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Relationship between density and deterministic complexity of MP-complete languages

  • Piotr Berman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 62)

Abstract

Let Σ be an arbitrary alphabet.
denotes ɛ∪Σ∪...∪Σn. We say that a function t, t :
is f-sparse iff card
for every natural n. The main theorem of this paper establishes that if CLIQUE has some f-sparse translation into another set, which is calculable by a deterministic Turing machine in time bounded by f, then all the sets belonging to NP are calculable in time bounded by a function polynomially related to f. The proof is constructive and shows the way of constructing a proper algorithm. The simplest and most significant corollary says that if there is an NP-complete language over a single letter alphabet, then P=NP.

Keywords

Polynomial Time Single Letter Partial Correctness Marked Vertex Proper Subgraph 
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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References

  1. [1]
    J.Hartmanis, L.Berman: On isomorphisms and density of NP and other complete sets. Proc. Eight ACM Sym. Theory of Computing, 30–40 (1976).Google Scholar
  2. [2]
    R.Book, C.Wrathhall, A.Selman and D.Dobkin: Inclusion Complete Tally Languages and Hartmanis-Berman Conjecture (1977).Google Scholar
  3. [3]
    A.V.Aho, J.E.Hopcroft and J.D.Ullman: The Design and Analysis of Computer Algorithms, Addison-Wesley Publishing Company, Readin, Mass., 1074.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Piotr Berman
    • 1
  1. 1.Uniwersytet WarszawskiWarszawaPoland

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