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Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}

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and a minimum-error decision time is Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}. Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives:

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TdecT_{\rm dec}

Symbol T_rm dec

TrT_rm dec is part of the quantity the equation computes from the expression on the right.

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IdecI_{\rm dec}

Symbol I_rm dec

IrI_rm dec is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}.T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}.

Equation 19 · Evolutionary Physics

How Fast Can a Horizon Learn Which Path You Took?

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

and a minimum-error decision time is Tdec(δ)=inf⁡{T:Idec(T)≥1−δ}T_{\rm dec}(\delta)= \inf\{T:I_{\rm dec}(T)\geq1-\delta\}. Both are deterministic transformations of the assumed overlap law. Neither is a new field-theory result. Numerically inverting the two binary-entropy equations gives:

Meanings in this article

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