@inbook{Petre2009,
    Abstract = {We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky--Sch{\"u}tzenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.},
    Address = {Berlin, Heidelberg},
    Author = {Petre, Ion and Salomaa, Arto},
    BookTitle = {Handbook of Weighted Automata},
    Editor = {Droste, Manfred and Kuich, Werner and Vogler, Heiko},
    File = {Algebraic Systems and Pushdown Automata - Petre-Salomaa2009\_Chapter\_AlgebraicSystemsAndPushdownAut - a - w.pdf},
    ISBN = {978-3-642-01492-5},
    Pages = {257--289},
    Publisher = {Springer Berlin Heidelberg},
    Title = {Algebraic Systems and Pushdown Automata},
    URL = {https://doi.org/10.1007/978-3-642-01492-5\_7},
    Year = {2009},
    bdsk-url-1 = {https://doi.org/10.1007/978-3-642-01492-5\_7},
    date-added = {2020-05-14 16:15:07 +0200},
    date-modified = {2020-05-14 16:15:07 +0200},
    doi = {10.1007/978-3-642-01492-5_7}
}

@inbook{Petre2009, Abstract = {We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky--Sch{\"u}tzenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.}, Address = {Berlin, Heidelberg}, Author = {Petre, Ion and Salomaa, Arto}, BookTitle = {Handbook of Weighted Automata}, Editor = {Droste, Manfred and Kuich, Werner and Vogler, Heiko}, File = {Algebraic Systems and Pushdown Automata - Petre-Salomaa2009_Chapter_AlgebraicSystemsAndPushdownAut - a - w.pdf}, ISBN = {978-3-642-01492-5}, Pages = {257--289}, Publisher = {Springer Berlin Heidelberg}, Title = {Algebraic Systems and Pushdown Automata}, URL = {https://doi.org/10.1007/978-3-642-01492-5_7}, Year = {2009}, bdsk-url-1 = {https://doi.org/10.1007/978-3-642-01492-5_7}, date-added = {2020-05-14 16:15:07 +0200}, date-modified = {2020-05-14 16:15:07 +0200}, doi = {10.1007/978-3-642-01492-5_7} }