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On the Lower Bounds for One-Way Quantum Automata

  • Farid Ablayev
  • Aida Gainutdinova
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1893)

Abstract

In the paper we consider measured-once (MO-QFA) oneway quantum finite automaton. We prove that for MO-QFA Q that (1/2+ε)-accepts (ε ∈ (0,1/2)) regular language L it holds that dim(Q) = Ω (log dim (A)/log log dim (A)). In the case ε (3/8, 1/2) we have more precise lower bound dim(Q) = Ω (log dim (A)) where A is a minimal deterministic finite automaton accepting L, dim(Q), and dim(A) are complexity (number of states) of automata Q and A respectively, (1/2 - ε) is the error of Q.

The example of language presented in [2] show that our lower bounds are tight enough.

Keywords

Transition Function Regular Language Input Word Deterministic Finite Automaton Deterministic Automaton 
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 2000

Authors and Affiliations

  • Farid Ablayev
    • 1
  • Aida Gainutdinova
    • 1
  1. 1.Dept. of Theoretical CyberneticsKazan State UniversityKazanRussia

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