TABLE I.

Summary of Notations.

U	The set of users in the database
i	The i-th user where i ∈ [1, |U|]
loc	Value domain {loc1, …, locn} of all user’s data
$l_i^t,l_i^t\prime$	The data of user i at time t, $l_i^t\in \mathit{loc}$, $l_i^t\ne l_i^t\prime$
Dt	The database at time t, $D^t=\{l_1^t,\dots ,l_n^t\}$
ℳt	Differentially private mechanism over Dt
rt	Differentially private output at time t
Ai	The adversary who targets user i, considered in traditional DP
$A_i^{\mathcal{T}}$	Adversary Ai with additional knowledge of temporal correlations
$P_i^B$	Transition matrix that represents $\mathrm{Pr}(l_i^{t-1}|l_i^t)$, i.e., backward temporal correlation, known to $A_i^{\mathcal{T}}$
$P_i^F$	Transition matrix that represents $\mathrm{Pr}(l_i^t|l_i^{t-1})$, i.e., forward temporal correlation, known to $A_i^{\mathcal{T}}$
$D_{\mathcal{K}}^t$	The subset of database $D^t-\{l_i^t\}$, known to $A_i^{\mathcal{T}}$