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)


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.


Transition Function Regular Language Input Word Deterministic Finite Automaton Deterministic Automaton 
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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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