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Uniform tag sequences

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Abstract

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

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References

  1. J. R. Büchi, Weak second-order arithmetic and finite automata,Z. Math. Logik Grundlagen Math. 6 (1960), 66–92.

    Google Scholar 

  2. R. Bumby andE. Ellentuck, Finitely additive measures and the first digit problem,Fund. Math. 65 (1969), 33–42.

    Google Scholar 

  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.

  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. B. D. Craven, On digital distribution in some integer sequences,J. Austral. Math. Soc. 5 (1965), 325–330.

    Google Scholar 

  6. C. C. Elgot, Decision problems of finite automata design and related arithmetics,Trans. Amer. Math. Soc. 98 (1961), 21–51.

    Google Scholar 

  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. B. J. Flehinger, On the probability that a random integer has initial digit A,Amer. Math. Monthly 73 (1966), 1056–1061.

    Google Scholar 

  9. F. R. Gantmacher,The Theory of Matrices (2 vols.), Chelsea, New York, 1960.

    Google Scholar 

  10. S. Ginsburg,The Mathematical Theory of Context-Free Languages, McGraw-Hill, New York, 1966.

    Google Scholar 

  11. W. H. Gottschalk andG. A. Hedlund,Topological Dynamics, Amer. Math. Soc., Providence, R.I., 1955.

    Google Scholar 

  12. H. Halberstam andK. F. Roth,Sequences, Vol. I, Oxford Univ. Press, Oxford, 1966.

    Google Scholar 

  13. G. H. Hardy andE. M. Wright,An Introduction to the Theory of Numbers, fourth edition, Oxford Univ. Press, Oxford, 1965.

    Google Scholar 

  14. J. Hartmanis andH. Shank, On the recognition of primes by automata,J. Assoc. Comput. Mach. 15 (1968), 328–389.

    Google Scholar 

  15. J. Hartmanis andR. E. Stearns, On the computational complexity of algorithms,Trans. Amer. Math. Soc. 117 (1965), 285–306.

    Google Scholar 

  16. G. A. Hedlund, Remarks on the work of Axel Thue on sequences,Nordisk Mat. Tidskr. 15 (1967), 148–150.

    Google Scholar 

  17. G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system,Math. Systems Theory 3 (1969), 320–375.

    Google Scholar 

  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. M. Keane, Generalized Morse sequences,Z. Wahrscheinlichkeitstheorie Verw. Gebiete 10 (1968), 335–353.

    Google Scholar 

  20. W. J. LeVeque,Topics in Number Theory (2 vols.), Addison-Wesley, Reading, Mass., 1956.

    Google Scholar 

  21. M. L. Minsky,Computation: Finite and Infinite Machines, Prentice-Hall, Englewood Cliffs, N.J., 1967.

    Google Scholar 

  22. M. Minsky andS. Papert, Unrecognizable sets of numbers,J. Assoc. Comput. Mach. 13 (1966), 281–286.

    Google Scholar 

  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. M. O. Rabin andD. Scott, Finite automata and their decision problems,IBM J. Res. Develop. 3 (1959), 114–125.

    Google Scholar 

  25. G. N. Raney, Sequential functions,J. Assoc. Comput. Mach. 5 (1958), 177–180.

    Google Scholar 

  26. R. W. Ritchie, Finite automata and the set of squares,J. Assoc. Comput. Mach. 10 (1963), 528–531.

    Google Scholar 

  27. H. S. Shank, Records of Turing machines,Math. Systems Theory 5 (1971), 50–55.

    Google Scholar 

  28. J. V. Uspensky andM. A. Heaslet,Elementary Number Theory, McGraw-Hill, New York, 1939.

    Google Scholar 

  29. H. Yamada, Real-time computation and recursive functions not real-time computable,IRE Trans. Electronic Computers EC-11 (1962), 753–760.

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Cobham, A. Uniform tag sequences. Math. Systems Theory 6, 164–192 (1972). https://doi.org/10.1007/BF01706087

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  • DOI: https://doi.org/10.1007/BF01706087

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