When a Little Nondeterminism Goes a Long Way

Abstract

History-deterministic automata are an intermediate automata model, in between deterministic and nondeterministic ones. An automaton is history-deterministic if its nondeterminism can be resolved on-the-fly, by only taking into account the prefix of the word read so far. This restricted form of nondeterminism yields a class of automata that retains some of the algorithmic properties of deterministic automata, while also enjoying some of the power of nondeterminism. History-determinism has received a lot of attention in the past few years and this article surveys some of the recent developments on the topic. It aims to showcase some of the key constructions and techniques involved in this line of research, while remaining fairly informal. We begin with a roughly chronological overview of research on history-determinism, intended as a quick reference to some of the main results on the subject. We then move onto a more detailed discussion of what are, in our view, the key aspects of history-determinism, highlighting throughout questions that remain open. Like any survey written on a topic that is actively worked on, this article aspires to be out-of-date as soon as it is published. We hope that it will remain useful as a gentle, if incomplete, introduction to the topic.