  Parikh automata on finite words were first introduced by Klaedtke and
Rue{\ss} [Automata, Languages and Programming, 2003]. In this paper, we
introduce several variants of Parikh automata on infinite words and study their
expressiveness. We show that one of our new models is equivalent to synchronous
blind counter machines introduced by Fernau and Stiebe [Fundamenta
Informaticae, 2008]. All our models admit {\epsilon}-elimination, which to the
best of our knowledge is an open question for blind counter automata. We then
study the classical decision problems of the new automata models.
