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Then there's Moore's algorithm which flags obviously non-equivalent nodes, before propagating those flags backwards. Any pairs of nodes not flagged afterwords are merged as equivalent. Has poor performance in some degenerate cases, & seemingly isn't well documented.

Or there's Brzozowski's Algorithm, though I wouldn't recommend it on a commodity PC. At least not yet.
I did use it as a core component in my hardware-browser hypothetical, to which it was well suited!

4/4 on DFA Minimization!