Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We describe an approach to modeling the dynamics of distributed systems. By distributed systems we mean systems consisting of concurrent processes communicating via shared ports and posing certain synchronization requirements, via the ports, to the adjacent processes. The basic idea is to use graphs to represent states of such systems, and graph rewriting to represent their evolution. The kind of graph rewriting we use is based on simple context-free productions which are, however, combined by means of a synchronization mechanism. This allows for a good level of expressivity in the system without sacrifying full distribution. To formally model this kind of graph rewriting, however, we do not adopt the classical graph rewriting style but a more general framework, called the tile model, which allows for a clear separation between sequential rewriting and synchronization. Then, since the problem of satisfying the synchronization requirements may be a complex combinatorial problem, we suggest exploiting existing techniques for constraint solving. This is based on the observation that the synchronization problem can be modeled as a (finite domain) constraint problem. In this respect, we propose to use both local consistency techniques, to remove the possible redundancies in a system state, and a distributed backtracking search algorithm, as used in distributed constraint solving. Our method has the following advantages: first, it provides a formal description of the way a distributed system evolves; second, it seems promising from the performance point of view, since the techniques we propose for combining productions have been proved to be very convenient in several cases; finally, the kind of system evolution we describe here is just a particular instance of what can be described by using the tile model in its most general form, thus suggesting the possibility of extending our approach to modeling more complex distributed systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Barendregt, H. P., van Eekelrn, M. C. J. D., Glauert, J. R. W., Kennaway, J. R., Plasmeijer, M. J., and Sleep, M. R.: Term graph reduction, in Proc. PARLE, Lecture Notes in Comput. Sci. 259, Springer-Verlag, Berlin, 1987, pp. 141-158.

    Google Scholar 

  2. Boehm, P., Fonio, H.-R., and Habel, A.: Amalgamation of graph transformations: A synchronization mechanism, J. Comput. System Sci. 34(2/3) (1987), 377-408.

    Google Scholar 

  3. Bruni, R. and Montanari, U.: Zero-safe nets, or transition synchronization made simple, in C. Palamidessi and J. Parrow (eds.), Proc. EXPRESS'97, Electron. Notes Theor. Comput. Sci., Vol. 7, http://www.elsevier.nl/locate/entcs/volume7.html.

  4. Bruni, R. and Montanari, U.: Zero-safe nets: The individual token approach, in F. Parisi-Presicce (ed.), Proc. 12th WADT Workshop on Algebraic Development Techniques, Lecture Notes in Comput. Sci. 1376, Springer-Verlag, Berlin, 1998, pp. 122-140.

    Google Scholar 

  5. Ciancarini, P. and Hankin, C. (eds.): Coordination Languages and Models, Proceedings, Lecture Notes in Comput. Sci. 1061, Springer-Verlag, Berlin, 1996.

    Google Scholar 

  6. Corradini, A., Degano, P., and Montanari, U.: Specifying highly concurrent data structure manipulation, in G. Bucci and G. Valle (eds.), Computing 85: A Broad Perspective of Current Developments, Elsevier, Amsterdam, 1985.

    Google Scholar 

  7. Corradini, A. and Gadducci, F.: An algebraic presentation of term graphs via Gs-monoidal categories, Appl. Categorical Structures, to appear. Available at http://www.di.unipi.it/ gadducci/papers/aptg.ps, 1997.

  8. Corradini, A. and Gadducci, F.: A 2-categorical presentation of term graph rewriting, in Proc. CTCS'97, Lecture Notes in Comput. Sci. 1290, 1997.

  9. Corradini, A. and Montanari, U. (eds.): Proc. SEGRAGRA95 (Joint COMPUGRAPH/SEMAGRAPH Workshop on Graph Rewriting and Computation), Electron. Notes Theor. Comput. Sci., Elsevier, Amsterdam, 1995.

    Google Scholar 

  10. Dechter, R.: From local to global consistency, Artif. Intell. 55 (1992), 87-107.

    Google Scholar 

  11. Degano, P. and Montanari, U.: A model for distributed systems based on graph rewritings, J. ACM 34(2) (1987).

  12. Dechter, R. and Pearl, J.: Network-based heuristics for constraint-satisfaction problems, in Kanal and Kumar (eds.), Search in Artificial Intelligence, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  13. Ehresmann, C.: Catégories structurées: I and II, Ann. Éc. Norm. Sup. 80, Paris (1963), 349-426; III, Topo. et Géo. Diff. V, Paris (1963).

    Google Scholar 

  14. Ehrig, H.: Introduction to the algebraic theory of graph grammars, in Proc. International Workshop on Graph Grammars, Lecture Notes in Comput. Sci. 73, Springer-Verlag, Berlin, 1978.

    Google Scholar 

  15. Ehrig, H.: Tutorial introduction to the algebraic theory of graph grammars, in Proc. 3rd International Workshop on Graph Grammars, Lecture Notes in Comput. Sci. 291, Springer-Verlag, Berlin, 1987.

    Google Scholar 

  16. Ferrari, G. and Montanari, U.: A Tile-based coordination view of π-calculus, in I. Prívara and P. Ruzicka (eds.), Mathematical Foundations of Computer Science 1997, Lecture Notes in Comput. Sci. 1295, Springer-Verlag, Berlin, 1997, pp. 52-70.

    Google Scholar 

  17. Ferrari, G. and Montanari, U.: Tiles for concurrent and located calculi, in C. Palamidessi and J. Parrow (eds.), Proc. EXPRESS'97, Electron. Notes Theor. Comput. Sci., Vol. 7, http://www.elsevier.nl/locate/entcs/volume7.html.

  18. Ferrari, G. and Montanari, U.: Tile formats for located and mobile systems, Inform. and Comput., to appear.

  19. Freuder, E.: Synthesizing constraint expressions, Comm. ACM 21(11) (1978).

  20. Freuder, E.: Backtrack-free and backtrack-bounded search, in Kanal and Kumar (eds.), Search in Artificial Intelligence, Springer-Verlag, Berlin, 1988.

    Google Scholar 

  21. Gadducci, F.: On the algebraic approach to concurrent term rewriting, PhD Thesis, Università di Pisa, Pisa. Technical Report TD-96-02, Department of Computer Science, University of Pisa, 1996.

    Google Scholar 

  22. Gadducci, F. and Montanari, U.: Tiles, rewriting rules and CCS, in J. Meseguer (ed.), Proc. 1st international workshop on Rewriting Logic and Applications, Electron. Notes Theor. Comput. Sci. 4, 1996, pp. 1-19.

  23. Gadducci, F. and Montanari, U.: The tile model, in G. Plotkin, C. Stirling and M. Tofte (eds.), Proofs, Languages and Interaction: Essays in Honour of Robin Milner, MIT Press, 1998.

  24. Habel, A.: Hyperedge replacement: Grammars and languages, PhD Thesis, University of Bremen, 1989.

  25. Kelly, G. M. and Street, R. H.: Review of the elements of 2-categories, Lecture Notes in Math. 420, 1974, pp. 75-103.

  26. Klop, J. W.: Term rewriting systems, in S. Abramsky, D. Gabbay, and T. Maibaum (eds.), Handbook of Logic in Computer Science, Vol. I, Oxford University Press, 1992, pp. 1-116.

  27. Larsen, K. G., and Xinxin, L.: Compositionality through an operational semantics of contexts, J. Logic Comput. 1(6) (1991) (conference version in Proc. ICALP'90, Lecture Notes in Comput. Sci. 443, Springer-Verlag, Berlin, 1990).

  28. Lawvere, F. W.: Functorial semantics of algebraic theories, Proc. Nat. Acad. Sci. 50 (1963), 869-872.

    Google Scholar 

  29. Mackworth, A. K.: Consistency in networks of relations, Artif. Intell. 8(1) (1977).

  30. Mackworth, A. K.: Encyclopedia of AI, Chapter Constraint Satisfaction, Springer-Verlag, Berlin, 1988, pp. 205-211.

    Google Scholar 

  31. Mackworth, A. K. and Freuder, E. C.: The complexity of some polynomial network consistency algorithms for constraint satisfaction problems, Artif. Intell. 25 (1985).

  32. Meseguer, J.: Conditional rewriting logic as a unified model of concurrency, Theoret. Comput. Sci. 96 (1992), 73-155.

    Google Scholar 

  33. Meseguer, J.: Rewriting logic as a semantic framework for concurrency: A progress report, in U. Montanari and V. Sassone (eds), CONCUR'96: Concurrency Theory, Lecture Notes in Comput. Sci. 1119, Springer-Verlag, Berlin, 1996, pp. 331-372.

    Google Scholar 

  34. Meseguer, J. and Montanari, U.: Mapping tile logic into rewriting logic, in F. Parisi-Presicce (ed.), Proc. 12th WADT Workshop on Algebraic Development Techniques, Lecture Notes in Comput. Sci., Springer-Verlag, Berlin, 1998, to appear. Paper available from http://www.csl.sri.com/ugo/wadt.ps.

    Google Scholar 

  35. Montanari, U.: Networks of constraints: Fundamental properties and application to picture processing, Inform. Sci. 7 (1974).

  36. Montanari, U. and Rossi, F.: Graph rewriting and constraint solving for modelling distributed systems with synchronization, in Proc. COORDINATION 96, Lecture Notes in Comput. Sci. 1061, Springer-Verlag, Berlin, 1996.

    Google Scholar 

  37. Nguyen, T. and Deville, Y.: A distributed arc-consistency algorithm, in Proc. of the CCP95 International Workshop, 1995.

  38. Plotkin, G.: A structural approach to operational semantics, Technical Report DAIMI FN-19, Computer Science Department, Aarhus University, 1981.

  39. Schneider, H. J. and Ehrig, H. (eds.): Graph Trasformations in Computer Science, Lecture Notes in Comput. Sci. 776, Springer-Verlag, Berlin, 1994.

    Google Scholar 

  40. Sleep, M. R., Plasmeijer, M. J., and van Eekelen, M. C. (eds.): Term Graph Rewriting: Theory and Practice, Wiley, New York, 1992.

    Google Scholar 

  41. van Beek, P. and Dechter, R.: Constraint tightness versus global consistency, in Proc. KR94, Morgan Kaufmann, San Mateo, CA, 1994.

    Google Scholar 

  42. Yokoo, M., Ishida, T., Durfee, E. H., and Kuwabara, K.: Distributed constraint satisfaction for formalizing distributed problem solving, in Proc. IEEE International Conference on Distributed Computing Systems, 1992.

  43. Yokoo, M.: Asynchronous weak-committment search for solving distributed constraint satisfaction problems, in Proc. CP95 (Principles and Practice of Constraint Programming), Lecture Notes in Comput. Sci. 976, Springer-Verlag, Berlin, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125, Pisa, Italy. e-mail

    Ugo Montanari & Francesca Rossi

Authors
  1. Ugo Montanari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesca Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Montanari, U., Rossi, F. Graph Rewriting, Constraint Solving and Tiles for Coordinating Distributed Systems. Applied Categorical Structures 7, 333–370 (1999). https://doi.org/10.1023/A:1008693303228

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008693303228

Search

Navigation