In respect to the "P versus NP" controversy, can't chaos theory be used to solve problems like the Sum Subset Problem with non exponential performance?
Like, chaotic equations, are like paths to very different places, according to the door you chose at the beginning. So can't like a chaotic equation be created and then the door would be the Set, that is the numbers in the set would be encoded in a number that would be provided to the chaotic equation, and then you would get like a 0 or a 1, or the number of combinations like if you applied to the equation to itself a number of times equal to the size of the set? That would be polynomial, I believe.
I don't know about mathematics and only a few about computer science but maybe people more knowledgeable can do it.
The use of chaotic dynamical systems in solving the (NP-hard) 3-sat problem has been studied. It turns out (so far) that while these methods provide an interesting way of looking at this problem, actually SOLVING them via solution of chaotic ODEs is WAY worse as far as (real)time performance is concerned, compared to state of the art combinatorial solvers. Theoretically, algorithm is polynomial continuous time, hence not polynomial discrete time. For more information, please see : Optimization hardness as transient chaos in an analog approach to constraint satisfaction
http://arxiv.org/abs/1208.0526