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Regularity of languages defined by formal series with isolatedcut point∗

Published online by Cambridge University Press:  02 August 2012

Alberto Bertoni ,
Maria Paola Bianchi  and
Flavi D’Alessandro
Alberto Bertoni
Affiliation:
Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. bertoni@di.unimi.it; bianchi@di.unimi.it
Maria Paola Bianchi
Affiliation:
Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. bertoni@di.unimi.it; bianchi@di.unimi.it
Flavi D’Alessandro
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza” Piazzale Aldo Moro 2, 00185 Roma, Italy; dalessan@mat.uniroma1.it
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Abstract

LetLϕ,λ = {ω ∈ Σ∗| ϕ(ω) > λ} be thelanguage recognized by a formal seriesϕ:Σ∗ → ℝ with isolated cut pointλ. We provide new conditions that guarantee the regularity of thelanguage Lϕ,λ in the case thatϕ is rational or ϕ is a Hadamard quotient of rationalseries. Moreover the decidability property of such conditions is investigated.

Keywords

Formal power seriesHadamard quotientregular languages
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 46 , Issue 4: Special Issue: Non-Classical Models ofAutomata and Applications III (NCMA-2011) , October 2012 , pp. 479 - 493
Copyright
© EDP Sciences 2012

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