Normality and Automata

We prove that finite-state transducers with injective behavior, deterministic or not, real-time or not, with no extra memory or a single counter, cannot compress any normal word. We exhaust all combinations of determinism, real-time, and additional memory in the form of counters or stacks, identifyi...

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Detalhes bibliográficos
Autores: Becher, Veronica Andrea, Carton, Olivier, Heiber, Pablo Ariel
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2015
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/59876
Acesso em linha:http://hdl.handle.net/11336/59876
Access Level:Acceso aberto
Palavra-chave:Finite Automata
Non-Deterministic Automata
Normal Numbers
https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
Descrição
Resumo:We prove that finite-state transducers with injective behavior, deterministic or not, real-time or not, with no extra memory or a single counter, cannot compress any normal word. We exhaust all combinations of determinism, real-time, and additional memory in the form of counters or stacks, identifying which models can compress normal words. The case of deterministic push-down transducers is the only one still open. We also present results on the preservation of normality by selection with finite automata. Complementing Agafonov's theorem for prefix selection, we show that suffix selection preserves normality. However, there are simple two-sided selection rules that do not.