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Weak monadic second order theory of succesor is not elementary-recursive

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Logic Colloquium

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 453))

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References

  1. Blum, M. A machine-independent theory of the complexity of recursive functions, Jour. Assoc. Comp. Mach., 14, 2 (April, 1967), 322–336.

    Article  MATH  Google Scholar 

  2. Blum, M. On effective procedures for speeding up algorithms, Jour. Assoc. Comp. Mach., 18, 2 (April, 1971), 290–305.

    Article  MATH  Google Scholar 

  3. Büchi, J.R. and C.C. Elgot, Decision problems of weak second order arithmetics and finite automata, Part I, (abstract), AMS Notices, 5 (1959), 834.

    Google Scholar 

  4. Büchi, J.R. Weak second order arithmetic and finite automata, Zeit. f. Math. Log. and Grund. der Math., 6 (1960), 66–92.

    Article  MATH  Google Scholar 

  5. Cooper, D.C. Theorem-proving in arithmetic without multiplication, Computer and Logic Group Memo. No. 16, U.C. of Swansea, April, 1972, to appear in Machine Intelligence 7.

    Google Scholar 

  6. Elgot, C.C. and M.O. Rabin, Decidability and undecidability of extensions of second (first) order theory of (generalized) successor, Jour. Symb. Logic, 31, 2 (June, 1966), 169–181.

    Article  MATH  Google Scholar 

  7. Ferrante, J. and C. Rackoff, A decision procedure for the first order theory of real addition with order, Project MAC Tech. Memo 33, Mass. Inst. of Technology (May, 1973), 16pp., to appear SIAM Jour. Comp.

    Google Scholar 

  8. Grzegorczyk, A. Some classes of recursive functions, Rozprawy Matematyczne, 4 (1953), Warsaw, 1–45.

    MathSciNet  Google Scholar 

  9. Meyer, A.R. Weak SIS cannot be decided (abstract 72T-E67), AMS Notices, 19, 5 (August, 1972), p. A-598.

    Google Scholar 

  10. Meyer, A.R. and L.J. Stockmeyer, The equivalence problem for regular expressions with squaring requires exponential space, 13 th Switching and Automata Theory Symp. (Oct. 1972), IEEE, 125–129.

    Google Scholar 

  11. Oppen, D.C. Elementary bounds for Presburger arithmetic, 5 th ACM Symp. Theory of Computing (April, 1973), 34–37.

    Google Scholar 

  12. Rabin, M.O. Decidability of second-order theories and automata on infinite trees, Trans. AMS, 141 (July, 1969), 1–35.

    MathSciNet  MATH  Google Scholar 

  13. Rabin, M.O. and D. Scott, Finite automata and their decision problems, IBM Jour. Research and Development, 3 (1959), 115–125.

    MathSciNet  Google Scholar 

  14. Ritchie, R.W. Classes of predictably computable functions, Trans. AMS, 106 (1963), 139–173.

    Article  MathSciNet  MATH  Google Scholar 

  15. Stearns, R.E., J. Hartmanis, and P.M. Lewis, III, Hierarchies of memory-limited computations, 6 th Switching Theory and Logical Design Symp. (1965), IEEE, 179–190.

    Google Scholar 

  16. Stockmeyer, L.J. and A.R. Meyer, Word problems requiring exponential time, 5 th ACM Symp. Theory of Computing (April, 1973), 1–9.

    Google Scholar 

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Rohit Parikh

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© 1975 Springer-Verlag Berlin · Heidelberg

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Meyer, A.R. (1975). Weak monadic second order theory of succesor is not elementary-recursive. In: Parikh, R. (eds) Logic Colloquium. Lecture Notes in Mathematics, vol 453. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064872

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  • DOI: https://doi.org/10.1007/BFb0064872

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  • Print ISBN: 978-3-540-07155-6

  • Online ISBN: 978-3-540-37483-1

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