Normal numbers and finite automata
We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the au...
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paperaa:paper_03043975_v477_n_p109_Becher2023-06-12T16:47:30Z Normal numbers and finite automata Theor Comput Sci 2013;477:109-116 Becher, V. Heiber, P.A. Finite state transducers Finite-state Input-output Lossless Normal numbers Output transition Real number Number theory Theorem proving Finite automata We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input-output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov's theorem on the preservation of normality on subsequences selected by finite automata.© 2012 Elsevier B.V. All rights reserved. Fil:Becher, V. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Heiber, P.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03043975_v477_n_p109_Becher |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
language |
Inglés |
orig_language_str_mv |
eng |
topic |
Finite state transducers Finite-state Input-output Lossless Normal numbers Output transition Real number Number theory Theorem proving Finite automata |
spellingShingle |
Finite state transducers Finite-state Input-output Lossless Normal numbers Output transition Real number Number theory Theorem proving Finite automata Becher, V. Heiber, P.A. Normal numbers and finite automata |
topic_facet |
Finite state transducers Finite-state Input-output Lossless Normal numbers Output transition Real number Number theory Theorem proving Finite automata |
description |
We give an elementary and direct proof of the following theorem: A real number is normal to a given integer base if, and only if, its expansion in that base is incompressible by lossless finite-state compressors (these are finite automata augmented with an output transition function such that the automata input-output behaviour is injective; they are also known as injective finite-state transducers). As a corollary we obtain V.N. Agafonov's theorem on the preservation of normality on subsequences selected by finite automata.© 2012 Elsevier B.V. All rights reserved. |
format |
Artículo Artículo publishedVersion |
author |
Becher, V. Heiber, P.A. |
author_facet |
Becher, V. Heiber, P.A. |
author_sort |
Becher, V. |
title |
Normal numbers and finite automata |
title_short |
Normal numbers and finite automata |
title_full |
Normal numbers and finite automata |
title_fullStr |
Normal numbers and finite automata |
title_full_unstemmed |
Normal numbers and finite automata |
title_sort |
normal numbers and finite automata |
publishDate |
2013 |
url |
http://hdl.handle.net/20.500.12110/paper_03043975_v477_n_p109_Becher |
work_keys_str_mv |
AT becherv normalnumbersandfiniteautomata AT heiberpa normalnumbersandfiniteautomata |
_version_ |
1769810336207077376 |