Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Short propositional formulas represent nondeterministic computations
Information Processing Letters
Journal of Computer and System Sciences
P = BPP if E requires exponential circuits: derandomizing the XOR lemma
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Graph nonisomorphism has subexponential size proofs unless the polynomial-time hierarchy collapses
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Separating Nondeterministic Time Complexity Classes
Journal of the ACM (JACM)
Time—space tradeoffs for satisfiability
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
In search of an easy witness: exponential time vs. probabilistic polynomial time
Journal of Computer and System Sciences - Complexity 2001
A Probabilistic-Time Hierarchy Theorem for "Slightly Non-uniform" Algorithms
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
Theoretical Computer Science - Australasian computer science
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
A hierarchy for nondeterministic time complexity
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Hierarchy Theorems for Probabilistic Polynomial Time
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Time-space lower bounds for satisfiability
Journal of the ACM (JACM)
A note on the circuit complexity of PP
Theoretical Computer Science
A Generic Time Hierarchy for Semantic Models with One Bit of Advice
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Circuit lower bounds for Merlin-Arthur classes
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Unconditional Lower Bounds against Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
Time hierarchies for sampling distributions
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Lower bounds on the complexity of MSO1 model-checking
Journal of Computer and System Sciences
Hi-index | 0.00 |
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 ∈ 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 recent theorem of 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.