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Problems known to be open in the literature and any problem that, after being posed, is decided to be open by the community.

5 votes
0 answers
571 views

Why can't we have superlinear bounds on Boolean circuit size for an explicit function?

I am interested about the minimal size (number of gates) of a family of circuits (with negation) over a complete Boolean basis (with fanin 2) that computes some explicit Boolean function. (In other wo …
Antoine Amarilli 'a3nm''s user avatar
26 votes
1 answer
1k views

Is it still open to determine the complexity of computing the treewidth of planar graphs?

For a constant $k \in \mathbb{N}$, one can determine in linear time, given an input graph $G$, whether its treewidth is $\leq k$. However, when both $k$ and $G$ are given as input, the problem is NP-h …
Antoine Amarilli 'a3nm''s user avatar