On the equality problem of finitely generated classes of exponentially-polynomial functions

IF 0.3 Q4 MATHEMATICS, APPLIED
S. Marchenkov
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引用次数: 0

Abstract

Abstract We consider the class EPℕ of exponentially-polynomial functions which can be obtained by arbitrary superpositions of the constants 0, 1 and arithmetic operations of addition, multiplication, and powering. For this class, we solve the algorithmic equality problem of two functions that assume a finite number of values. Next, this class is restricted to the class PEPℕ, in which the function xy is replaced by a sequence of functions { pix $\begin{array}{} \displaystyle p_i^x \end{array}$}, where p0, p1, … are all prime numbers. For the class PEPℕ, the problem of membership of a function to a finitely generated class is effectively reduced to the equality problem of two functions. In turn, the last problem is effectively solved for the set of all one-place PEPℕ-functions.
有限生成类指数多项式函数的等式问题
摘要考虑一类指数多项式函数ep_1,该类函数可由常数0、1的任意叠加和加法、乘法、乘幂等算术运算得到。对于这门课,我们解决了两个假设有限个数的函数的算法等式问题。接下来,该类被限制为类PEP∈,其中函数xy被函数序列{pix$\begin{array}{} \displaystyle p_i^x \end{array}$}取代,其中p0, p1,…都是素数。对于PEP类,将函数与有限生成类的隶属关系问题有效地简化为两个函数的相等问题。反过来,最后一个问题有效地解决了所有单位PEP -函数的集合。
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来源期刊
CiteScore
0.60
自引率
20.00%
发文量
29
期刊介绍: The aim of this journal is to provide the latest information on the development of discrete mathematics in the former USSR to a world-wide readership. The journal will contain papers from the Russian-language journal Diskretnaya Matematika, the only journal of the Russian Academy of Sciences devoted to this field of mathematics. Discrete Mathematics and Applications will cover various subjects in the fields such as combinatorial analysis, graph theory, functional systems theory, cryptology, coding, probabilistic problems of discrete mathematics, algorithms and their complexity, combinatorial and computational problems of number theory and of algebra.
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