Languages recognized by nondeterministic quantum finite automata

  • Authors:
  • Abuzer Yakaryilmaz;A. C. Cem Say

  • Affiliations:
  • Boǧaziçi University, Department of Computer Engineering, Istanbul, Turkey;Boǧaziçi University, Department of Computer Engineering, Istanbul, Turkey

  • Venue:
  • Quantum Information & Computation
  • Year:
  • 2010

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Abstract

The nondeterministic quantum finite automaton (NQFA) is the only known case wherea one-way quantum finite automaton (QFA) model has been shown to be strictly superiorin terms of language recognition power to its probabilistic counterpart. We give acharacterization of the class of languages recognized by NQFAs, demonstrating that itis equal to the class of exclusive stochastic languages. We also characterize the class oflanguages that are recognized necessarily by two-sided error by QFAs. It is shown thatthese classes remain the same when the QFAs used in their definitions are replaced byseveral different model variants that have appeared in the literature. We prove severalclosure properties of the related classes. The ramifications of these results about classicaland quantum sublogarithmic space complexity classes are examined.