Parikh Automata on Finite and Infinite Words

We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as well as the non-deterministic variants and study closure properties, expressiveness, and common decision problems with applications to model checking. Furthermore, we compare our models to other models with counting mechanisms operating on infinite words.