Translations between flowchart schemes and process graphs

  • J. A. Bergstra
  • Gh. Ştefanescu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 710)


In a flowchart scheme an atomic action is modelled as a vertex (box), while in a process graph an atomic action is modelled as an edge. We define translations between these two graphical representations. By using these translations, we show that the classical bisimulation equivalence on process graphs coincides with the natural extension of the classical step-bystep flowchart equivalence to the nondeterministic case. This result allows us to translate axiomatisation results from flowcharts to processes and viceversa.


Normal Form Monoidal Category Atomic Action Computation Sequence Iteration Theory 
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. 1.
    J. Baeten and W. Weijland. Process algebra. Cambridge University Press, 1990.Google Scholar
  2. 2.
    J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77–121, 1985.CrossRefGoogle Scholar
  3. 3.
    J.A. Bergstra, J.W. Klop, and E.R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal of Computing, 17:1134–1177, 1988.CrossRefGoogle Scholar
  4. 4.
    S.L. Bloom, Z. Esik, and D. Taubner. Iteration theory of synchronization trees. Information and Computation, 103:1–55, 1993.CrossRefGoogle Scholar
  5. 5.
    B. Courcelle. Fundamental properties of infinite trees. Theoretical Computer Science, 25:95–169, 1983.CrossRefGoogle Scholar
  6. 6.
    V.E. Cazanescu and Gh. Stefanescu. Towards a new algebraic foundation of flowchart scheme theory. Fundamenta Informaticae, 13:171–210, 1990.MathSciNetGoogle Scholar
  7. 7.
    V.E. Cazanescu and Gh. Stefanescu. Classes of finite relations as initial abstract data types I. Discrete Mathematics, 90:233–265, 1991.CrossRefGoogle Scholar
  8. 8.
    V.E. Cazanescu and Gh. Stefňescu. A general result of abstarct flowchart schemes with applications to the study of accessibility, reduction and minimization. Theoretical Computer Science, 99:1–63, 1992. (Fundamental Study).CrossRefGoogle Scholar
  9. 9.
    C.C. Elgot. Manadic computation and iterative algebraic theories. In Proceedings Logic Colloquium'73, pages 175–230. North-Holland, 1975. Studies in Logic and the Foundations of Mathematics, Volume 80.Google Scholar
  10. 10.
    C.C. Elgot. Finite automata from the a flowchart schemes point of view. In Proceedings MFCS'77. Springer, 1977. Lecture Notes in Computer Science.Google Scholar
  11. 11.
    C.C. Elgot. Some geometrical categories associated with flowchart schemes. In Proceedings FCT'77, pages 256–259. Springer, 1977. Lecture Notes in Computer Science.Google Scholar
  12. 12.
    C.C. Elgot, S.L. Bloom, and R. Tindell. On the algebraic structure of rooted trees. Journal of Computer and System Sciences, 16:362–399, 1978.CrossRefGoogle Scholar
  13. 13.
    R. Milner. A calculus of communicating systems. Springer, 1980.Google Scholar
  14. 14.
    R. Milner. Communication and concurrency. Prentice Hall International, 1989.Google Scholar
  15. 15.
    Gh. Stefanescu. On flowchart theories I: The determinisitc case. Journal of Computer and System Sciences, 35:163–191, 1987.CrossRefGoogle Scholar
  16. 16.
    Gh. Stefanescu. On flowchart theories II: The nondeterministic case. Theoretical Computer Science, 52:307–340, 1987.CrossRefGoogle Scholar
  17. 17.
    Gh. Stefanescu. Determinism and nondeterminism in program scheme theory: algebraic aspects. PhD thesis, University of Bucharest, 1991.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • J. A. Bergstra
    • 1
    • 2
  • Gh. Ştefanescu
    • 1
    • 2
  1. 1.Programming Research GroupUniversity of AmsterdamDB Amsterdam
  2. 2.Institute of MathematicsRomanian AcademyBucharest

Personalised recommendations