Mixed Nondeterministic-Probabilistic Automata: Blending graphical probabilistic models with nondeterminism

TL;DR

This paper introduces Mixed Automata, a new model combining nondeterministic and probabilistic automata, unifying graphical probabilistic models with nondeterminism, and supporting composition, simulation, and message passing.

Contribution

It develops a novel automata framework that subsumes both nondeterministic automata and graphical probabilistic models, enabling integrated reasoning and algorithms.

Findings

Mixed Automata can represent Segala's Probabilistic Automata.

Supports parallel composition and message passing.

Unifies nondeterministic and probabilistic reasoning.

Abstract

Graphical models in probability and statistics are a core concept in the area of probabilistic reasoning and probabilistic programming-graphical models include Bayesian networks and factor graphs. In this paper we develop a new model of mixed (nondeterministic/probabilistic) automata that subsumes both nondeterministic automata and graphical probabilistic models. Mixed Automata are equipped with parallel composition, simulation relation, and support message passing algorithms inherited from graphical probabilistic models. Segala's Probabilistic Automatacan be mapped to Mixed Automata.