Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
On the power of quantum finite state automata
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1-way quantum finite automata: strengths, weaknesses and generalizations
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Exploiting the Difference in Probability Calculation between Quantum and Probabilistic Computations
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Various Aspects of Finite Quantum Automata
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Revisiting the power and equivalence of one-way quantum finite automata
ICIC'10 Proceedings of the Advanced intelligent computing theories and applications, and 6th international conference on Intelligent computing
Complexity of quantum uniform and nonuniform automata
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Quantum automata theory – a review
Algebraic Foundations in Computer Science
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In the paper we consider measured-once (MO-QFA) one-way quantum finite automaton. We prove that for MO-QFA Q that (1=2+Ɛ)-accepts (Ɛ ∈ (0, 1=2)) regular language L it holds that dim(Q) = Ω (log dim(A)/log log dim(A)). In the case Ɛ ∈ (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-Ɛ) is the error of Q. The example of language presented in [2] show that our lower bounds are tight enough.