4 research outputs found
On simply normal numbers with digit dependencies
Given an integer and a set of prime numbers, the set of
Toeplitz numbers comprises all elements of whose digits
in the base- expansion satisfy for all
and . Using a completely additive arithmetical function, we
construct a number in~ that is simply Borel normal if, and only if,
. We then provide an effective bound for the
discrepancy
Finite-State Independence
In this work we introduce a notion of independence based on finite-state automata: two infinite words are independent if no one helps to compress the other using one-to-one finite-state transducers with auxiliary input. We prove that, as expected, the set of independent pairs of infinite words has Lebesgue measure 1. We show that the join of two independent normal words is normal. However, the independence of two normal words is not guaranteed if we just require that their join is normal. To prove this we construct a normal word x1x2x3… where x2n = xn for every n. This construction has its own interest.Fil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; ArgentinaFil: Carton, Olivier. Université Paris Diderot - Paris 7; FranciaFil: Heiber, Pablo Ariel. Consejo Nacional de Investigaciones CientÃficas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Computación; Argentin
Finite-state independence and normal sequences
We consider the previously defined notion of finite-state independence and we focus specifically on normal words. We characterize finite-state independence of normal words in three different ways, using three different kinds of asynchronous deterministic finite automata with two input tapes containing infinite words. Based on one of the characterizations we give an algorithm to construct a pair of finite-state independent normal words.Fil: Alvarez, Nicolás Alejandro. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Centro CientÃfico Tecnológico Conicet - BahÃa Blanca. Instituto de Ciencias e IngenierÃa de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e IngenierÃa de la Computación. Instituto de Ciencias e IngenierÃa de la Computación; ArgentinaFil: Becher, Veronica Andrea. Consejo Nacional de Investigaciones CientÃficas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigación en Ciencias de la Computación. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigación en Ciencias de la Computación; ArgentinaFil: Carton, Olivier. Université Paris Diderot - Paris 7; Franci