Congruences for Stochastic Automata

TL;DR

This paper develops a framework for congruences in stochastic automata, constructing and analyzing factor automata over analytic spaces, with a focus on behavior under finite and infinite streams.

Contribution

It introduces a novel approach to factor automata via multi-part congruences, extending the theory to stochastic automata over analytic spaces.

Findings

Congruences can be decomposed into multiple parts for automata factoring.

Factor automata can be constructed over analytic spaces.

Behavior under finite and infinite streams is characterized.

Abstract

Congruences for stochastic automata are defined, the correspondin factor automata are constructed and investigated for automata ove analytic spaces. We study the behavior under finite and infinite streams. Congruences consist of multiple parts, it is shown that factoring can be done in multiple steps, guided by these parts.