Search results for "QUANTUM FINITE AUTOMATA"
showing 10 items of 73 documents
NON-CONSTRUCTIVE METHODS FOR FINITE PROBABILISTIC AUTOMATA
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. However, the proof is non-constructive. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures not proved but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
Counting with Probabilistic and Ultrametric Finite Automata
2014
We investigate the state complexity of probabilistic and ultrametric finite automata for the problem of counting, i.e. recognizing the one-word unary language \(C_n=\left\{ 1^n \right\} \). We also review the known results for other types of automata.
Superiority Of One-Way And Realtime Quantum Machines
2012
In automata theory, quantum computation has been widely examined for finite state machines, known as quantum finite automata (QFAs), and less attention has been given to QFAs augmented with counters or stacks. In this paper, we focus on such generalizations of QFAs where the input head operates in one-way or realtime mode, and present some new results regarding their superiority over their classical counterparts. Our first result is about the nondeterministic acceptance mode: Each quantum model architecturally intermediate between realtime finite state automaton and one-way pushdown automaton (one-way finite automaton, realtime and one-way finite automata with one-counter, and realtime push…
Quantum Finite Automata and Logics
2006
The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.
Language Recognition Power and Succinctness of Affine Automata
2016
In this work we study a non-linear generalization based on affine transformations of probabilistic and quantum automata proposed recently by Diaz-Caro and Yakaryilmaz [6] referred as affine automata. First, we present efficient simulations of probabilistic and quantum automata by means of affine automata which allows us to characterize the class of exclusive stochastic languages. Then, we initiate a study on the succintness of affine automata. In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata, whereas the number of states of any quantum and probabilistic automata cannot be bounded. Finally, we present the characterization …
On the Class of Languages Recognizable by 1-Way Quantum Finite Automata
2007
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.
Quantum Pushdown Automata
2000
Quantum finite automata, as well as quantum pushdown automata were first introduced by C. Moore, J. P. Crutchfield [13]. In this paper we introduce the notion of quantum pushdown automata (QPA) in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [11]. It is established that the unitarity criteria of QPA are not equivalent to the corresponding unitarity criteria of quantum Turing machines [4]. We show that QPA can recognize every regular language. Finally we present some simple languages recognized by QPA, two of them are not recognizable by deterministic pushdown automata and one seems to be not recognizable by probabilistic pushdown …
One Alternation Can Be More Powerful Than Randomization in Small and Fast Two-Way Finite Automata
2013
We show a family of languages that can be recognized by a family of linear-size alternating one-way finite automata with one alternation but cannot be recognized by any family of polynomial-size bounded-error two-way probabilistic finite automata with the expected runtime bounded by a polynomial. In terms of finite automata complexity theory this means that neither 1Σ2 nor 1Π2 is contained in 2P2.
Artin’s Conjecture and Size of Finite Probabilistic Automata
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
The complexity of probabilistic versus deterministic finite automata
1996
We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains \(\Omega \left( {2^{n\tfrac{{\log \log n}}{{\log n}}} } \right)\) states.