# Slowly synchronizing DFAs of 7 states and maximal slowly synchronizing DFAs

## TL;DR

This paper exhaustively analyzes 7-state synchronizing deterministic finite automata (DFAs), identifying those with maximal synchronization lengths and exploring alphabet size ranges for various classes of these automata.

## Contribution

It provides a comprehensive enumeration of 7-state synchronizing DFAs with high synchronization lengths and characterizes alphabet size bounds for different DFA categories.

## Key findings

- All 7-state synchronizing DFAs with length >= 29 are computed.
- Alphabet size ranges for maximal, minimal, and semi-minimal DFAs with up to 7 states are determined.
- Maximal synchronizing DFAs with 7 states are characterized.

## Abstract

We compute all synchronizing DFAs with 7 states and synchronization length >= 29. Furthermore, we compute alphabet size ranges for maximal, minimal and semi-minimal synchronizing DFAs with up to 7 states.