# All Questions

5,579 questions
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### Is there a regular tree language in which the average height of a tree of size $n$ is neither $\Theta(n)$ nor $\Theta(\sqrt{n})$?

We define a regular tree language as in the book TATA: It is the set of trees accepted by a non-deterministic finite tree automaton (Chapter 1) or, equivalently, the set of trees generated by a ...
337 views

### Finding an $st$-path in a planar graph which is adjacent to the fewest number of faces

I am curious whether the following problems has been studied before, but wasn't able to find any papers about it: Given a planar graph $G$, and two vertices $s$ and $t$, find an $s$-$t$ path $P$ ...
695 views

### Graph problem known to be $NP$-complete only under Cook reduction

The theory of NP-completeness was initially built on Cook (polynomial-time Turing) reductions. Later, Karp introduced polynomial-time many-to-one reductions. A Cook reduction is more powerful than a ...
484 views

### Can a calculus have incremental copying and closed scopes?

A few days ago, I proposed the Abstract Calculus, a minimal untyped language that is very similar to the Lambda Calculus, except for the main difference that substitutions are ...
449 views

### Largest set of cocircular points

Given $n$ points with integer coordinates in the plane, determine the maximum number of points that lie on the same circle (on its circumference, not its interior). This can be done in $O(n^3)$ ...
434 views

### Approximate minimum-weighted tree decomposition on complete graphs

Say I have a weighted undirected complete graph $G = (V, E)$. Each edge $e = (u, v, w)$ is assigned with a positive weight $w$. I want to calculate the minimum-weighted $(d, h)$-tree-decomposition. By ...
503 views