Displaying similar documents to “On the size of one-way quantum finite automata with periodic behaviors”

Quantum finite automata with control language

Carlo Mereghetti, Beatrice Palano (2006)

RAIRO - Theoretical Informatics and Applications

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Bertoni  introduced in (2003) 1–20 a new model of 1-way quantum finite automaton (1qfa) called . This model, whose recognizing power is exactly the class of regular languages, generalizes main models of 1qfa's proposed in the literature. Here, we investigate some properties of 1qfc's. In particular, we provide algorithms for constructing 1qfc's accepting the inverse homomorphic images and quotients of languages accepted by 1qfc's. Moreover, we give instances ...

Note on the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata

Carlo Mereghetti, Beatrice Palano, Giovanni Pighizzini (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We investigate the succinctness of several kinds of unary automata by studying their state complexity in accepting the family { L m } of cyclic languages, where L m = { a k m | k ∈ ℕ } . In particular, we show that, for any m , the number of states necessary and sufficient for accepting the unary language L m with isolated cut point on one-way probabilistic finite automata is p 1 α 1 + p 2 α 2 + ⋯ + p s α s , with p 1 α 1 p 2 α 2 ⋯ p s α s being the factorization of m . To prove this result, we give a general state lower bound for accepting unary languages with isolated...

On the state complexity of semi-quantum finite automata

Shenggen Zheng, Jozef Gruska, Daowen Qiu (2014)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Some of the most interesting and important results concerning quantum finite automata are those showing that they can recognize certain languages with (much) less resources than corresponding classical finite automata. This paper shows three results of such a type that are stronger in some sense than other ones because (a) they deal with models of quantum finite automata with very little quantumness (so-called semi-quantum one- and two-way finite automata); (b) differences, even comparing...

Translation from classical two-way automata to pebble two-way automata

Viliam Geffert, L'ubomíra Ištoňová (2010)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata equipped with some ℓ additional “pebbles” that are movable along the input tape, but their use is restricted (nested) in a stack-like fashion. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic two-way automata with ℓ nested pebbles....

Abstract β -expansions and ultimately periodic representations

Michel Rigo, Wolfgang Steiner (2005)

Journal de Théorie des Nombres de Bordeaux

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For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is ℚ ( β ) if the dominating eigenvalue β > 1 of the automaton accepting the language is a Pisot number. Moreover, if β is neither a Pisot nor a Salem number, then there exist points in ℚ ( β ) which do not have any ultimately periodic representation.

Note on the complexity of Las Vegas automata problems

Galina Jirásková (2006)

RAIRO - Theoretical Informatics and Applications

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We investigate the complexity of several problems concerning Las Vegas finite automata. Our results are as follows. (1) The membership problem for Las Vegas finite automata is in NL. (2) The nonemptiness and inequivalence problems for Las Vegas finite automata are NL-complete. (3) Constructing for a given Las Vegas finite automaton a minimum state deterministic finite automaton is in NP. These results provide partial answers to some open problems posed by Hromkovič and Schnitger...

Hyper-minimizing minimized deterministic finite state automata

Andrew Badr, Viliam Geffert, Ian Shipman (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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We present the first (polynomial-time) algorithm for reducing a given deterministic finite state automaton (DFA) into a hyper-minimized DFA, which may have fewer states than the classically minimized DFA. The price we pay is that the language recognized by the new machine can differ from the original on a finite number of inputs. These hyper-minimized automata are optimal, in the sense that every DFA with fewer states must disagree on infinitely many inputs. With small modifications,...