no. 4
Regularity of languages defined by formal series with isolated cut point
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 479-493.

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

DOI : 10.1051/ita/2012019
Classification : 68Q45, 68Q70
Mots clés : formal power series, Hadamard quotient, regular languages 
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     author = {Bertoni, Alberto and Bianchi, Maria Paola and D{\textquoteright}Alessandro, Flavi},
     title = {Regularity of languages defined by formal series with isolated cut point},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {479--493},
     publisher = {EDP-Sciences},
     volume = {46},
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     year = {2012},
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     mrnumber = {3107860},
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     url = {http://www.numdam.org/articles/10.1051/ita/2012019/}
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Bertoni, Alberto; Bianchi, Maria Paola; D’Alessandro, Flavi. Regularity of languages defined by formal series with isolated cut point. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 46 (2012) no. 4, pp. 479-493. doi : 10.1051/ita/2012019. http://www.numdam.org/articles/10.1051/ita/2012019/

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