In [6], we introduced a class data automata, called Predicate Automata, which recognize languages over an alphabet \(\varSigma \times \mathbb {N}\) where \(\varSigma \) is a finite alphabet. These automata were designed to capture the behaviour of parametrized programs, i.e. programs with an unbounded number of threads, and their correctness proofs. Since the focus of [6] was on the verification problem, the paper does not investigate the properties of these automata beyond the minimum which is necessary for the verification problem. In this paper, we study some of their key properties and relate them to other classes of data automata.