The averaging trick and the Cerny conjecture

TL;DR

This paper introduces the averaging trick, a simple yet powerful idea that unifies and simplifies the derivation of results related to the Černý conjecture in automata theory.

Contribution

It formalizes the averaging trick as a proof scheme, providing a new axiomatic framework that explains its implicit use in existing literature.

Findings

Unifies multiple results on the Černý conjecture

Provides an axiomatic formalization of the averaging trick

Simplifies proofs in automata theory

Abstract

The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof scheme axiomatically. Instead, authors axiomatized classes of automata to which it applies.