Computing

, Volume 14, Issue 3, pp 285–312 | Cite as

Function iteration logics and flowchart schemata

  • J. Cherniavsky
Article
Received:

Abstract

An interpreted two-sorted logic is defined to allow the representation of a subclass of flowchart schemata. A decision procedure for the equivalence of simple representing formulae within the logic is developed and as a consequence a decision procedure for flowchart schemata within the subclass is demonstrated. Applications of the techniques developed within the paper result in further decision procedures for the equivalence of flowchart schemata in other subclasses. In addition, a decision procedure for the equivalence of programs in a simple programming language is given.

Keywords

Computational Mathematic Programming Language Decision Procedure Function Iteration Simple Programming 
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.

Funktion-Wiederholungslogiken und Flußdiagrammschemata

Zusammenfassung

Eine interpretierte zweisortige Logik wird so definiert, daß sie die Repräsentation einer Unterklasse von Flußdiagrammschemata erlaubt. Ein Entscheidungsverfahren wird entwickelt für die Äquivalenz einfacher Darstellungsformeln innerhalb der Logik und infolgedessen wird ein Entscheidungsverfahren für Flußdiagrammschemata innerhalb der Unterklasse demonstriert. Anwendungen der in der Arbeit entwickelten Techniken haben weitere Entscheidungsverfahren zur Folge. Ein Entscheidungsverfahren für die Äquivalenz von Programmen in einer einfachen Programmiersprache wird auch angegeben.

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References

  1. [1]
    Allen, F. E.: Control Flow Analysis. SIGPLAN Notices5, 1 (1970).Google Scholar
  2. [2]
    Brown, J. S.: Program Schemata and Information Flow. Ph. D. Dissertation, Cornell University, Ithaca, N. Y., 1972.Google Scholar
  3. [3]
    Brown, J. S., Gries, D., Szymanski, T.: Program Schemes with Pushdown Stores. SIAM Journal on Computing1, 242 (1972).Google Scholar
  4. [4]
    Cherniavsky, J. C.: Logical Theories for Representing Flowchart Schemata. Ph. D. Dissertation, Cornell University, Ithaca, N. Y., 1972.Google Scholar
  5. [5]
    Cherniavsky, J. C., Constable, R. L.: Representing Schemata in Logic. Proceedings of the Thirteenth SWAT Conference27 (1972).Google Scholar
  6. [6]
    Cocke, J., Miller, R. E.: Some Analysis Techniques for Optimizing Computer Programs. Proc. Second International Conference on System Sciences, Honolulu, Hawaii, 1969.Google Scholar
  7. [7]
    Constable, R. L.: Loop Schemata. Proceedings of the Third Annual Symposium on Theory of Computing24 (1971).Google Scholar
  8. [8]
    Constable, R. L., Gries, D.: On Classes of Program Schemata. SIAM Journal on Computing1, 66, (1972).Google Scholar
  9. [9]
    Constable, R. L., Muchnick, S. S.: Subrecursive Program Schemata I & II. JCSS6, 480 (1972).Google Scholar
  10. [10]
    Engeler, E.: Algorithmic Properties of Structures. MST3, 183 (1967).Google Scholar
  11. [11]
    Engeler, E.: Structure and Meaning of Elementary Programs. Symp. on Semantics of Algorithmic Languages (Lecture Notes in Mathematics, Vol. 188) p. 89. Berlin-Heidelberg-New York: Springer 1971.Google Scholar
  12. [12]
    Garland, S. J., Luckham, D. C.: Program Schemes, Recursion Schemes and Formal Languages. JCSS7, 119 (1973).Google Scholar
  13. [13]
    Hecht, M. S., Ullman, J. D.: Flow Graph Reducibility. SIAM Journal on Computing1, 188 (1972).Google Scholar
  14. [14]
    Kaplan, D. M.: The Formal Theoretic Analysis of Strong Equivalence for Elemental Programs. Ph. D. Dissertation, Stanford University, 1968.Google Scholar
  15. [15]
    Luckham, D. C., Park, D. M. R., Paterson, M. S.: On Formalised Computer Programs. JCSS4, 220 (1970).Google Scholar
  16. [16]
    Manna, Z.: Properties of Programs and the First Order Predicate Calculus. JACM16, 244 (1969).Google Scholar
  17. [17]
    Meyer, A. R., Ritchie, D. M.: The Complexity of Loop Programs. Proc. 22nd National Conf. ACM, ACM Pub. P-67, p. 465. Washington, D.C.: Thompson Book Co. 1967.Google Scholar
  18. [18]
    Paterson, M. S.: Equivalence Problems in a Model of Computation. Ph.D. Dissertation, Cambridge University, Cambridge, GB, 1967.Google Scholar
  19. [19]
    Presberger, M.: Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. Spawozdanie z I Kongresu Matematykow Krajow Slowianskich, p. 92. Warsaw 1930.Google Scholar
  20. [20]
    Schaefer, M.: A Mathematical Theory of Global Flow Analysis. Englewood Cliffs, N. J.: Prentice-Hall 1973.Google Scholar
  21. [21]
    Strong, H. R.: Translating Recursion Equations into Flowcharts. JCSS5, 254 (1971).Google Scholar
  22. [22]
    Tsichritzis, D.: The Equivalence Problem of Simple Programs. JACM17, 729 (1970).Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • J. Cherniavsky
    • 1
  1. 1.Department of Computer ScienceState University of New York at Stony BrookStony BrookUSA

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