On the synchronization of planar automata

TL;DR

This paper investigates the role of planar automata in understanding the synchronization problem of deterministic finite automata, providing evidence that planar automata may reflect the general difficulty of the problem.

Contribution

It offers evidence supporting the conjecture that cerny's conjecture holds if and only if it holds for planar automata, highlighting their representativeness in synchronization complexity.

Findings

Planar automata are representative of the algorithmic hardness of synchronization.

Evidence supports the conjecture linking cerny's conjecture to planar automata.

The class of planar automata may be key to understanding the general synchronization problem.

Abstract

Planar automata seems to be representative of the synchronizing behavior of deterministic finite state automata. We conjecture that \v{C}erny's conjecture holds true, if and only if, it holds true for planar automata. In this paper we have gathered some evidence concerning this conjecture. This evidence amounts to show that the class of planar automata is representative of the algorithmic hardness of synchronization