The topology of provability in complexity theory

  • Kenneth W. Regan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


Peano Arithmetic Springer LNCS Provable Formula Recursive Language Recursive Enumeration 
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. [A-S84]
    K. Ambos-Spies. Sublattices of the polynomial-time degrees. STACS '84, Paris, France, April 1984. / Inform. and Control 65, April 1985, pp 63–84.Google Scholar
  2. [A-S85]
    K. Ambos-Spies. Three theorems on polynomial degrees of NP sets. Proc. 26th FOCS, 1985, pp 51–55.Google Scholar
  3. [BGS75]
    T. Baker, J. Gill, and R. Solovay. Relativisations of the P=NP? question. SIAM J. Comput. 4, No. 4, 1975, pp 431–442.CrossRefGoogle Scholar
  4. [BaSö85]
    J. Balcázar and U. Schöning. Bi-immune sets for complexity classes. Math. Syst. Theory 18, 1985.Google Scholar
  5. [BH77]
    L. Berman and J. Hartmanis. On isomorphisms and density of NP and other complete sets. SIAM J. Comput. 6, No. 2, June 1977, pp 305–321.CrossRefGoogle Scholar
  6. [Brt78]
    S. Breidtbart. On splitting recursive sets. J. Comp. Sys. Sci. 17, 1987, pp 56–64.Google Scholar
  7. [CM81]
    P. Chew and M. Machtey. A note on structure and looking-back... J. Comp. Sys. Sci. 22, 1981, pp 53–59.CrossRefGoogle Scholar
  8. [Cu80]
    N. Cutland. Computability. (Cambridge, UK: Camb. University Press, 1980.)Google Scholar
  9. [Dug66]
    J. Dugundy. Topology. (Boston: Allyn and Bacon, 1966.)Google Scholar
  10. [Haj79]
    P. Hajek, Arithmetical hierarchy and complexity of Computation. Theor. Comp. Sci. 8, 1979, pp 227–237.Google Scholar
  11. [Har78]
    J. Hartmanis. Feasible computations and provable complexity properties. Monograph, Society for Industrial and Applied Mathematics, 1978.Google Scholar
  12. [Har84]
    J. Hartmanis. Independence results about context-free languages and lower bounds. Draft, Cornell University, 1984/Info. Proc. Lett., to appear.Google Scholar
  13. [HU79]
    J. Hopcroft and J. Ullman. Introduction to Automata Theory, Languages, and Computation. (Reading, Mass.: Addison-Wesley, 1979).Google Scholar
  14. [Kow84]
    W. Kowalczyk. Some connections between presentability of complexity classes and the power of formal systems of reasoning. Proc. MFCS '84, Prague, Czechoslovakia, Aug. 1984. Springer LNCS 201, 1984, pp 364–368.Google Scholar
  15. [Koz80]
    D. Kozen. Indexings of subrecursive classes. Theor. Comp. Sci. 11, 1980, pp 277–301.Google Scholar
  16. [Lad75]
    R. Ladner. On the structure of polynomial-time reducibility. J.ACM 22, No. 1, 1975, pp 155–171.CrossRefGoogle Scholar
  17. [Lake75]
    J. Lake. Characterizating the largest countable partial ordering. Zeitschr. f. Math. Logik und Grund-lagen d. Math. 21, 1975, pp 353–354.Google Scholar
  18. [Lei82]
    D. Leivant. Unprovability of theorems of complexity theory in weak number theories. Theor. Comp. Sci. 18, 1982, pp 259–268.Google Scholar
  19. [Mah81]
    S. Mahaney. On the number of isomorphism classes of NP-complete sets. Proc. 22nd FOCS, 1984, pp 271–278.Google Scholar
  20. [MaYg83]
    S. Mahaney and P. Young. Orderings of polynomial isomorphism types. Draft, 1983. / Theor. Comp. Sci. 39, No. 2, August 1985, pp 207–224.Google Scholar
  21. [Mel76]
    K. Melhorn. Polynomial and abstract subrecursive classes. Proc. 14th FOCS, 1976, pp 96–109.Google Scholar
  22. [Re83a]
    K. Regan. On diagonalization methods and the structure of language classes. Proc. FCT '83, Borgholm, Sweden. Springer LNCS 158, pp 368–380.Google Scholar
  23. [Re83b]
    K. Regan. Arithmetical degrees of index sets for complexity classes. Proc. Logic & Machines '83, Muenster, W. Germany, May 1983. Springer LNCS 171, 1984, pp 118–130.Google Scholar
  24. [Rog67]
    H. Rogers. Theory of Recursive Functions and Effective Computability. (New York: McGraw-Hill, 1967).Google Scholar
  25. [Sdt83]
    D. Schmidt. On the complement of one complexity class in another. Proc. Logic and Machines '83, ibid. Borgholm, Sweden. Springer LNCS 171, 1984, pp 77–87.Google Scholar
  26. [Sdt85]
    D. Schmidt. The recursion-theoretic structure of complexity classes. Theor. Comp. Sci. 38, Nos. 2–3, 1985, pp 143–156.Google Scholar
  27. [Sö81]
    U. Schöning. Untersuchungen zur Struktur von NP... Ph.D. dissertation, University of Stuttgart, 1981.Google Scholar
  28. [Sö82]
    U. Schöning. A uniform approach to obtain diagonal sets in complexity classes. Theor. Comp. Sci. 18, 1982, pp 95–103.CrossRefGoogle Scholar
  29. [Vis80]
    A. Visser. Numerations, λ-calculus, and arithmetic. In: To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus, and Formalism. (London/New York: Academic Press, 1980.)Google Scholar
  30. [Yg83]
    P. Young. Some structural properties of polynomial reducibilities and sets in NP. Proc. 15th STOC, 1983, pp 392–401.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Kenneth W. Regan
    • 1
  1. 1.Merton CollegeOxfordEngland

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