Grid Protocol Specifications

  • Jan A. Bergstra
  • Alban Ponse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1546)


A grid protocol models concurrent computation, and consists of one or more modules repeatedly performing parallel I/O and computation. We provide several concise specification formats and correctness results on (external) I/O behaviour, and illustrate our approach by examples


Connected Network Output Channel Sequential Composition Process Algebra Early Read 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [BB94]
    J.C.M. Baeten and J.A. Bergstra. On sequential composition, action prefixes and process prefix. Formal Aspects of Computing, 6(3):83–98, 1994.CrossRefGoogle Scholar
  2. [BBK87]
    J.C.M. Baeten, J.A. Bergstra, and J.W. Klop. Conditional axioms and α/β calculus in process algebra. In M. Wirsing, editor, Formal Description of Programming Concepts-III, Proceedings of the 3 rd IFIP WG 2.2 working conference, Ebberup 1986, pages 53–75, Amsterdam, 1987. North-Holland.Google Scholar
  3. [BHP97]
    J.A. Bergstra, J.A. Hillebrand, and A. Ponse. Grid protocols based on synchronous communication, Science of Computer Programming, 29:199–233, 1997.CrossRefMathSciNetGoogle Scholar
  4. [BJM97]
    E. van Buiten, M. de Jonge, and R. Monajemi. Beating Grid Protocols, PAII-thesis, University of Amsterdam, 1997.Google Scholar
  5. [Pou97]
    M. Pouw. Beating Grid Protocols, Master’s Thesis, Utrecht University, 1997.Google Scholar
  6. [BK84]
    J.A. Bergstra and J.W. Klop. The algebra of recursively defined processes and the algebra of regular processes. In J. Paredaens, editor, Proceedings 11 th ICALP, Antwerpen, volume 172 of Lecture Notes in Computer Science, pages 82–95. Springer-Verlag, 1984. An extended version appeared in [PVV95], pages 1–25, 1995.Google Scholar
  7. [BK85]
    J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77–121, 1985.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [BT84]
    J.A. Bergstra and J.V. Tucker. Top down design and the algebra of communicating processes. Science of Computer Programming, 5(2):171–199, 1984.MathSciNetGoogle Scholar
  9. [BT95]
    J.A. Bergstra and J.V. Tucker. Equational specifications, complete term rewriting systems, and computable and semicomputable algebras. Journal of the ACM, 42(6):1194–1230, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [BW90]
    J.C.M. Baeten and W.P. Weijland. Process Algebra. Cambridge Tracts in Theoretical Computer Science 18. Cambridge University Press, 1990.Google Scholar
  11. [FJL+88]
    G. Fox, M. Johnson, G. Lyzenga, S. Otto, J. Salmon, and D. Walker. General Techniques and Regular Problems, volume 1 of Solving Problems on Concurrent Processors. Prentice-Hall International, 1988.Google Scholar
  12. [Fok97]
    W.J. Fokkink, Axiomatizations for the perpetual loop in process algebra. In P. Degano, R. Gorrieri, and A. Marchetti-Spaccamela, editors, Proc. 24th Colloquium on Automata, Languages and Programming-ICALP’97, pages 571–581. Lecture Notes in Computer Science Vol. 1256, Springer-Verlag, Berlin, 1997.Google Scholar
  13. [GK95]
    J.F. Groote and H. Korver. A correctness proof of the bakery protocol in μCRL. In [PVV95], pages 63–86, 1995.Google Scholar
  14. [GP91c]
    J.F. Groote and A. Ponse. Proof theory for μCRL. (Extended version.) Report CS-R9138, CWI, Amsterdam, 1991.Google Scholar
  15. [GP94b]
    J.F. Groote and A. Ponse. Proof theory for μCRL: a language for processes with data. In D.J. Andrews, J.F. Groote, and C.A. Middelburg, editors, Proceedings of the International Workshop on Semantics of Specification Languages, pages 232–251. Workshops in Computing, Springer-Verlag, 1994.Google Scholar
  16. [GP95]
    J.F. Groote and A. Ponse. The syntax and semantics of μCRL. In [PVV95], pages 26–62, 1995.Google Scholar
  17. Hil96]
    J.A. Hillebrand. A simple language for the specification of grid protocols (working title). Technical Report, Programming Research Group, University of Amsterdam, tto appear.Google Scholar
  18. [Kle56]
    S.C. Kleene. Representation of events in nerve nets and finite automata. In Automata Studies, pages 3–41. Princeton University Press, 1956.Google Scholar
  19. [Mil89]
    R. Milner. Communication and Concurrency. Prentice-Hall International, Englewood Cliffs, 1989.zbMATHGoogle Scholar
  20. [PVV95]
    A. Ponse, C. Verhoef, and S.F.M. vanVlijmen, editors. Algebra of Communicating Processes, Utrecht 1994, Workshops in Computing. Springer-Verlag, 1995.Google Scholar
  21. [Smi65]
    G.D. Smith. Numerical Solution of Partial Differential Equations, Oxford University Press, 1965.Google Scholar
  22. [TT94]
    B.C. Thompson and J.V. Tucker. Equational specification of Synchronous Concurrent Algorithms and architectures (Second Edition). Report CSR 15–94, University of Wales, Swansea, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jan A. Bergstra
    • 1
    • 2
  • Alban Ponse
    • 1
  1. 1.Programming Research GroupUniversity of AmsterdamSJ AmsterdamThe Netherlands
  2. 2.Department of PhilosophyUtrecht UniversityTC UtrechtThe Netherlands

Personalised recommendations