Results 261 to 270 of about 210,142 (295)

Semirings of Formal Power Series

Southeast Asian Bulletin of Mathematics, 2000
Let \((S,+,\cdot)\) be an additively commutative semiring with absorbing zero 0 and identity \(1\not=0\). An element \(a\in S\) is called semi-invertible if there are \(s,t\in S\) such that \(1+ra=sa\) and \(1+ar=as\). The set \(U\) of all semi-invertible elements of \(S\) is a subsemigroup of \((S,\cdot)\), \(M=S\setminus U\) is the union of all ...
Adhikari, M. R., Sen, M. K.
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Formal Power Series

Journal of Automated Reasoning, 2010
This paper presents a formalization of the topological ring of formal power series in \texttt{Isabelle/HOL}. The following constructions are formalized: division, the formal derivative, various basic manipulations on formal power series (shifting, differentiating, general convolutions and powers), as well as radicals, composition and reverses.
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Schützenberger’s theorem on formal power series follows from Kleene’s theorem

Theoretical Computer Science, 2008
We derive Schützenberger’s characterisation of the set of recognizable formal power series as a formal corollary from Kleene’s characterisation of the set of regular ...
Dietrich Kuske
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Formal languages and power series

Proceedings of the third annual ACM symposium on Theory of computing - STOC '71, 1971
Section 1 of this paper presents the basic mathematical definitions for our work. Section 2 defines the notion of a weighted phrase-structure grammar over either a semiring or zero monoid coefficient structure. The notion of canonical derivations (from Griffiths [1968]) and top-down derivations is defined in section 3, along with some of their basic ...
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Formal Power Series

2011
This chapter is somewhat different from the other chapters in this book. It contains not many symbolic sums, hardly any recurrence equations, and only few asymptotic estimates. We provide here the algebraic background on which the notion of a generating function rests.
Manuel Kauers, Peter Paule
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Schur’s criterion for formal power series

Sbornik: Mathematics, 2019
Abstract A criterion for when a formal power series can be represented by a formal Schur continued fraction is stated. The proof proposed is based on a relationship, revealed here, between Hankel two-point determinants of a series and its Schur determinants. Bibliography: 10 titles.
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Formal Power Series and B-Series

2010
We study vector fields, their associated dynamical systems and phase flows together with their algorithmic approximations in R N from the formal power series approach.
Kang Feng, Mengzhao Qin
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Formal Power Series

The American Mathematical Monthly, 1969
(1969). Formal Power Series. The American Mathematical Monthly: Vol. 76, No. 8, pp. 871-889.
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Rational Transformations of Formal Power Series

2001
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.
Manfred Droste, Guo-Qiang Zhang 0001
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Lazy multiplication of formal power series

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97, 1997
For most fast algorithms to manipulate formal power series, a fast multiplication algorithm is essential. If one desires to compute all coe cients of a product of two power series up to a given order, then several e cient algorithms are available, such as fast Fourier multiplication.
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