Two Recursively Inseparable Problems for Probabilistic Automata

TL;DR

This paper explores decision problems for numberless probabilistic automata, revealing two properties that are recursively inseparable, thus highlighting fundamental limits in analyzing these automata.

Contribution

It introduces the concept of numberless probabilistic automata and proves the recursive inseparability of two key properties related to their values.

Findings

Properties are recursively inseparable

Highlights limits of decision procedures

Advances understanding of probabilistic automata complexity

Abstract

This paper introduces and investigates decision problems for numberless probabilistic automata, i.e. probabilistic automata where the support of each probabilistic transitions is specified, but the exact values of the probabilities are not. A numberless probabilistic automaton can be instantiated into a probabilistic automaton by specifying the exact values of the non-zero probabilistic transitions. We show that the two following properties of numberless probabilistic automata are recursively inseparable: - all instances of the numberless automaton have value 1, - no instance of the numberless automaton has value 1.