TABLE 1.

Summary of Notations

U	The set of users in the database
i	The ith 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, $l_i^t\in loc$, $l_i^t\ne l_i^{t^{\prime }}$
Dt	The database at time t, $D^t=\left\{l_1^t,\mathrm{\dots },l_n^t\right\}$
${\mathcal{M}}^t$	Differentially private mechanism over Dt
rt	Differentially private output at time t
Ai	Adversary who targets user i without temporal correlations
$A_i^{\mathcal{T}}$	Adversary Ai with temporal correlations
$P_i^B$	Transition matrix that represents $\mathrm{Pr}\left(l_i^{t-1}|l_i^t\right)$, i.e., backward temporal correlation, known to $A_i^{\mathcal{T}}$
$P_i^F$	Transition matrix that represents $\mathrm{Pr}\left(l_i^t|l_i^{t-1}\right)$, i.e., forward temporal correlation, known to $A_i^{\mathcal{T}}$
$D_{\mathcal{K}}^t$	The subset of database $D^t-\left\{l_i^t\right\}$ known to $A_i^{\mathcal{T}}$