On synchronization of partial automata

Abstract

A goal of this paper is to introduce the new construction of an automaton with shortest synchronizing word of length $O(d^{\frac{n}{d}})$, where $d\in \mathbb{N}$ and $n$ is the number of states for that automaton. Additionally we introduce new transformation from any synchronizable DFA or carefully synchronizable PFA of $n$ states to carefully synchronizable PFA of $d\cdot n$ states with shortest synchronizing word of length $\Omega (d^{\frac{n}{d}})$.

9 pages, 1 figures