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- W2950613500 abstract "Let $F$ be the set of functions from an infinite set, $S$, to an ordered ring, $R$. For $f$, $g$, and $h$ in $F$, the assertion $f = g + O(h)$ means that for some constant $C$, $|f(x) - g(x)| leq C |h(x)|$ for every $x$ in $S$. Let $L$ be the first-order language with variables ranging over such functions, symbols for $0, +, -, min, max$, and absolute value, and a ternary relation $f = g + O(h)$. We show that the set of quantifier-free formulas in this language that are valid in the intended class of interpretations is decidable, and does not depend on the underlying set, $S$, or the ordered ring, $R$. If $R$ is a subfield of the real numbers, we can add a constant 1 function, as well as multiplication by constants from any computable subfield. We obtain further decidability results for certain situations in which one adds symbols denoting the elements of a fixed sequence of functions of strictly increasing rates of growth." @default.
- W2950613500 created "2019-06-27" @default.
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- W2950613500 date "2007-01-10" @default.
- W2950613500 modified "2023-09-27" @default.
- W2950613500 title "A decision procedure for linear big O equations" @default.
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