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Using inductive counting to simulate nondeterministic computation

  • Gerhard Buntrock
  • Lane A. Hemachandra
  • Dirk Siefkes
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)

Abstract

Immerman and Szelepcsényi's inductive counting technique demonstrated that, for space classes, the nondeterministic acceptance mechanism can simulate with no space penalty any reasonable acceptance mechanism based on censuses of configurations. However, the efficiency with which other acceptance mechanisms can simulate nondeterminism remains an open question. This paper uses inductive counting to study the cost of simulating nondeterminism with Valiant's paradigm of unique computation—nondeterministic computation in which each input generates at most one accepting computation. We show that unique computation can simulate nondeterministic computation with a space penalty logarithmic in the ambiguity of the nondeterministic computation tree. Relatedly, we show that unique AuxPDAs, logspace reductions to unambiguous context-free languages, and PRAMs can efficiently simulate ambiguity-bounded nondeterministic computation. In particular, all nondeterministic logspace languages of polynomial ambiguity are in CREW1, and thus have fast parallel algorithms.

Keywords

Turing Machine Computation Tree Computation Path Unique Computation Acceptance Mechanism 
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 1990

Authors and Affiliations

  • Gerhard Buntrock
    • 1
  • Lane A. Hemachandra
    • 2
  • Dirk Siefkes
    • 3
  1. 1.Department of Computer ScienceUniversity of WürzburgWürzburgWest Germany
  2. 2.Department of Computer ScienceUniversity of RochesterRochester
  3. 3.Department of Computer ScienceTechniche Universität BerlinBerlinWest Germany

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