On probabilistic analog automata

TL;DR

This paper investigates probabilistic automata on general state spaces, showing that under mild conditions, their computational power is limited to recognizing regular languages, thus connecting models of probabilistic and analog computation.

Contribution

It generalizes Rabin's reduction theorem to probabilistic automata on general state spaces, establishing limitations on their computational power.

Findings

Automata recognize only regular languages under mild conditions

Generalization of Rabin's reduction theorem

Limits of analog and probabilistic computation models

Abstract

We consider probabilistic automata on a general state space and study their computational power. The model is based on the concept of language recognition by probabilistic automata due to Rabin and models of analog computation in a noisy environment suggested by Maass and Orponen, and Maass and Sontag. Our main result is a generalization of Rabin's reduction theorem that implies that under very mild conditions, the computational power of the automaton is limited to regular languages.