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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. [email protected]; [email protected]
Maria Paola Bianchi
Affiliation:
Dipartimento di Informatica, Università degli Studi di Milano, Via Comelico 39, 20135 Milano, Italy. [email protected]; [email protected]
Flavi D’Alessandro
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza” Piazzale Aldo Moro 2, 00185 Roma, Italy; [email protected]
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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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References

Anselmo, M. and Bertoni, A., On 2pfas and the Hadamard quotient of formal power series. Bull. Belg. Math. Soc. 1 (1994) 165–173. Google Scholar
J. Berstel and C. Reutenauer, Rational Series and Their Languages. Springer-Verlag (1988).
Bertoni, A., The solution of problems relative to probabilistic automata in the frame of the formal languages theory, in Vierte Jahrestagung der Gesellschaft for Informatik. Lect. Notes Comput. Sci. 26 (1975) 107–112. Google Scholar
Bertoni, A., Mauri, G. and Torelli, M., Some recursively unsolvable problems relating to isolated cutpoints in probabilistic automata, in Proc. of 4th International Colloquium on Automata, Languages and Programming. Lect. Notes Comput. Sci. 52 (1977) 87–94. Google Scholar
A. Bertoni, C. Mereghetti and B. Palano, Quantum Computing : 1-Way Quantum Automata, in Proc. of Developments in Language Theory. Lect. Notes Comput. Sci. (2003) 1–20.
Blondel, V.D. and Canterini, V., Undecidable problems for probabilistic automata of fixed dimension. Theor. Comput. Syst. 36 (2003) 231–245. Google Scholar
Blondel, V.D., Jeandel, E., Koiran, P. and Portier, N., Decidable and undecidable problems about quantum automata. SIAM J. Comput. 34 (2005) 1464–1473 Google Scholar
A. Brodsky and N. Pippenger, Characterization of 1-way quantum finite automata. Available on http://xxx.lanl.gov/abs/quant-ph/9903014.
C. Choffrut, Private communication to the authors, July 2011.
N. Chomsky and M.P. Schützenberger, The Algebraic Theory of Context-Free Languages, in Computer Programming and Formal Systems. North-Holland, Amsterdam (1963).
M. Droste, W. Kuich and H. Vogler, Handbook of weighted automata. EATCS Series Springer (2009).
Dwork, C. and Stockmeyer, L., A time complexity gap for two-way probabilistic finite-state automata. SIAM J. Comput. 19 (1990) 1011–1023. Google Scholar
R. Freivalds, Probabilistic Two-way Machines, in Proc. of Int. Symp. Math. Found. Comput. Sci. Lect. Notes Comput. Sci. 118 (1981) 33–45.
Jacob, G., La finitude des représentations linéaires des semigoupes est décidable. J. Algebra 52 (1978) 437–459. Google Scholar
J. Kaneps and R. Freivalds, Running time to recognize nonregular languages by two-way probabilistic automata, in Proc. of ICALP 91. Lect. Notes Comput. Sci. 510 (1991) 174–185. CrossRef
O. Madani, S. Hanks and A. Condon, On the undecidability of probabilistic planning and infinite-horizon partially observable markov decision problems, in Proc. of the 6th National Conference on Artificial Intelligence (1999).
A. Paz, Introduction to Probabilistic Automata. Academic Press (1971).
Rabin, M., Probabilistic automata. Inf. Control 6 (1963) 230–245. Google Scholar
A. Salomaa and M. Soittola, Automata-theoretic aspects of formal power series. Springer (1978).
Schützenberger, M.P., On the definition of a family of automata. Inf. Control 4 (1961) 245–270. Google Scholar
Van Der Poorten, A.J., Solution de la conjecture de Pisot sur le quotient de Hadamard de deux fractions rationnelles. C. R. Acad. Sci. Paris, Sér. I 306 (1988) 97–102. Google Scholar