On the Class of Languages Recognizable by 1-Way Quantum Finite Automata
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some neces- sary and some sufficient conditions for a (regular) language to be recog- nizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient.
Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.
KeywordsRegular Language Classi Cation Probabilistic Automaton Minimal Automaton Recognizable Language
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- [ABFK 99]A. Ambainis, R. Bonner, R. Freivalds, A. Ķikusts. Probabilities to accept languages by quantum finite automata. Proc. COCOON’99, Lecture Notes in Computer Science, 1627:174–183. Also quant-ph/99040664.Google Scholar
- [AF 98]A. Ambainis, R. Freivalds. 1-way quantum finite automata: strengths, weaknesses and generalizations. Proc. FOCS’98, pp. 332–341. Also quant-ph/9802062.Google Scholar
- [ANTV 98]A. Ambainis, A. Nayak, A. Ta-Shma, U. Vazirani. Dense quantum coding and a lower bound for 1-way quantum automata. Proc. STOC’99, pp. 376–383. Also quant-ph/9804043.Google Scholar
- [AW 99]A. Ambainis, J. Watrous. Two-way finite automata with quantum and classical states. cs.CC/9911009. Submitted to Theoretical Computer Science.Google Scholar
- [BV 97]
- [BP 99]A. Brodsky, N. Pippenger. Characterizations of 1-way quantum finite automata. quant-ph/9903014.Google Scholar
- [G 00]
- [KS 76]J. Kemeny, J. Laurie Snell. Finite Markov Chains. Springer-Verlag, 1976.Google Scholar
- [K 98]A. Ķikusts. A small 1-way quantum finite automaton. quant-ph/9810065.Google Scholar
- [KW 97]A. Kondacs, J. Watrous. On the power of quantum finite state automata. Proc. FOCS’97, pp. 66–75.Google Scholar
- [MT 69]
- [MC 97]
- [N 99]A. Nayak. Optimal lower bounds for quantum automata and random access codes. Proc. FOCS’99, pp. 369–376. Also quant-ph/9904093.Google Scholar