[Verse 1]
There's a question that keeps us awake at night
A puzzle that's haunted us decades now
P and NP dancing in the light
Computer science asking why and how
P means polynomial time to solve
While NP verifies in that same speed
Can we make that solving gap dissolve
Or is there something more that we need
[Chorus]
P versus NP, the million dollar mystery
Can quick checking mean quick solving too
P versus NP, rewriting history
If they're equal then computing breaks right through
But most believe they're not the same
P not equal NP in this game
[Verse 2]
Imagine you're checking a massive maze
Someone claims they found the exit route
You can trace their path in polynomial days
But finding it yourself might take a brute
Force search through every possible way
That's the gap between the two we see
Verification versus discovery
The heart of computational theory
[Chorus]
P versus NP, the million dollar mystery
Can quick checking mean quick solving too
P versus NP, rewriting history
If they're equal then computing breaks right through
But most believe they're not the same
P not equal NP in this game
[Bridge]
Traveling salesman seeks the shortest road
Boolean satisfiability calls
Knapsack problems with their heavy load
All NP complete behind these walls
If one falls quickly then they all fall down
That's the beauty of reduction's crown
[Verse 3]
Clay Institute offers their reward
One million for the proof that's sound
But forty years of searching toward
This answer and it still can't be found
The asymmetry feels so real
Between the checking and the search
Yet proof remains beyond our reach
Still standing at complexity's church
[Chorus]
P versus NP, the million dollar mystery
Can quick checking mean quick solving too
P versus NP, rewriting history
If they're equal then computing breaks right through
But most believe they're not the same
P not equal NP in this game
[Outro]
So the question stands for you and me
In the realm of possibility
P versus NP