Skip to main content
Log in

P-selective sets, tally languages, and the behavior of polynomial time reducibilities onNP

Mathematical systems theory Aims and scope Submit manuscript

Abstract

The notion ofp-selective sets, and tally languages, are used to study polynomial time reducibilities onNP. P-selectivity has the property that a setA belongs to the classP if and only if bothĀ ≤ p m A andA isp-selective. We prove that for every tally language set inNP there exists a polynomial time equivalent set inNP that isp-selective. From this result it follows that if NEXT ≠ DEXT, then polynomial time Turing and many-one reducibilities differ onNP.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. R. Book, On languages accepted in polynomial time,SIAM J. Comput. 1 281–287 (1972).

    Google Scholar 

  2. R. Book, Tally languages and complexity classes,Information and Control 26 186–193 (1974).

    Google Scholar 

  3. R. Book, Comparing complexity classes,J. Computer System Sci. 9 213–229 (1974).

    Google Scholar 

  4. R. Book, C. Wrathall, A. Selman, and D. Dobkin, Inclusion complete tally languages and the Hartmanis-Berman conjecture,Math. Systems Theory 11 1–8 (1977).

    Google Scholar 

  5. S. Cook, The complexity of theorem-proving procedures, Third annual ACM Symposium on Theory of Computing 151–158 (1971).

  6. S. Cook, Characterizations of pushdown machines in terms of time-bounded computers,J. Assoc. Comput. Mach. 18 4–18 (1971).

    Google Scholar 

  7. C. Jockusch, Semirecursive sets and positive reducibility,Trans. Amer. Math. Soc. 131 420–436 (1968).

    Google Scholar 

  8. N. Jones and A. Selman, Turing machines and the spectra of first-order formulas,J. Symbolic Logic 29 139–150 (1974).

    Google Scholar 

  9. R. Karp, Reducibility among combinatorial problems,Complexity of Computer Computations, R. Miller and J. Thatcher, eds., Plenum Press, New York, 85–103 (1972).

    Google Scholar 

  10. R. Karp, Combinatories= ? linear programming + number theory, Project MAC Workshop on Complexity Computations 1973.

  11. R. Ladner, On the structure of polynomial time reducibility,J. Assoc. Comput. Mach. 22 155–171 (1975).

    Google Scholar 

  12. R. Ladner, N. Lynch, and A. Selman, A comparison of polynomial time reducibilities,Theoretical Computer Sci. 1 103–123 (1975).

    Google Scholar 

  13. V. Pratt, Every prime has a succinct certificate,SIAM J. Comput. 4 214–220 (1975).

    Google Scholar 

  14. I. Simon and J. Gill, Polynomial reducibilities and upward diagonalizations, Ninth annual ACM Symposium on Theory of Computing 186–194 (1977).

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported in part by the National Science Foundation under grant MCS 77-23493

Rights and permissions

Reprints and permissions

About this article

Cite this article

Selman, A.L. P-selective sets, tally languages, and the behavior of polynomial time reducibilities onNP . Math. Systems Theory 13, 55–65 (1979). https://doi.org/10.1007/BF01744288

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01744288

Key words and phrases

Navigation