Counting the number of inequivalent arithmetic expressions on n variables
CoRR(2024)
摘要
An expression is any mathematical formula that contains certain formal
variables and operations to be executed in a specified order. In computer
science, it is usually convenient to represent each expression in the form of
an expression tree. Here, we consider only arithmetic expressions, i.e., those
that contain only the four standard arithmetic operations: addition,
subtraction, multiplication and division, alongside additive inversion. We
first provide certain theoretical results concerning the equivalence of such
expressions and then disclose a Θ(n^2) algorithm that computes the
number of inequivalent arithmetic expressions on n distinct variables.
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