Languages Recognizable by Quantum Finite Automata
- Rūsiņš FreivaldsAffiliated withInstitute of Mathematics and Computer Science, University of Latvia
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The end of the paper is devoted to unpublished results of the description of the class of the recognizable languages in terms of the second order predicate logics.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 , Trakhtenbrot  (description of regular languages in terms of MSO), R.Fagin [5,6] (description of NP in terms of ESO), von Neumann  (quantum logics), Barenco, Bennett et al. (universal quantum gates).
- Languages Recognizable by Quantum Finite Automata
- Book Title
- Implementation and Application of Automata
- Book Subtitle
- 10th International Conference, CIAA 2005, Sophia Antipolis, France, June 27-29, 2005, Revised Selected Papers
- pp 1-14
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
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- Editor Affiliations
- 16. Sophia Antipolis, Laboratoire I3S, Les Algorithmes - bât. Euclide B, Université de Nice
- 17. Sophia Antipolis, Ecole Polytechnique, Université de Nice
- 18. Laboratoire I3S, Université de Nice
- Rūsiņš Freivalds (19)
- Author Affiliations
- 19. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulv. 29, Rīga, Latvia
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