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On log-time alternating Turing machines of alternation depth k

Extended abstract
  • Liming Cai
  • Jianer Chen
Session 5A: Machine Models
  • 120 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)

Abstract

Several input read-modes for alternating Turing machines have been proposed in the literature. For each input read-mode and for each fixed integer k ≥ 1, a precise circuit characterization is established for log-time alternating Turing machines of k alternations, which is a nontrivial refinement of Ruzzo's circuit characterization of alternating Turing machines. Complete languages in strong sense for each level of the log-time hierarchy are presented, refining a result by Buss. The class GC(s(n), Π k B ) is investigated, which is the class of languages accepted by log-time alternating Turing machines of k alternations enhanced by an extra ability of guessing a string of length s(n). A systematic technique is developed to show that for many functions s(n) and for every integer k>1, the class GC(s(n), Π k B ) has natural complete languages. Connections of these results to computational optimization problems are exhibited.

Keywords

Turing Machine Vertex Cover Computation Path Output Gate Proper Subclass 
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 1995

Authors and Affiliations

  • Liming Cai
    • 1
  • Jianer Chen
    • 2
  1. 1.East Carolina UniversityGreenvilleUSA
  2. 2.Texas A&M UniversityCollege StationUSA

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