Quantum versus Probabilistic One-Way Finite Automata with Counter

Bonner, R.; Freivalds, Rūsiņš; Kravtsev, Maksim

doi:10.1007/3-540-45627-9_15

Cited by 13 publications

(13 citation statements)

References 2 publications

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“…They go on to demonstrate a KQ1CA that recognizes L 2 with error bound 1 4 . Together with our simulation result (Theorem 1), this would establish the superiority of rtQ1CAs over rtP1CAs, however, the argument in [2] about L 2 's unrecognizability by rtP1CAs is unfortunately flawed. A brief description of this problem follows: Bonner et al start by proving that no deterministic rt1CA can recognize the language L 1 , and note that L 1 can therefore not be recognized with zero error by a rtP1CA either.…”

Section: Computational Power Of Quantum One-counter Automatasupporting

confidence: 58%

“…It is easier to construct well-formed rt1CAs which obey the additional restriction that the counter increment c ∈ ♦ associated with each transition to state q ′ upon reading tape symbol σ is determined by the pair (q ′ , σ), for any (q ′ , σ) ∈ Q ×Σ. Such machines are said to be "simple" [10,2,25,24]. We denote the above-mentioned relation by the function D c : Q ×Σ → ♦.…”

Section: Real-time One-counter Automatamentioning

confidence: 99%

“…As a result, these QFAs are strictly less powerful than even classical deterministic finite automata [9], and this weakness also affected the Kravtsev model of quantum counter automata, with Yamasaki et al even demonstrating [25] a regular language which they could not recognize with bounded error. On the other hand, Bonner et al [2] claimed to demonstrate a Kravtsev machine recognizing a particular language that could not be recognized by any probabilistic real-time one-counter automaton.…”

Section: Introductionmentioning

confidence: 99%

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Quantum Counter Automata

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Yakaryılmaz

2012

Int. J. Found. Comput. Sci.

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The question of whether quantum real-time one-counter automata (rtQ1CAs) can outperform their probabilistic counterparts has been open for more than a decade. We provide an affirmative answer to this question, by demonstrating a non-context-free language that can be recognized with perfect soundness by a rtQ1CA. This is the first demonstration of the superiority of a quantum model to the corresponding classical one in the real-time case with an error bound less than 1. We also introduce a generalization of the rtQ1CA, the quantum one-way one-counter automaton (1Q1CA), and show that they too are superior to the corresponding family of probabilistic machines. For this purpose, we provide general definitions of these models that reflect the modern approach to the definition of quantum finite automata, and point out some problems with previous results. We identify several remaining open problems. ⋆ A preliminary version of this paper appeared as Şefika Yüzsever. Quantum one-way one-counter automata. In Rūsiņš Freivalds, editor, Randomized and quantum computation, pages 25-34, 2010 (Satellite workshop of MFCS and CSL 2010).

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Section: Computational Power Of Quantum One-counter Automatasupporting

confidence: 58%

Section: Real-time One-counter Automatamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Counter Automata

Say

Yakaryılmaz

2012

Int. J. Found. Comput. Sci.

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“…As for quantum counter automata, which is the second simplest model of quantum computation, also various kinds of models have been proposed and their power has been analyzed [7], [11], [19], [20]. It is known that several types of quantum counter automata can be more powerful than classical counterparts.…”

Section: Introductionmentioning

confidence: 99%

On the Weakness of One-Way Quantum Pushdown Automata

Nakanishi

2010

2010 Fourth International Conference on Quantum, Nano and Micro Technologies

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In general, quantum computation models are expected to be more powerful than classical counterparts. However, sometimes this is not the case. It is known that there exists some regular language which one-way quantum finite automata and one-way quantum counter automata cannot recognize. This is due to the restriction of reversibility which quantum models must satisfy. Thus, it is an interesting question: what kinds of quantum models suffer from/overcome the restriction? To tackle this problem, we focus on (empty-stack acceptance) oneway quantum pushdown automata, and show that there exists a regular language which one-way quantum pushdown automata cannot recognize. This implies adding a stack to one-way finite automata cannot overcome the restriction of reversibility if we adopt empty-stack acceptance as the acceptance mode.

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“…Quantum finite automata are the simplest model of quantum computation, and have been investigated intensively [3,4,5,7,8,13,14,15,17,21,22,23,25,26,27]. Several quantum automata augmented with additional computational resources have also been proposed, including quantum counter automata and quantum pushdown automata [6,12,16,17,18,19,22,28,29].…”

Section: Introductionmentioning

confidence: 99%

Quantum Pushdown Automata with a Garbage Tape

Nakanishi

2015

Lecture Notes in Computer Science

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Abstract. Several kinds of quantum pushdown automaton models have been proposed, and their computational power is investigated intensively. However, for some quantum pushdown automaton models, it is not known whether quantum models are at least as powerful as classical counterparts or not. This is due to the reversibility restriction. In this paper, we introduce a new quantum pushdown automaton model that has a garbage tape. This model can overcome the reversibility restriction by exploiting the garbage tape to store popped symbols. We show that the proposed model can simulate any quantum pushdown automaton with a classical stack as well as any probabilistic pushdown automaton. We also show that our model can solve a certain promise problem exactly while deterministic pushdown automata cannot. These results imply that our model is strictly more powerful than classical counterparts in the setting of exact, one-sided error and non-deterministic computation.

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Quantum versus Probabilistic One-Way Finite Automata with Counter

Cited by 13 publications

References 2 publications

Quantum Counter Automata

Quantum Counter Automata

On the Weakness of One-Way Quantum Pushdown Automata

Quantum Pushdown Automata with a Garbage Tape

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