Parikh Automata on Infinite Words

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.