[Verse 1]
When the machine meets any string at all
Does it halt and give an answer to your call?
If it always stops and tells you yes or no
Then decidable is the way this language flows
Never stuck in endless computation's maze
Always reaching verdict in a finite phase
[Chorus]
Decidable means it halts on every case
Recognizable might vanish without a trace
If the word belongs, it stops and says okay
If it doesn't fit, might loop until doomsday
Both directions need recognition's embrace
For decidable to claim its rightful place
[Verse 2]
Recursively enumerable takes one side
Accepts what's in the language with machine pride
But rejection might just spiral round and round
Never giving you a negative-answer sound
Half the story told with partial guarantee
Missing complement means no decidability
[Chorus]
Decidable means it halts on every case
Recognizable might vanish without a trace
If the word belongs, it stops and says okay
If it doesn't fit, might loop until doomsday
Both directions need recognition's embrace
For decidable to claim its rightful place
[Bridge]
DFA acceptance lives in solvable terrain
Context-free grammars play the same refrain
Emptiness questions get their answers clean
Equivalence testing keeps the record keen
These problems bow to algorithmic might
Decidable domains shining crystal bright
[Outro]
Language and its opposite both recognized
That's the secret to being truly decidable-ized
When both sides halt with verdicts crystal clear
Decidability makes the pathway crystal clear