Lower bounds by recursion theoretic arguments

  • Uwe Schöning
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 226)


Using methods and notions stemming from recursion theory, new lower bounds on the "distance" between certain intractable sets (like NP-complete or EXPTIME-complete sets) and the sets in P are obtained. Here, the distance of two sets A and B is a function on natural numbers that, for each n, gives the number of strings of size n on which A and B differ. Yesha [6] has shown that each NP-complete set has a distance of at least O(log log n) from each set in P, assuming P ≠ NP. Similarly, whithout an additional assumption, each EXPTIME-complete set has a distance of at least O(log log n) from each set in P.

In this paper the following will be shown:

  1. 1.

    Assuming P ≠ NP, no NP-complete set that is a (weak) p-cylinder can be within a distance of q(n) to any set in P where q is any polynomial. (Note that all "naturally known" NP-complete sets have been shown to be p-cylinders [3]).

  2. 2.

    No EXPTIME-complete set can be within a distance of 2nc to any set in P for some constant c>0.


The second result improves Yesha's by at least two exponentials.


Polynomial Time SIAM Journal Recursive Function Random Oracle Recursion Theory 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Uwe Schöning
    • 1
  1. 1.EWH Koblenz, InformatikKoblenzWest Germany

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