Convex Language Semantics for Nondeterministic Probabilistic Automata

TL;DR

This paper investigates the semantics of automata that combine nondeterminism and probability, revealing their expressive power, undecidability issues, and proposing a computable metric for approximate analysis.

Contribution

It identifies two natural semantics for nondeterministic probabilistic automata, compares their expressiveness, and introduces a computable discounted metric for language similarity.

Findings

Two natural semantics are identified for nondeterministic probabilistic automata.

These automata are more expressive than deterministic probabilistic automata.

Language equivalence checking is undecidable, but a computable metric is provided.

Abstract

We explore language semantics for automata combining probabilistic and nondeterministic behavior. We first show that there are precisely two natural semantics for probabilistic automata with nondeterminism. For both choices, we show that these automata are strictly more expressive than deterministic probabilistic automata, and we prove that the problem of checking language equivalence is undecidable by reduction from the threshold problem. However, we provide a discounted metric that can be computed to arbitrarily high precision.