Expressive Power of Quantum Pushdown Automata with Classical Stack Operations under the Perfect-Soundness Condition

Nakanishi, Masaki; Hamaguchi, Kiyoharu; Kashiwabara, Toshinobu

doi:10.1093/ietisy/e89-d.3.1120

Cited by 7 publications

(16 citation statements)

References 14 publications

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“…In this paper, we show that the proposed model can simulate any quantum pushdown automaton with a classical stack, which is proposed in [19], as well as any classical pushdown automaton. It is known that quantum pushdown automata with a classical stack are strictly more powerful than classical counterparts in the setting of one-sided error and non-deterministic computation [19].…”

Section: Introductionmentioning

confidence: 91%

“…It is known that QCPDAs can recognize a certain non-context-free language with one-sided error [19]. This means that QPAGs are strictly more powerful than classical pushdown automata in the setting of one-sided error as well as non-deterministic computation.…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…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%

“…It is known that quantum pushdown automata with a classical stack are strictly more powerful than classical counterparts in the setting of one-sided error and non-deterministic computation [19]. Thus, so is our model.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 91%

Section: ⊓ ⊔mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum Pushdown Automata with a Garbage Tape

Nakanishi

2015

Lecture Notes in Computer Science

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“…For quantum pushdown automata (the model proposed by Golovkins), it remains open whether they are at least as powerful as probabilistic pushdown automata. The authors proposed quantum pushdown automata with a classical stack and showed that they are strictly more powerful than probabilistic pushdown automata in the one-sided error setting [14]. This implies that quantum finite automata with a classical stack can overcome the restriction of reversibility.…”

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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Superiority of one-way and realtime quantum machines

Yakaryılmaz

2012

RAIRO-Theor. Inf. Appl.

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In automata theory, the quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to the QFAs augmented with counters or stacks. Moreover, to our knowledge, there is no result related to QFAs having more than one input head. In this paper, we focus on such generalizations of QFAs whose input head(s) operate(s) in one-way or realtime mode and present many superiority of them to their classical counterparts. Furthermore, we propose some open problems and conjectures in order to investigate the power of quantumness better. We also give some new results on classical computation. keywords: quantum computation, randomization, quantum automata, pushdown automaton, blind counter automaton, multihead finite automaton, nondeterminism, bounded error * This work was partially supported by TÜBİTAK with grant 108E142 and FP7 FET-Open project QCS.1 They are also known as quantum Turing machines with constant space. 2Abuzer Yakaryılmaz not reflect the full power of quantum computation [34]. Therefore, we use "modern" definitions for the quantum models (e.g. [4,15]).After a concise background given in Section 2, we present our results in Section 3, in which we classify the results under four subsections: (3.1) nondeterminism, (3.2) blind counter automata, (3.3) multihead finite automata, and (3.4) multihead pushdown automata. BackgroundWe specifically give the definitions of three models in order to trace the proofs presented in the paper: generalized finite automaton, one-way quantum finite automaton, and realtime quantum automaton with one-blind counter. The quantum models are defined based on a generic template that is given in Subsection (3.2). We refer the reader to [10,14,16,27,31] for the definitions of classical machines; to [15,42] for the definitions of the QFAs generalizing their classical counterparts; and, to [25] for a standard reference of quantum computation.Throughout the paper, we use the following notations: Σ not containing ¢ and $ (the left and right end-markers) denotes the input alphabet;Σ = Σ ∪ {¢, $}; Q is the set of (internal) states; q 0 ∈ Q is the initial state; Q a ⊆ Q is the set of accepting states; δ is the transition function; f M (w) is the accepting probability (or value) of machine M on w; w i is the i th symbol of w; |w| is the length of w; |w| σ is the number of the occurrence of σ in w, where w ∈ Σ * . The list of abbreviations used for models is given below:• the prefixes "1" and "rt" stand for one-way 2 and realtime 3 input head(s), respectively;• the letters "D", "N", "P", and "Q" used after "1" or "rt" stand for deterministic, nondeterministic, probabilistic, and quantum, respectively;• the abbreviations "FA", "kFA", "PDA", "PDkA", and "kBCA" stand for finite automaton, finite automaton with k input heads, pushdown automaton, pushdown automaton with k input heads, and automaton with k blind counter(s), respectively, where k > 0.For all models (except GFAs), the input w ∈ Σ * is placed on a read-only t...

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Expressive Power of Quantum Pushdown Automata with Classical Stack Operations under the Perfect-Soundness Condition

Cited by 7 publications

References 14 publications

Quantum Pushdown Automata with a Garbage Tape

Quantum Pushdown Automata with a Garbage Tape

On the Weakness of One-Way Quantum Pushdown Automata

Superiority of one-way and realtime quantum machines

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