From bfb34379041d0e88253c6579674b9184fb412974 Mon Sep 17 00:00:00 2001 From: Manos Date: Sun, 19 Sep 2021 23:39:57 +0200 Subject: [PATCH] thething: Reviewed pf:thething-prv --- text/problem/thething/problem.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/text/problem/thething/problem.tex b/text/problem/thething/problem.tex index 319dcbf..ecd167c 100644 --- a/text/problem/thething/problem.tex +++ b/text/problem/thething/problem.tex @@ -173,11 +173,11 @@ Theorem~\ref{theor:thething-prv} proposes how to achieve the desired privacy for % Due to space constraints, we omit the proof of Theorem~\ref{theor:thething-prv} and defer it for a longer version of this paper. \begin{proof} \label{pf:thething-prv} - All mechanisms use independent randomness, and therefore for a series of events $S_T = {D_1, \dots, D_T}$ and outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$ it holds that + All mechanisms use independent randomness, and therefore for a time series $S_T = {D_1, \dots, D_T}$ and outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$ it holds that $$Pr[\mathcal{M}(S_T) = (\pmb{o}_1, \dots, \pmb{o}_T)] = \prod_{i \in [1, T]} Pr[\mathcal{M}_i(D_i) = \pmb{o}_i]$$ - Likewise, for any {\thething}-neighboring series of events $S'_T$ of $S_T$ with the same outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$ + Likewise, for any {\thething}-neighboring time series $S'_T$ of $S_T$ with the same outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$ $$Pr[\mathcal{M}(S'_T) = (\pmb{o}_1, \dots, \pmb{o}_T)] = \prod_{i \in [1, T]} Pr[\mathcal{M}_i(D'_i) = \pmb{o}_i]$$