Distributed Graph Automata

TL;DR

This paper introduces a new class of distributed finite graph automata that recognize graph languages definable in monadic second-order logic, generalizing finite automata to graphs and establishing a hierarchy of automata variants.

Contribution

It presents a novel class of distributed graph automata that generalize finite automata to graphs and explores their expressive power and decidability properties.

Findings

Automata recognize exactly monadic second-order definable graph languages.

Hierarchy of automata variants with differing expressive powers.

Decidability of the emptiness problem for weaker automata variants.

Abstract

Inspired by distributed algorithms, we introduce a new class of finite graph automata that recognize precisely the graph languages definable in monadic second-order logic. For the cases of words and trees, it has been long known that the regular languages are precisely those definable in monadic second-order logic. In this regard, the automata proposed in the present work can be seen, to some extent, as a generalization of finite automata to graphs. Furthermore, we show that, unlike for finite automata on words and trees, the deterministic, nondeterministic and alternating variants of our automata form a strict hierarchy with respect to their expressive power. For the weaker variants, the emptiness problem is decidable.