Zur Entscheidbarkeit der funktionalen Äquivalenz

Part of the Lecture Notes in Computer Science book series (LNCS, volume 33)


In this paper we consider the equivalence problem for several classes of programs. We show that it is unsolvable for all "acceptable" program classes of the Grzegorczyk class ɛ0 and of the polynominals over the integers formed with ∸ instead of -. Furthermore we show that the equivalence problem is solvable for the class L1(∸1) of loop programs with the additional instruction X := X∸1, but again unsolvable for the class L1(∸1, +) and the Cleave-Ritchie-classes
and L 2 1 (∸1).


Equivalence Problem Loop Program Primitive Recursive Function Dann Gilt 
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  1. Grzegorczyk, A.: "Some classes of recursive functions", Rozprawy Mathematyczne 4. (1953)Google Scholar
  2. Matijasevič, J.V.: "Enumerable sets are Diophantine", Soviet Math. Dokl. 11, 354–358. (1970)Google Scholar
  3. Meyer, A.R., D.M. Ritchie: "The complexity of loop programs", Proc. 22nd Nat. Conf. ACM, 1967, ACM Pub P-67, pp. 465–469Google Scholar
  4. Presburger, M.: "über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchen die Addition als einzige Operation hervortritt", Comptesrendus du I Congrès des Mathématiciens des Pays Slaves, Warsaw (1930) pp. 92–101, 395Google Scholar
  5. Tsichritzis, D.: "The equivalence problem of simple programs", Journal of the Association for Computing Machinery 17: 729–738. (1970)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • H. Beck
    • 1
  1. 1.Institut für Informatik IUniversität KarlsruheKarlsruhe 1

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