Arithmetic Complexity, Kleene Closure, and Formal Power Series
نویسندگان
چکیده
منابع مشابه
Corrigendum for Arithmetic Complexity, Kleene Closure, and Formal Power Series
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...
متن کاملArithmetic Complexity, Kleene Closure, and Formal Power Series
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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We investigate the theory of skew (formal) power series introduced by Droste, Kuske [5, 6], if the basic semiring is a Conway semiring. This yields Kleene Theorems for skew power series, whose supports contain finite and infinite words. We then develop a theory of convergence in semirings of skew power series based on the discrete convergence. As an application this yields a Kleene Theorem prov...
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We prove that the automaton presented by Maslov [Soviet Math. Doklady 11, 1373–1375 (1970)] meets the upper bound 3/4 · 2n on the state complexity of Kleene closure. This fixes a small error in this paper that claimed the upper bound 3/4 · 2n − 1. Our main result shows that the upper bounds 2n−1 + 2n−1−k on the state complexity of Kleene closure of a language accepted by an n-state DFA with k f...
متن کاملALGEBRAIC 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)
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ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2003
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-003-1077-7