Semirings, automata, languages
Semirings, automata, languages
Algorithms for determining relative star height and star height
Information and Computation
Rational series and their languages
Rational series and their languages
Semirings and formal power series: their relevance to formal languages and automata
Handbook of formal languages, vol. 1
Automata, Boolean matrices, and ultimate periodicity
Information and Computation
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
Methods and Applications of (MAX, +) Linear Algebra
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Regularity preserving functions
ACM SIGACT News
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Formal power series are an extension of formal languages. Recognizable formal power series can be captured by the so-called weighted finite automata, generalizing finite state machines. In this paper, motivated by codings of formal languages, we introduce and investigate two types of transformations for formal power series. We characterize when these transformations preserve rationality, generalizing the recent results of Zhang [15] to the formal power series setting. We show, for example, that the "square-root" operation, while preserving regularity for formal languages, preserves rationality for formal power series when the underlying semiring is commutative or locally finite, but not in general.