The Parikh automaton model equips a finite automaton with integer registers and imposes a semilinear constraint on the set of their final settings. Here the theory of typed monoids is used to characterize the language classes that arise algebraically. Complexity bounds are derived, such as containment of the unambiguous Parikh automata languages in NC1. Noting that DetAPA languages are positive supports of rational Z-series, DetAPA are further shown stronger than Parikh automata on unary langages. This suggests unary DetAPA languages as candidates for separating the two better known variants of uniform NC1.