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I write paper and I want to distinguish between the class of decision problems which can be decided in polynomial time and the class functions which can be computed in polynomial time. The first is just written as $\mathrm{P}$ or $\mathrm{PTIME}$, right? Can the latter be denoted as $m^{\mathcal{O}(1)}$ or is this a confusing definition?

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    $\begingroup$ $m^{O(1)}$ just denotes functions of polynomial growth rate, so that would be indeed confusing. The class you are looking for us usually denoted $\mathsf{FP}$. $\endgroup$ – Jan Johannsen Nov 12 '12 at 17:11
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    $\begingroup$ @JanJohannsen maybe make this an answer ? $\endgroup$ – Suresh Venkat Nov 12 '12 at 19:07
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    $\begingroup$ I guess this is more fitting for cs.stackexchange.com $\endgroup$ – funkstar Nov 14 '12 at 8:01
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The notation $m^{O(1)}$ just denotes the set of functions of polynomial growth rate, so that would be indeed confusing. The class of functions computable in polynomial time is usually denoted $\mathsf{FP}$.

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