The Parikh finite word automaton model (PA) was introduced and studied by Klaedtke and Ruess in 2003. Here, by means of related models, it is shown that the bounded languages recognized by PA are the same as those recognized by deterministic PA. Moreover, this class of languages is the class of bounded languages whose set of iterations is semilinear.
@article{arxiv.1108.3625,
title = {Bounded Parikh Automata},
author = {Michaël Cadilhac and Alain Finkel and Pierre McKenzie},
journal= {arXiv preprint arXiv:1108.3625},
year = {2011}
}