Automata and the arithmetic of formal power series
نویسندگان
چکیده
منابع مشابه
On 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...
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The aim of this paper is to use formal power series techniques to study the structure of small arithmetic complexity classes such as GapNC and GapL. More precisely, we apply the Kleene closure of languages and the formal power series operations of inversion and root extraction to these complexity classes. We define a counting version of Kleene closure and show that it is intimately related to i...
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Pierre McKenzie and Sambuddha Roy pointed out that the proof of statements (b) and (c) in Theorem 7.3 are buggy. The main flaw is that the identity e of the group F may not be the identity of the monoid, and so the claim that w ∈ (A F,r) * ⇐⇒ w ∈ Test does not work. In this corrigendum, we show: • With a slight change to Definition 7.1, the statement of Theorem 7.3 holds unchanged. In our opini...
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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...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1986
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-46-3-211-214