Book Review: Automata-theoretic aspects of formal power series
نویسندگان
چکیده
منابع مشابه
ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملHYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملOn the Hurwitz Product of Formal Power Series and Automata
Kiister, G., On the Hurwitz product of formal power series and automata, Theoretical Computer Science 83 (1991) 261-273. The Hurwitz (shuffle) product defined on formal power series is generalized to matrices and therefore to automata. The resulting constructions are then used to study commutative power series and abstract families of power series. In particular, the families of power series re...
متن کاملFormal Power Series
with coefficients ak ∈ C (k ∈ Z ) are important in many branches of mathematics. Maple supports the computation of truncated series with its series command, and through the powerseries package [6] infinite series are available. In the latter case, the series is represented as a table of coefficients that have already been determined together with a function for computing additional coefficients...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1979
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1979-14660-3