We study the existence of time hierarchies for heuristic (average-case) algorithms. We prove that a time hierarchy exists for heuristics algorithms in such syntactic classes as NP and co-NP, and also in semantic classes AM and MA. Earlier, Fortnow and Santhanam (FOCS'04) proved the existence of a time hierarchy for ... more >>>

A monotone planar circuit (MPC) is a Boolean circuit that can be
embedded in a plane, and that has only AND and OR
gates. Yang showed that the one-input-face
monotone planar circuit value problem (MPCVP) is in NC^2, and
Limaye et. al. improved the bound to ... more >>>

The perfect matching problem is known to
be in P, in randomized NC, and it is hard for NL.
Whether the perfect matching problem is in NC is one of
the most prominent open questions in complexity
theory regarding parallel computations.

Grigoriev and Karpinski studied the perfect matching problem
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