We consider the problem of checking the differential privacy of online
randomized algorithms that process a stream of inputs and produce outputs
corresponding to each input. This paper generalizes an automaton model called
DiP automata (See arXiv:2104.14519) to describe such algorithms by allowing
multiple real-valued storage variables. A DiP automaton is a parametric
automaton whose behavior depends on the privacy budget 系. An automaton
A will be said to be differentially private if, for some D, the
automaton is D系-differentially private for all values of
系>0. We identify a precise characterization of the class of all
differentially private DiP automata. We show that the problem of determining if
a given DiP automaton belongs to this class is PSPACE-complete. Our PSPACE
algorithm also computes a value for D when the given automaton is
differentially private. The algorithm has been implemented, and experiments
demonstrating its effectiveness are presented