Parikh Automata on Infinite Words

TL;DR

This paper introduces variants of Parikh automata on infinite words, explores their expressiveness, establishes equivalences with existing models, and addresses open problems like epsilon-elimination.

Contribution

The paper presents new variants of Parikh automata on infinite words, proves their equivalence to known models, and solves the epsilon-elimination problem for these automata.

Findings

One model is equivalent to synchronous blind counter machines.

All models admit epsilon-elimination.

Addresses classical decision problems for the new automata.

Abstract

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.