PPAD (complexity)
In computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of TFNP based on functions that can be shown to be total by a parity argument. The class attracted significant attention in the field of algorithmic game theory because it contains the problem of computing a Nash equilibrium, and this problem was shown by Chen and Deng in 2005 to be complete for the class.
PPAD is a class of problems that are believed to be hard, but obtaining PPAD-completeness is a weaker evidence of intractability than that of obtaining NP-completeness. PPAD problems cannot be NP-complete, for the technical reason that NP is a class of decision problems, but the answer of PPAD problems is always yes, as a solution is known to exist, even though it might be hard to find that solution. It could still be the case that PPAD is the same class as P, and still have that P 
NP, though it seems unlikely. Examples of PPAD-complete problems include finding Nash equilibria, Brouwer and Borsuk-Ulam fixpoints, finding Arrow-Debreu equilibria in markets and more. The Ham sandwich theorem is known to lie in PPAD but it remains an open question as to whether or not it is PPAD-complete.
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Boom
by: P.O.D.Push up
Haha, I never knew that a kid like me
Could take his mic around the world
(World)
Flash the big S.D.
And rock the masses
From Madrid to Calabasas
Tijuana, Mexico
Bootleg demos in Tokyo
Say they know me though
'Cause I'll be puttin' in work
Commit my life to rebirth
Well respected, 'cause that's my word
And I'm sure you heard
(Heard)
'Bout a new sound goin' 'round
She might have left my hood
But she was born in my town
You didn't know, thought we was new on the scene
(Well it's alright, it's alright)
I know you know, I see you smilin' at me
(Well it's alright, it's alright)
Boom!
Here comes the
Boom!
Ready or not?
Here comes the boys from the South
Boom!
Here comes the
Boom!
Ready or not?
How you like me now?, I say
We rep the South
So what you talkin' 'bout?
I'm not runnin' off my mouth
I know this without a doubt
'Cause if you know these streets
Then these streets know you
An' when it's time to handle business
Then you know what to do
(What to do)
Me and my crew
We stay true, old skool or new
Many were called
But the chosen are few
(We are few)
We rise to the top
What you want, just in case you forgot
Rush the stage, grab my mic
Show me what you got?
You didn't know, thought we was new on the scene
(Well it's alright, it's alright)
I know you know, I see you smiling at me
(Well it's alright, it's alright)
Boom!
Here comes the
Boom!
Ready or not?
Here comes the boys from the South
Boom!
Here comes the
Boom!
Ready or not ?
How you like me now?, I say
Boom!
Here comes the
Boom!
Ready or not?
Here comes the boys from the South
Boom!
Here comes the
Boom!
Ready or not?
How you like me now?
Is that all you got?, haha
I'll take your best shot
Is that all you got?, ha ha
I'll take your best shot
Is that all you got?, I'll take your best shot
Is that all you got?, I'll take your best shot
Is that all you got?, I'll take your best shot
I'll take your best shot, I'll take your best shot
Is that all you got?
(Well it's alright, it's alright)
I'll take your best shot
Is that all you got?
(Well it's alright, it's alright)
I'll take your best shot
Is that all you got?, I'll take your best shot
(Well it's alright, it's alright)
Take your best shot, take your best shot
Is that all you got?, I'll take your best shot
(Well it's alright, it's alright)
Take your best shot, take your best shot
Boom!
Here comes the
Boom!
Ready or not?
Here comes the boys from the South
Boom!
Here comes the
Boom!
Ready or not?
Haha, how you like me now?, I say
Boom!
Here comes the
Boom!
Ready or not?
Here comes the boys from the South
Boom!
Here comes the
Boom!
Ready or not?