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On synchronization of partial automata (2004.08801v2)
Published 19 Apr 2020 in cs.FL and cs.DM
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 $\Omega(d{\frac{n}{d}})$.