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showing 10 items of 4869 documents
The small-world of 'Le Petit Prince': Revisiting the word frequency distribution
2016
[EN] Many complex systems are naturally described through graph theory, and different kinds of systems described as networks present certain important characteristics in common. One of these features is the so-called scale-free distribution for its node s connectivity, which means that the degree distribution for the network s nodes follows a power law. Scale-free networks are usually referred to as small-world because the average distance between their nodes do not scale linearly with the size of the network, but logarithmically. Here we present a mathematical analysis on linguistics: the word frequency effect for different translations of the Le Petit Prince in different languages. Compar…
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 …
Languages Recognizable by Quantum Finite Automata
2006
There are several nonequivalent definitions of quantum finite automata. Nearly all of them recognize only regular languages but not all regular languages. On the other hand, for all these definitions there is a result showing that there is a language l such that the size of the quantum automaton recognizing L is essentially smaller than the size of the minimal deterministic automaton recognizing L. For most of the definitions of quantum finite automata the problem to describe the class of the languages recognizable by the quantum automata is still open. The partial results are surveyed in this paper. Moreover, for the most popular definition of the QFA, the class of languages recognizable b…
On the size of transducers for bidirectional decoding of prefix codes
2012
In a previous paper [L. Giambruno and S. Mantaci, Theoret. Comput. Sci. 411 (2010) 1785–1792] a bideterministic transducer is defined for the bidirectional deciphering of words by the method introduced by Girod [ IEEE Commun. Lett. 3 (1999) 245–247]. Such a method is defined using prefix codes. Moreover a coding method, inspired by the Girod’s one, is introduced, and a transducer that allows both right-to-left and left-to-right decoding by this method is defined. It is proved also that this transducer is minimal. Here we consider the number of states of such a transducer, related to some features of the considered prefix code X . We find some bounds of such a number of states in relation wi…
Quantum Finite Multitape Automata
1999
Quantum finite automata were introduced by C. Moore, J. P. Crutchfield [4], and by A. Kondacs and J. Watrous [3]. This notion is not a generalization of the deterministic finite automata. Moreover, in [3] it was proved that not all regular languages can be recognized by quantum finite automata. A. Ambainis and R. Freivalds [1] proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by deterministic or probabilistic finite automata. This …
Probabilistic Reversible Automata and Quantum Automata
2002
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.
Implications of quantum automata for contextuality
2014
We construct zero error quantum finite automata (QFAs) for promise problems which cannot be solved by bounded error probabilistic finite automata (PFAs). Here is a summary of our results: There is a promise problem solvable by an exact two way QFA in exponential expected time but not by any bounded error sublogarithmic space probabilistic Turing machine (PTM). There is a promise problem solvable by an exact two way QFA in quadratic expected time but not by any bounded error o(loglogn) space PTMs in polynomial expected time. The same problem can be solvable by a one way Las Vegas (or exact two way) QFA with quantum head in linear (expected) time. There is a promise problem solvable by a Las …
Amount of Nonconstructivity in Finite Automata
2009
When D. Hilbert used nonconstructive methods in his famous paper on invariants (1888), P.Gordan tried to prevent the publication of this paper considering these methods as non-mathematical. L. E. J. Brouwer in the early twentieth century initiated intuitionist movement in mathematics. His slogan was "nonconstructive arguments have no value for mathematics". However, P. Erdos got many exciting results in discrete mathematics by nonconstructive methods. It is widely believed that these results either cannot be proved by constructive methods or the proofs would have been prohibitively complicated. R.Freivalds [7] showed that nonconstructive methods in coding theory are related to the notion of…
Quantum Finite State Transducers
2001
We introduce quantum finite state transducers (qfst), and study the class of relations which they compute. It turns out that they share many features with probabilistic finite state transducers, especially regarding undecidability of emptiness (at least for low probability of success). However, like their 'little brothers', the quantum finite automata, the power of qfst is incomparable to that of their probabilistic counterpart. This we show by discussing a number of characteristic examples.