and Rozenberg, G. (eds.) Advances in Petri Nets, Lecture Notes in Computer Science, vol. 255, Springer, 279324.
Mazza, D. (2005). Multiport interaction nets and concurrency. In: Abadi, M. and de Alfaro, L. (eds.) In: Proceedings of CONCUR 2005, Lecture Notes in Computer Science, Springer, 2135.
Mazza, D. (2006). Interaction nets: Semantics and concurrent extensions. Ph.D. Thesis, Université de la Méditerranée / Università degli Studi Roma Tre.
Melliès, P.-A. (2004). Asynchronous games 2: The true concurrency of innocence. Theoretical Computer Science 358 (2–3) 200228.
Mimram, S. (2008). Sémantique des jeux asynchrone et réécriture 2-dimensionelle. Ph.D. Thesis, Université Paris-Diderot (Paris 7).
Nielsen, M., Plotkin, G.D. and Winskel, G. (1981). Petri nets, event structures and domains, part I. Theoretical Computer Science 13 (1) 85108.
Parrow, J. (2008). Expressiveness of process algebras. Electronic Notes in Theoretical Computer Science 209 173186.
Parrow, J. and Sjodin, P. (1992). Multiway synchrinizaton verified with coupled simulation. In: Cleaveland, R. (ed.) Proceedings of CONCUR'92, Lecture Notes in Computer Science (LNCS), vol. 630, Springer, 518533.
Parrow, J. and Victor, B. (1998). The fusion calculus: Expressiveness and symmetry in mobile processes. In: Proceedings of LICS, IEEE Computer Society, 176185.
Rabinovitch, A. and Traktenbrot, B. (1988). Behaviour structures and nets. Fundamenta Informatica 11 (4) 357404.
Rozenberg, G. and Engelfriet, J. (1996). Elementary net systems. In: Dagstuhl Lectures on Petri Nets, Lecture Notes in Computer Science, vol. 1491, Springer, 12121.
Stark, E.W. (1989). Concurrent transition systems. Theoretical Computer Science 64 (3) 221269.
van Glabeek, R.J. and Goltz, U. (1989). Equivalence notions for concurrent systems and refinement of actions. In: Proceedings of MFCS 1989, Lecture Notes in Computer Science (LNCS), vol. 379, Springer-Verlag.
Varacca, D., Völzer, H. and Winskel, G. (2006). Probabilistic event structures and domains. Theoretical Computer Science 358 (2–3) 173199.
Winskel, G. (1982). Event structure semantics of CCS and related languages. In: Nielsen, M. and Schmidt, E.M. (eds.), Proceedings of ICALP 1982, Lecture Notes in Computer Science vol. 140, Springer, 561576.
Winskel, G. and Nielsen, M. (1995). Models for concurrency. In: Handbook of Logic in Computer Science, vol. 4, Oxford University Press.
Wischik, L. and Gardner, P. (2005). Explicit fusions. Theoretical Computer Science 340 (3) 606630.
Yoshida, N., Berger, M. and Honda, K. (2004). Strong normalisation in the pi-calculus. Information and Computation 191 (2) 145202.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

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