On the Succinctness of Good-for-MDPs Automata

TL;DR

This paper investigates the succinctness differences among classes of nondeterministic automata, establishing exponential gaps between good-for-MDPs, good-for-games, and general nondeterministic automata, even under certain restrictions.

Contribution

It proves that the size gaps between good-for-MDPs and good-for-games automata, as well as between nondeterministic automata and good-for-MDPs, are exponential, including restricted automata classes.

Findings

Exponential size gap between good-for-MDPs and good-for-games automata.

Exponential size gap between nondeterministic automata and good-for-MDPs.

Gaps remain exponential under restrictions to separating safety or unambiguous reachability automata.

Abstract

Good-for-MDPs and good-for-games automata are two recent classes of nondeterministic automata that reside between general nondeterministic and deterministic automata. Deterministic automata are good-for-games, and good-for-games automata are good-for-MDPs, but not vice versa. One of the question this raises is how these classes relate in terms of succinctness. Good-for-games automata are known to be exponentially more succinct than deterministic automata, but the gap between good-for-MDPs and good-for-games automata as well as the gap between ordinary nondeterministic automata and those that are good-for-MDPs have been open. We establish that these gaps are exponential, and sharpen this result by showing that the latter gap remains exponential when restricting the nondeterministic automata to separating safety or unambiguous reachability automata.