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Formal languages and power series
Proceedings of the third annual ACM symposium on Theory of computing - STOC '71, 1971Section 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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Canadian Mathematical Bulletin, 1971
In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
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In this brief exposition we collect several results on rings of formal power series with coefficients from a field or a ring with some special properties. The results that are catalogued below are mostly algebraic in nature.
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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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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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Inverting Polynomials and Formal Power Series
SIAM Journal on Computing, 1993The problem of inverting a general polynomial of degree $d > 0$, the inverse being a formal power series with coefficients $z_0 ,z_1 ,z_2 , \ldots $ is considered. It is shown that computing $z_0 , \ldots ,z_n $ can be carried out in $n + (2d - 1)\lceil {\log _2 n} \rceil + 2$ nonscalar operations over any infinite field.
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Controllability of (max,+) Formal Power Series
IFAC Proceedings Volumes, 2009Controllability of (max,+) automata and formal power series is studied within a behavioral framework. An extension of classical tensor product of their linear representations as a parallel composition of controller with the plant (max,+) automaton is used.
Komenda, Jan +2 more
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Formal Power Series and B-Series
2010We 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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The American Mathematical Monthly, 1969
(1969). Formal Power Series. The American Mathematical Monthly: Vol. 76, No. 8, pp. 871-889.
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(1969). Formal Power Series. The American Mathematical Monthly: Vol. 76, No. 8, pp. 871-889.
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1993
This chapter discusses a variety of algorithms for manipulating formal power series. Formal power series are infinite power series where we are not concerned with issues of convergence. Thus, both f(t) and g(t) $$ \begin{array}{*{20}{c}} {f\left( t \right) = 1 + t + \frac{{{t^2}}}{{2!}} + \frac{{{t^3}}}{{3!}} + \frac{{{t^4}}}{{4!}} + \cdots ,} \\ {g\
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This chapter discusses a variety of algorithms for manipulating formal power series. Formal power series are infinite power series where we are not concerned with issues of convergence. Thus, both f(t) and g(t) $$ \begin{array}{*{20}{c}} {f\left( t \right) = 1 + t + \frac{{{t^2}}}{{2!}} + \frac{{{t^3}}}{{3!}} + \frac{{{t^4}}}{{4!}} + \cdots ,} \\ {g\
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Schur’s criterion for formal power series
Sbornik: Mathematics, 2019Abstract 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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Some remarks on formal power series and formal Laurent series
Mathematica Slovaca, 2017Abstract In this article we consider the topology on the set of formal Laurent series induced by the ultrametric defined via the order. In particular, we establish that the product of formal Laurent series, considered in [GAN, X. X.—BUGAJEWSKI, D.:On formal Laurent series, Bull. Braz. Math. Soc. 42 (2011), 415–437], is not continuous. We
Dariusz Bugajewski, Xiao-Xiong Gan
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