Quantum Computing: 1-Way Quantum Automata

Bertoni, Alberto; Mereghetti, Carlo; Palano, Beatrice

doi:10.1007/3-540-45007-6_1

Cited by 74 publications

(95 citation statements)

References 19 publications

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“…The class of languages recognized by MM-1qfa's with bounded error probabilities strictly bigger than that by MO-1qfa's, but both MO-1qfa's and MM-1qfa's recognize proper subclass of regular languages with bounded error probabilities [1,24,11,23,7,8]. On the other hand, the class of languages recognized by MM-1qfa's with bounded error probabilities is not closed under the binary Boolean operations (intersection, union, complement) [1,4,11,8], and by contrast MO-1qfa's satisfy the closure properties of the languages recognized with bounded error probabilities under binary Boolean operations [11,10]. A more powerful model of quantum computation than its classical counterpart is 2qfa's that were first studied by Kondacs and Watrous [23].…”

Section: Introductionmentioning

confidence: 96%

Some Observations on Two-Way Finite Automata with Quantum and Classical States

Qiu¹

2008

Lecture Notes in Computer Science

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Two-way finite automata with quantum and classical states (2qcfa's) were introduced by Ambainis and Watrous. Though this computing model is more restricted than the usual two-way quantum finite automata (2qfa's) first proposed by Kondacs and Watrous, it is still more powerful than the classical counterpart. In this note, we focus on dealing with the operation properties of 2qcfa's. We prove that the Boolean operations (intersection, union, and complement) and the reversal operation of the class of languages recognized by 2qcfa's with error probabilities are closed; as well, we verify that the catenation operation of such class of languages is closed under certain restricted condition. The numbers of states of these 2qcfa's for the above operations are presented. Some examples are included, and {xx R |x ∈ {a, b} * , # x (a) = # x (b)} is shown to be recognized by 2qcfa with one-sided error probability, where x R is the reversal of x, and # x (a) denotes the a's number in string x.

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Section: Introductionmentioning

confidence: 96%

Some Observations on Two-Way Finite Automata with Quantum and Classical States

Qiu¹

2008

Lecture Notes in Computer Science

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“…Quantum finite automata (QFAs) [9][10][11][12][13][14][15][16]22]. In particular, the study of QFAs provides a good insight into the nature of quantum computation, since QFAs can be viewed as the simplest theoretical model based on quantum mechanism.…”

mentioning

confidence: 99%

Corrigendum to “Another approach to the equivalence of measure-many one-way quantum infinite automata and its application” [J. Comput. Syst. Sci. 78 (3) (2012) 807–821]

Lin¹

2015

Journal of Computer and System Sciences

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In this paper, we present a much simpler, direct and elegant approach to the equivalence problem of measure many one-way quantum finite automata (MM1QFAs). The approach is essentially generalized from the work of Carlyle [J. Math. Anal. Appl. 7 (1963) 167-175]. Namely, we reduce the equivalence problem of MM-1QFAs to that of two (initial) vectors.As an application of the approach, we utilize it to address the equivalence problem of Enhanced one-way quantum finite automata (E-1QFAs) introduced by Nayak [Proceedings of the 40th Annual IEEE Symposium on Foundations ofComputer Science, 1999, pp. 369-376]. We prove that two E-1QFAs A 1 and A 2 over Σ are equivalence if and only if they are n 2 1 + n 2 2 − 1-equivalent where n 1 and n 2 are the numbers of states in A 1 and A 2 , respectively.Keywords: quantum finite automata, measure-many one-way quantum finite automata, enhanced one-way quantum finite automata, equivalence

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“…, q n−1 or in q n+1 . If it halts in one of the states q i , with 0 i < n, then the automaton A i also halts in q i and CHICAGO JOURNAL OF THEORETICAL COMPUTER SCIENCE 2010, Article 2, pages [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]The languages L 0 , . .…”

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confidence: 99%

Varieties Generated by Certain Models of Reversible Finite Automata

Golovkins

2006

Lecture Notes in Computer Science

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Reversible finite automata with halting states (RFA) were first considered by Ambainis and Freivalds to facilitate the research of Kondacs-Watrous quantum finite automata. In this paper we consider some of the algebraic properties of RFA, namely the varieties these automata generate. Consequently, we obtain a characterization of the Boolean closure of the classes of languages recognized by these models.We also obtain an equality which relates varieties of ordered J-trivial monoids with the variety of R-trivial monoids.

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Quantum Computing: 1-Way Quantum Automata

Cited by 74 publications

References 19 publications

Some Observations on Two-Way Finite Automata with Quantum and Classical States

Some Observations on Two-Way Finite Automata with Quantum and Classical States

Corrigendum to “Another approach to the equivalence of measure-many one-way quantum infinite automata and its application” [J. Comput. Syst. Sci. 78 (3) (2012) 807–821]

Varieties Generated by Certain Models of Reversible Finite Automata

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