Pushing undecidability of the isolation problem for probabilistic automata

TL;DR

This paper proves that the isolation problem remains undecidable even for probabilistic automata with only one probabilistic transition, by developing a simulation technique that reduces general cases to this restricted form.

Contribution

It introduces a novel simulation method demonstrating the undecidability of the isolation problem for a restricted class of probabilistic automata.

Findings

Undecidability of the isolation problem for automata with one probabilistic transition

Development of a simulation technique for automata reduction

Extension of known undecidability results to more restricted automata classes

Abstract

This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on the number of probabilistic transitions. In this note, we develop a simulation technique that allows to simulate any probabilistic automaton with one having only one probabilistic transition.