# A new lower bound for reset threshold of synchronizing automata with sink state

## TL;DR

This paper introduces a new series of binary automata with sink states that have a higher reset threshold than previously known, advancing the understanding of synchronization complexity.

## Contribution

It provides a new lower bound for the reset threshold of binary synchronizing automata with sink states, improving prior results.

## Key findings

- Reset threshold of the automata is n^2/4 + 2n - 9.
- The new lower bound surpasses previous bounds for binary automata with sink states.
- The series of automata demonstrates slow synchronization with higher thresholds.

## Abstract

We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the maximum reset threshold of binary synchronizing $n$-state automata with sink state.