7 Minimization of DFAs

boogie celtic, havana trap

Listen on 93

Lyrics

[Verse 1]
Two machines that speak the same tongue
Different paths but songs they've sung
Are identical in every way
Equivalent we always say
When languages match perfectly
Though states may differ drastically

[Chorus]
Fill the table, mark the pairs
Find the states that just don't care
About each other's destiny
Distinguishable they'll always be
Minimal and unique it stands
The smallest automaton in your hands

[Verse 2]
Draw a grid of every state
Cross them out when they can't relate
If one accepts and one rejects
Mark that pair, show disrespect
Keep on going, mark some more
Till no new marks can you explore

[Chorus]
Fill the table, mark the pairs
Find the states that just don't care
About each other's destiny
Distinguishable they'll always be
Minimal and unique it stands
The smallest automaton in your hands

[Bridge]
Faster execution waits
Fewer transistors, fewer gates
Memory shrinks when redundance dies
Optimization's greatest prize
Merge the unmarked, keep the rest
Your minimal machine's the best

[Verse 3]
Algorithm guarantees
Uniqueness up to naming sprees
Call them A or call them One
The structure's carved, the work is done
No smaller DFA exists
Mathematics never twists

[Chorus]
Fill the table, mark the pairs
Find the states that just don't care
About each other's destiny
Distinguishable they'll always be
Minimal and unique it stands
The smallest automaton in your hands

[Outro]
Equivalent machines unite
In minimal form, burning bright
Table-filling shows the way
To the leanest DFA

← 6 Non-Regular Languages & the Pumping Lemma | 1 Context-Free Grammars (CFG) →