thething: Reviwed def:thething-prv

text/problem/thething/problem.tex

@@ -139,8 +139,8 @@ We proceed to propose \emph{{\thething} privacy}, a configurable variation of di
 \begin{definition}
   % [{\Thething} privacy]
   \label{def:thething-prv}
-  Let $\mathcal{M}$ be a privacy mechanism with range $\mathcal{O}$ and domain $\mathcal{S}_T$ being the set of all  time series with length $|T|$, where $T$ is a sequence of timestamps.
-  $\mathcal{M}$ satisfies {\thething} $\varepsilon$-differential privacy (or, simply, {\thething} privacy) if for all sets $O \subseteq \mathcal{O}$, and for every pair of {\thething}-neighboring time series $S_T$, $S_T'$,
+  Let $\mathcal{M}$ be a privacy mechanism with range $\mathcal{O}$ that takes as input a time series.
+  We say that $\mathcal{M}$ satisfies {\thething} $\varepsilon$-differential privacy (or, simply, {\thething} privacy) if for all sets of possible outputs $O \subseteq \mathcal{O}$, and for every pair of {\thething}-neighboring time series $S_T$, $S_T'$,
   % and all $T = (t)_{t \in \mathbb{N}}$, 
   it holds that
   $$Pr[\mathcal{M}(S_T) \in O] \leq e^\varepsilon Pr[\mathcal{M}(S_T') \in O]$$