Mathematical systems theory

, Volume 6, Issue 1–2, pp 164–192 | Cite as

Uniform tag sequences

  • Alan Cobham


Structural properties, local and asymptotic, of members of a class of simple, realtime generable sequences are analyzed.


Generable Sequence Structural Property Computational Mathematic 
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.


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  1. [1]
    J. R. Büchi, Weak second-order arithmetic and finite automata,Z. Math. Logik Grundlagen Math. 6 (1960), 66–92.Google Scholar
  2. [2]
    R. Bumby andE. Ellentuck, Finitely additive measures and the first digit problem,Fund. Math. 65 (1969), 33–42.Google Scholar
  3. [3]
    A. Cobham, “On the Hartmanis-Stearns problem for a class of tag machines”, IEEE Conference Record of the 1968 Ninth Annual Symposium on Switching and Automata Theory, Schenectady (1968), 51–60.Google Scholar
  4. [4]
    A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata,Math. Systems Theory 3 (1969), 186–192.Google Scholar
  5. [5]
    B. D. Craven, On digital distribution in some integer sequences,J. Austral. Math. Soc. 5 (1965), 325–330.Google Scholar
  6. [6]
    C. C. Elgot, Decision problems of finite automata design and related arithmetics,Trans. Amer. Math. Soc. 98 (1961), 21–51.Google Scholar
  7. [7]
    P. C. Fischer, A. R. Meyer andA. L. Rosenberg, Time-restricted sequence generation,J. Comput. System Sci. 4 (1970), 50–73.Google Scholar
  8. [8]
    B. J. Flehinger, On the probability that a random integer has initial digit A,Amer. Math. Monthly 73 (1966), 1056–1061.Google Scholar
  9. [9]
    F. R. Gantmacher,The Theory of Matrices (2 vols.), Chelsea, New York, 1960.Google Scholar
  10. [10]
    S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.Google Scholar
  11. [11]
    W. H. Gottschalk andG. A. Hedlund,Topological Dynamics, Amer. Math. Soc., Providence, R.I., 1955.Google Scholar
  12. [12]
    H. Halberstam andK. F. Roth,Sequences, Vol. I, Oxford Univ. Press, Oxford, 1966.Google Scholar
  13. [13]
    G. H. Hardy andE. M. Wright,An Introduction to the Theory of Numbers, fourth edition, Oxford Univ. Press, Oxford, 1965.Google Scholar
  14. [14]
    J. Hartmanis andH. Shank, On the recognition of primes by automata,J. Assoc. Comput. Mach. 15 (1968), 328–389.Google Scholar
  15. [15]
    J. Hartmanis andR. E. Stearns, On the computational complexity of algorithms,Trans. Amer. Math. Soc. 117 (1965), 285–306.Google Scholar
  16. [16]
    G. A. Hedlund, Remarks on the work of Axel Thue on sequences,Nordisk Mat. Tidskr. 15 (1967), 148–150.Google Scholar
  17. [17]
    G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system,Math. Systems Theory 3 (1969), 320–375.Google Scholar
  18. [18]
    L. Hellerman, W. L. Duda andS. Winograd, Continuity and realizability of sequence transformations,IEEE Trans. Electronic Computers EC-15 (1966), 560–569.Google Scholar
  19. [19]
    M. Keane, Generalized Morse sequences,Z. Wahrscheinlichkeitstheorie Verw. Gebiete 10 (1968), 335–353.Google Scholar
  20. [20]
    W. J. LeVeque,Topics in Number Theory (2 vols.), Addison-Wesley, Reading, Mass., 1956.Google Scholar
  21. [21]
    M. L. Minsky,Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, N.J., 1967.Google Scholar
  22. [22]
    M. Minsky andS. Papert, Unrecognizable sets of numbers,J. Assoc. Comput. Mach. 13 (1966), 281–286.Google Scholar
  23. [23]
    D. J. Newman, On the number of binary digits in a multiple of three,Proc. Amer. Math. Soc. 21 (1969), 719–721.Google Scholar
  24. [24]
    M. O. Rabin andD. Scott, Finite automata and their decision problems,IBM J. Res. Develop. 3 (1959), 114–125.Google Scholar
  25. [25]
    G. N. Raney, Sequential functions,J. Assoc. Comput. Mach. 5 (1958), 177–180.Google Scholar
  26. [26]
    R. W. Ritchie, Finite automata and the set of squares,J. Assoc. Comput. Mach. 10 (1963), 528–531.Google Scholar
  27. [27]
    H. S. Shank, Records of Turing machines,Math. Systems Theory 5 (1971), 50–55.Google Scholar
  28. [28]
    J. V. Uspensky andM. A. Heaslet,Elementary Number Theory, McGraw-Hill, New York, 1939.Google Scholar
  29. [29]
    H. Yamada, Real-time computation and recursive functions not real-time computable,IRE Trans. Electronic Computers EC-11 (1962), 753–760.Google Scholar

Copyright information

© Swets & Zeitlinger B.V. 1972

Authors and Affiliations

  • Alan Cobham
    • 1
  1. 1.IBM Watson ResearchYorktown HeightsUSA

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