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Standard factors of Sturmian words

Gwénaël Richomme, Kalle Saari, Luca Q. Zamboni (2010)

RAIRO - Theoretical Informatics and Applications

Among the various ways to construct a characteristic Sturmian word, one of the most used consists in defining an infinite sequence of prefixes that are standard. Nevertheless in any characteristic word c, some standard words occur that are not prefixes of c. We characterize all standard words occurring in any characteristic word (and so in any Sturmian word) using firstly morphisms, then standard prefixes and finally palindromes.

State complexity of cyclic shift

Galina Jirásková, Alexander Okhotin (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The cyclic shift of a language L , defined as s h i f t ( L ) = { v u | u v L } , is an operation known to preserve both regularity and context-freeness. Its descriptional complexity has been addressed in Maslov’s pioneering paper on the state complexity of regular language operations [Soviet Math. Dokl. 11 (1970) 1373–1375], where a high lower bound for partial DFAs using a growing alphabet was given. We improve this result by using a fixed 4-letter alphabet, obtaining a lower bound (n-1)! · 2 ( n - 1 ) ( n - 2 ) , which shows that the state complexity...

State complexity of cyclic shift

Galina Jirásková, Alexander Okhotin (2007)

RAIRO - Theoretical Informatics and Applications

The cyclic shift of a language L, defined as SHIFT(L) = {vu | uv ∈ L}, is an operation known to preserve both regularity and context-freeness. Its descriptional complexity has been addressed in Maslov's pioneering paper on the state complexity of regular language operations [Soviet Math. Dokl.11 (1970) 1373–1375], where a high lower bound for partial DFAs using a growing alphabet was given. We improve this result by using a fixed 4-letter alphabet, obtaining a lower bound (n-1)! . 2(n-1)(n-2), which...

Statistical-learning control of multiple-delay systems with application to ATM networks

Chaouki T. Abdallah, Marco Ariola, Vladimir Koltchinskii (2001)

Kybernetika

Congestion control in the ABR class of ATM network presents interesting challenges due to the presence of multiple uncertain delays. Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to challenging control problems. In this paper, using some recent results by the authors, an efficient statistical algorithm is used to design a robust, fixed-structure, controller for a high-speed communication network with multiple uncertain propagation...

Steady state and scaling limit for a traffic congestion model

Ilie Grigorescu, Min Kang (2010)

ESAIM: Probability and Statistics

In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...

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