Rational series and their languages
Rational series and their languages
Varieties of formal series on trees and Eilenberg's theorem
Information Processing Letters
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 3
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata, Languages, and Machines
Varieties Of Formal Languages
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Journal of Automata, Languages and Combinatorics - Special issue: Selected papers of the workshop weighted automata: Theory and applications (Dresden University of Technology (Germany), March 4-8, 2002)
Positive varieties of tree languages
Theoretical Computer Science
Definable transductions and weighted logics for texts
DLT'07 Proceedings of the 11th international conference on Developments in language theory
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We introduce varieties of recognizable @S-tree series (K@S-VTS for short) over a field K and a ranked alphabet @S. Our variety theorem establishes a bijective correspondence between these K@S-VTSs and the varieties of finite-dimensional K@S-algebras (K@S-VFDA for short); a K@S-algebra is a K-vector space equipped with multilinear @S-operations. The link between K@S-VTSs and K@S-VFDAs is provided by the syntactic K@S-algebras of tree series. The most immediate predecessors of this study are Berstel's and Reutenauer's (1982) [2] work on tree series over fields, Reutenauer's (1980) [27] theory of varieties of string series, Bozapalidis' and his associates (1983, 1989, 1991) [8,5,4] work on syntactic K@S-algebras, Steinby's (1979, 1992) [30,31] theory of varieties of tree languages, and our previous work (2009) on series of general algebras and their syntactic K@S-algebras.