On the lower bounds for one-way quantum automata

Abstract

© Springer-Verlag Berlin Heidelberg 2000. In the paper we consider measured-once (MO-QFA) one way quantum finite automaton. We prove that for MO-QFA Q that (1/2+ε)-accepts (ε Є (0,1/2)) regular language L it holds that dim(formula presented). In the case ε Є (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.