Regularity of languages defined by formal series with isolated cut point

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

[1]  Jean Berstel,et al.  Rational series and their languages , 1988, EATCS monographs on theoretical computer science.

[2]  Giancarlo Mauri,et al.  Some Recursive Unsolvable Problems Relating to Isolated Cutpoints in Probabilistic Automata , 1977, ICALP.

[3]  Vincent D. Blondel,et al.  Undecidable Problems for Probabilistic Automata of Fixed Dimension , 2003, Theory of Computing Systems.

[4]  Noam Chomsky,et al.  The Algebraic Theory of Context-Free Languages* , 1963 .

[5]  Alberto Bertoni,et al.  Quantum Computing: 1-Way Quantum Automata , 2003, Developments in Language Theory.

[6]  Azaria Paz,et al.  Probabilistic automata , 2003 .

[7]  Azaria Paz,et al.  Introduction to Probabilistic Automata , 1971 .

[8]  Alberto Bertoni,et al.  On 2{PFA}s and the Hadamard quotient of formal power series , 1994 .

[9]  Cynthia Dwork,et al.  A Time Complexity Gap for Two-Way Probabilistic Finite-State Automata , 1990, SIAM J. Comput..

[10]  M. Droste,et al.  Handbook of Weighted Automata , 2009 .

[11]  Gérard Jacob.  La finitude des représentations linéaires des semi-groupes est décidable , 1978 .

[12]  Rusins Freivalds,et al.  Probabilistic Two-Way Machines , 1981, MFCS.

[13]  Arto Salomaa,et al.  Automata-Theoretic Aspects of Formal Power Series , 1978, Texts and Monographs in Computer Science.

[14]  A. Bertoni.  The Solution of Problems Relative to Probabilistic Automata in the Frame of the Formal Languages Theory , 1974, GI Jahrestagung.

[15]  Anne Condon,et al.  On the Undecidability of Probabilistic Planning and Infinite-Horizon Partially Observable Markov Decision Problems , 1999, AAAI/IAAI.

[16]  Marcel Paul Schützenberger,et al.  On the Definition of a Family of Automata , 1961, Inf. Control..

[17]  Vincent D. Blondel,et al.  Decidable and Undecidable Problems about Quantum Automata , 2005, SIAM J. Comput..