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On the amount of nondeterminism and the power of verifying

Extended abstract
  • Liming Cai
  • Jianer Chen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

The relationship between nondeterminism and other computational resources is studied based on a special interactive-proof system model GC. Let s(n) be a function and C be a complexity class. Define GC(s(n), C) to be the class of languages that are accepted by verifiers in C that can make an extra O(s(n)) amount of nondeterminism. Our main results are (1) A systematic technique is developed to show that for many functions s(n) and for many complexity classes C, the class GC(s(n), C) has natural complete languages; (2) The class h 0 of languages accepted by log-time alternating Turing machines making h alternations is precisely the class of languages accepted by uniform families of circuits of depth h; (3) The classes GC(s(n), IIh0), h ≥ 1, characterize precisely the fixed-parameter intractability of NP-hard optimization problems. In particular, the (2h)th level W[2h] of W-hierarchy introduced by Downey and Fellows collapses if and only if \(GC(s(n),\prod _{2h}^0 ) \subseteq P\) for some s(n)=ω(log n).

Keywords

Turing Machine Computation Path Input Length Fixed Parameter Tractability Circuit Family 
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 1993

Authors and Affiliations

  • Liming Cai
    • 1
  • Jianer Chen
    • 1
  1. 1.Texas A&M UniversityCollege StationUSA

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