On sets having only hard subsets

  • P. Flajolet
  • J. M. Steyaert
Thursday Afternoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 14)


We investigate properties of sets having no infinite subset in a given family of sets. We study the case when this family is defined by a complexity measure or one of the usual complexity notions in automata or recursive function theory.


Turing Machine Recursive Function Threshold Relation Infinite Subset Universal Machine 
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  1. [1]
    Blum M. "A machine-independent theory of the complexity of recursive functions", JACM 14 (1967),322–336.CrossRefGoogle Scholar
  2. [2]
    Blum M. "On the size of machines", Inf. & Cont. 11 (1967),257–265.Google Scholar
  3. [3]
    Constable R. "Hierarchy theorems for axiomatic complexity", Computational complexity (Randall Rustin ed.) Algorithmics Press Inc. (1973),37–63.Google Scholar
  4. [4]
    Cudia D. "The degree hierarchy of undecidable problems of formal grammars", Proc. of 2nd ACM Symp. on theory of computing (1970) 10–21.Google Scholar
  5. [5]
    Flajolet P., Steyaert J.M., "Une formalisation de la notion d'algorithme de tri non récurrent", Thèse de 3° cycle. Université PARIS VII (1973).Google Scholar
  6. [6]
    Flajolet P., Steyaert J.M., "Decision problems for multihead finite automata" Proc. of MFCS Symp. (1973), 225–230.Google Scholar
  7. [7]
    Flajolet P., Steyaert J.M., "Une généralisation de la notion d'ensemble immune", RAIRO Rl (1974), 37–48.Google Scholar
  8. [8]
    Hartmanis J., Hopcroft J., "An overview of the theory of computational complexity", JACM 18 (1971), 444–475.CrossRefGoogle Scholar
  9. [9]
    Hennie F., Stearns R., "Two-tape simulation of multitape Turing machines", JACM 13 (1966), 533–546.CrossRefGoogle Scholar
  10. [10]
    Lewis F., "On unsolvability in subrecursive classes of predicates", Harvard University report (1972).Google Scholar
  11. [11]
    Meyer A, "Program size in restricted programming languages", Inf. & Cont. 21 (1972) 382–394.Google Scholar
  12. [12]
    Meyer A., Ritchie D., "Computational complexity and program structure", I.B.M. research report RC 1817 (1967).Google Scholar
  13. [13]
    Rogers H., Theory of recursive functions and effective computability, Mc Graw Hill (1966).Google Scholar
  14. [14]
    Rosenberg A., "On multihead finite automata", I.B.M. Journal (1966), 388–394.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • P. Flajolet
    • 1
  • J. M. Steyaert
    • 1
  1. 1.I.R.I.A. 78 RocquencourtFrance

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