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.
The research supported by Russia Fund for Basic Research 99-01-00163 and Fund “Russia Universities” 04.01.52. The research partially done while first author visited Aahen and Trier Universities
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References
P. Alexandrov, Introduction to set theory and general topology, Moscow, Nauka, 1977 (in Russian).
A. Ambainis and R. Freivalds, 1-way quantum finite automata: strengths, weaknesses and generalization, In Proceeding of the 39th IEEE Conference on Foundation of Computer Science, 1998, 332–342. See also quant-ph/9802062 v3
A. Brodsky and N. Pippenger, Characterizations of 1-way quantum finite automata, quant-ph/9903014, 1999
http://xxx.lanl.gov/archive/quant-ph. See also its Russian mirror: http://xxx.itep.ru.
A. Kondacs, J. Watrous, On the power of quantum finite state automata. In Proceeding of the 38th IEEE Conference on Foundation of Computer Science, 1997, 66–75.
C. Moore and J. Crutchfield, Quantum automata and quantum grammars, quant-ph/9707031
A. Nayak, Optimal lower bounds for quantum automata and random access codes, Proceeding of the 40th IEEE Conference on Foundation of Computer Science, 1999, 369–376. See also quant-ph/9904093
P. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. on Computing, 26(5), 1997, 1484–1509.
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Ablayev, F., Gainutdinova, A. (2000). On the Lower Bounds for One-Way Quantum Automata. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_9
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DOI: https://doi.org/10.1007/3-540-44612-5_9
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