Search results for "Language and speech"
showing 10 items of 166 documents
The Phagocyte Lattice of Dyck Words
2006
We introduce a new lattice structure on Dyck words. We exhibit efficient algorithms to compute meets and joins of Dyck words.
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.
Probabilities to Accept Languages by Quantum Finite Automata
1999
We construct a hierarchy of regular languages such that the current language in the hierarchy can be accepted by 1-way quantum finite automata with a probability smaller than the corresponding probability for the preceding language in the hierarchy. These probabilities converge to 1/2.
Finite State Transducers with Intuition
2010
Finite automata that take advice have been studied from the point of view of what is the amount of advice needed to recognize nonregular languages. It turns out that there can be at least two different types of advice. In this paper we concentrate on cases when the given advice contains zero information about the input word and the language to be recognized. Nonetheless some nonregular languages can be recognized in this way. The help-word is merely a sufficiently long word with nearly maximum Kolmogorov complexity. Moreover, any sufficiently long word with nearly maximum Kolmogorov complexity can serve as a help-word. Finite automata with such help can recognize languages not recognizable …
Size of Quantum Finite State Transducers
2007
Sizes of quantum and deterministic finite state transducers are compared in the case when both quantum and deterministic finite state transducers exist. The difference in size may be exponential.
Measurement of ultra-low heating rates of a single antiproton in a cryogenic Penning trap
2019
Physical review letters 122(4), 043201 (2019). doi:10.1103/PhysRevLett.122.043201
Inducing the Lyndon Array
2019
In this paper we propose a variant of the induced suffix sorting algorithm by Nong (TOIS, 2013) that computes simultaneously the Lyndon array and the suffix array of a text in $O(n)$ time using $\sigma + O(1)$ words of working space, where $n$ is the length of the text and $\sigma$ is the alphabet size. Our result improves the previous best space requirement for linear time computation of the Lyndon array. In fact, all the known linear algorithms for Lyndon array computation use suffix sorting as a preprocessing step and use $O(n)$ words of working space in addition to the Lyndon array and suffix array. Experimental results with real and synthetic datasets show that our algorithm is not onl…
Cyclic Complexity of Words
2014
We introduce and study a complexity function on words $c_x(n),$ called \emph{cyclic complexity}, which counts the number of conjugacy classes of factors of length $n$ of an infinite word $x.$ We extend the well-known Morse-Hedlund theorem to the setting of cyclic complexity by showing that a word is ultimately periodic if and only if it has bounded cyclic complexity. Unlike most complexity functions, cyclic complexity distinguishes between Sturmian words of different slopes. We prove that if $x$ is a Sturmian word and $y$ is a word having the same cyclic complexity of $x,$ then up to renaming letters, $x$ and $y$ have the same set of factors. In particular, $y$ is also Sturmian of slope equ…
Quantum, stochastic, and pseudo stochastic languages with few states
2014
Stochastic languages are the languages recognized by probabilistic finite automata (PFAs) with cutpoint over the field of real numbers. More general computational models over the same field such as generalized finite automata (GFAs) and quantum finite automata (QFAs) define the same class. In 1963, Rabin proved the set of stochastic languages to be uncountable presenting a single 2-state PFA over the binary alphabet recognizing uncountably many languages depending on the cutpoint. In this paper, we show the same result for unary stochastic languages. Namely, we exhibit a 2-state unary GFA, a 2-state unary QFA, and a family of 3-state unary PFAs recognizing uncountably many languages; all th…
On generalized Lyndon words
2018
Abstract A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every word in the free monoid can be factorized in a unique way as a nonincreasing factorization of generalized Lyndon words. We give new characterizations of the first and the last factor in this factorization as well as new characterization of generalized Lyndon words. We also give more specific results on two special cases: the classical one and the one arising from the alternating lexicographical order.