Size lower bounds for quantum automata

Bianchi, Maria Paola; Mereghetti, Carlo; Palano, Beatrice

doi:10.1016/j.tcs.2014.07.004

Cited by 10 publications

(34 citation statements)

References 14 publications

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“…Some recent work (e. g. [5,11,13,16]) shows that semi-quantum automata like CL-1QFA, 1QFAC and 1QFAC are much more concise than equivalent DFA. In order to see the limit of the descriptional power of these models, size lower bounds were given in [4,3,13] for these models.…”

Section: The Main Resultsmentioning

confidence: 99%

“…In addition, a lower bound on the size of 1QFAC was given in [13], which stated that 1QFAC can be at most exponentially more concise than DFA, and the bound was shown to be tight by giving some languages witnessing this exponential gap. Size lower bounds were also reported for CL-1QFA in [4] and for 1QCFA in [3] (no detailed proof was given in [3] for the bound of 1QCFA), but they were not proved to be tight. By the way, we mention that the result obtained in [3] that 1QFCA recognize only regular languages follows directly from [9], although a relatively complex procedure was used in [3] to deduce this result.…”

Section: Introductionmentioning

confidence: 99%

“…Specially, one can see that complex technical treatments were used in [4] to derive the bound for CL-1QFA and one may find that some key steps in [4] were confused such that the proof there may have some flaws, which will be explained more clearly in Section 4. It is also worth mentioning that the method used in [4] is tailored for CL-1QFA and is not easy to adopt to other models.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, we first obtain a lower bound on the size of MO-1gQFA and then apply it to the three hybrid models by using the relationship between them and MO-1gQFA. Compared with a recent work [4], our method is much more concise and universal, and it can be applied to the three existing main models of semi-quantum automata. In addition, our method may fix a potential mistake in [4] that will be indicated later on.…”

Section: Introductionmentioning

confidence: 99%

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Lower bounds on the size of semi-quantum finite automata

Qiu

2016

Theoretical Computer Science

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In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata. In this paper, we compare the descriptional power of these models with that of DFA. Specifically, we present a uniform method that gives a lower bound on the size of the three existing main models of semi-quantum automata, and this bound shows that semi-quantum automata can be at most exponentially more concise than DFA. Compared with a recent work (Bianchi, Mereghetti, Palano, Theoret. Comput. Sci., 551(2014), 102-115), our method shows the following two advantages: (i) our method is much more concise; and (ii) our method is universal, since it is applicable to the three existing main models of semi-quantum automata, instead of only a specific model.

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Section: The Main Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Lower bounds on the size of semi-quantum finite automata

Qiu

2016

Theoretical Computer Science

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“…Concerning the state complexity of 1qfa's, there were a few results in the past literature. Bianchi, Mereghetti, and Palano [7], for example, demonstrated an exponential gap between the state complexities of 1dfa's and 1qfa's. Here, we obtain the following relationships, which are partly due to [1,2,38].…”

Section: One-way Quantum Finite Automata Familiesmentioning

confidence: 99%

Nonuniform Families of Polynomial-Size Quantum Finite Automata and Quantum Logarithmic-Space Computation with Polynomial-Size Advice

Yamakami

2019

Language and Automata Theory and Applications

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The state complexity of a finite(-state) automaton intuitively measures the size of the description of the automaton. Sakoda and Sipser [STOC 1972, pp. 275-286] were concerned with nonuniform families of finite automata and they discussed the behaviors of nonuniform complexity classes defined by families of such finite automata having polynomial-size state complexity. In a similar fashion, we introduce nonuniform state complexity classes using families of quantum finite automata. Our primarily concern is one-way quantum finite automata empowered by garbage tapes. We show inclusion and separation relationships among nonuniform state complexity classes of various one-way finite automata, including deterministic, nondeterministic, probabilistic, and quantum finite automata of polynomial size. For two-way quantum finite automata equipped with garbage tapes, we discover a close relationship between the nonuniform state complexity of such a polynomial-size quantum finite automata family and the parameterized complexity class induced by quantum logarithmic-space computation assisted by polynomial-size advice.

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