On the structure of polynomial time degrees

  • Klaus Ambos-Spies
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


The main results of this paper are the following. 1) For both the polynomial time many-one and the polynomial time Turing degrees of recursive sets, every countable distributive lattice can be embedded in any interval of degrees. Furthermore, certain restraints — like preservation of the least or greatest element — can be imposed on the embeddings. 2) The upper semilattice of polynomial time many-one degrees is distributive, whereas that of the polynomial time Turing degrees is nondistributive. This gives the first (elementary) difference between the algebraic structures of p-many-one and p-Turing degrees, respectively.


Polynomial Time Partial Ordering Distributive Lattice Polynomial Degree Great Element 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K.Ambos-Spies, Sublattices of the polynomial time degrees, in preparation.Google Scholar
  2. 2.
    K.Ambos-Spies, Splittings of recursive sets and their polynomial degrees, preprint.Google Scholar
  3. 3.
    J.L. Balcazar and J. Diaz, A note on a theorem by Ladner, Inform. Proc. Letters 15 (1982) 84–86.Google Scholar
  4. 4.
    G.Birkhoff, Lattice Theory, Amer. Math. Soc. Colloquium Publications, vol.25, Third Edition, Providence, 1973.Google Scholar
  5. 5.
    P. Chew and M. Machtey, A note on structure and looking back applied to relative complexity of computable functions, JCSS 22 (1981) 53–59.Google Scholar
  6. 6.
    S.A.Cook, The complexity of theorem proving procedures, Proc. Third Annual ACM Symp. on Theory of Comp., 1971, 151–158.Google Scholar
  7. 7.
    R.M. Karp, Reducibility among combinatorial problems, In: R.E. Miller and J.W. Thatcher, Eds., Complexity of computer computations, Plenum, New York, 1972, 85–103.Google Scholar
  8. 8.
    R.E. Ladner, On the structure of polynomial time reducibility, JACM 22 (1975) 155–171.Google Scholar
  9. 9.
    R.E. Ladner, N.A. Lynch and A.L. Selman, A comparision of polynomial time reducibilities, TCS 1 (1976) 103–123.Google Scholar
  10. 10.
    L.H. Landweber, R.J. Lipton and E.L. Robertson, On the structure of sets in NP and other complexity classes, TCS 15 (1981) 181–200.Google Scholar
  11. 11.
    D.Schmidt, On the complexity of one complexity class in another, In: E.Börger G.Hasenjäger and D.Rödding, Eds., Logic and Machines: Decision problems and complexity, SLNCS (to appear in 1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  1. 1.Lehrstuhl für Informatik IIUniversität DortmundDortmund 50W.Germany

Personalised recommendations