[Verse 1] Regular languages dancing through the state machine maze Building blocks that stack and merge in mathematically sound ways Take two DFAs and weave their product construction tight Union keeps both paths alive, intersection finds the shared light [Chorus] Five closure properties, they never break apart Union, intersection, complement - that's just the start Concatenation chains them up, Kleene star repeats forever Regular languages stay closed, mathematical endeavor [Verse 2] Complement's the simplest trick when DFA's complete Just flip the accept and reject, make the pattern obsolete But hold your horses with NFAs, they don't play by the same rules Convert to DFA first or you'll be swimming with the fools [Chorus] Five closure properties, they never break apart Union, intersection, complement - that's just the start Concatenation chains them up, Kleene star repeats forever Regular languages stay closed, mathematical endeavor [Bridge] Product construction builds the grid States combine where logic's hid First machine's state meets the second's frame Cartesian pairs in the closure game [Verse 3] Reversal flips the strings around, mirror image of the code Homomorphism maps each symbol down a substitution road Seven operations total but the core five rule the land Regular sets stay regular when these transforms take command [Chorus] Five closure properties, they never break apart Union, intersection, complement - that's just the start Concatenation chains them up, Kleene star repeats forever Regular languages stay closed, mathematical endeavor [Outro] From finite automata to the expressions that we write Closure keeps the family whole, sealed mathematically tight
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