Computer Science – Computational Complexity
Scientific paper
2010-12-09
Computer Science
Computational Complexity
Scientific paper
We define and study a new notion of "robust simulations" between complexity classes which is intermediate between the traditional notions of infinitely-often and almost-everywhere, as well as a corresponding notion of "significant separations". A language L has a robust simulation in a complexity class C if there is a language in C which agrees with L on arbitrarily large polynomial stretches of input lengths. There is a significant separation of L from C if there is no robust simulation of L in C. The new notion of simulation is a cleaner and more natural notion of simulation than the infinitely-often notion. We show that various implications in complexity theory such as the collapse of PH if NP = P and the Karp-Lipton theorem have analogues for robust simulations. We then use these results to prove that most known separations in complexity theory, such as hierarchy theorems, fixed polynomial circuit lower bounds, time-space tradeoffs, and the theorems of Allender and Williams, can be strengthened to significant separations, though in each case, an almost everywhere separation is unknown. Proving our results requires several new ideas, including a completely different proof of the hierarchy theorem for non-deterministic polynomial time than the ones previously known.
Fortnow Lance
Santhanam Rahul
No associations
LandOfFree
Robust Simulations and Significant Separations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Robust Simulations and Significant Separations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Robust Simulations and Significant Separations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-77285