Descriptional complexity issues in quantum computing
Journal of Automata, Languages and Combinatorics
MSO definable string transductions and two-way finite-state transducers
ACM Transactions on Computational Logic (TOCL)
Quantum automata and quantum grammars
Theoretical Computer Science
Dense quantum coding and quantum finite automata
Journal of the ACM (JACM)
Characterizations of 1-Way Quantum Finite Automata
SIAM Journal on Computing
On the Class of Languages Recognizable by 1-Way Quantum Finite Automata
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Descriptive and Computational Complexity
FCT '89 Proceedings of the International Conference on Fundamentals of Computation Theory
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
The complexity of relational query languages (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Relational queries computable in polynomial time (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Probabilities to accept languages by quantum finite automata
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Quantum inductive inference by finite automata
Theoretical Computer Science
Hamming, permutations and automata
SAGA'07 Proceedings of the 4th international conference on Stochastic Algorithms: foundations and applications
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There are several nonequivalent definitions of quantum finite automata. Nearly all of them recognize only regular languages but not all regular languages. On the other hand, for all these definitions there is a result showing that there is a language l such that the size of the quantum automaton recognizing L is essentially smaller than the size of the minimal deterministic automaton recognizing L. For most of the definitions of quantum finite automata the problem to describe the class of the languages recognizable by the quantum automata is still open. The partial results are surveyed in this paper. Moreover, for the most popular definition of the QFA, the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant. The end of the paper is devoted to unpublished results of the description of the class of the recognizable languages in terms of the second order predicate logics. This research is influenced by the results of Büchi [1,2], Elgot [3], Trakhtenbrot [4] (description of regular languages in terms of MSO), R.Fagin [5,6] (description of NP in terms of ESO), von Neumann [7] (quantum logics), Barenco, Bennett et al. [8](universal quantum gates).