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Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata.
We study the question of how to compute a point in the convex hull of an input set $S$ of $n$ points in ${mathbb R}^d$ in a differentially private manner. This question, which is trivial non-privately, turns out to be quite deep when imposing differe
Given a finite set of points $P subseteq mathbb{R}^d$, we would like to find a small subset $S subseteq P$ such that the convex hull of $S$ approximately contains $P$. More formally, every point in $P$ is within distance $epsilon$ from the convex hul
A subset $A$ of a Banach space is called Banach-Saks when every sequence in $A$ has a Ces{`a}ro convergent subsequence. Our interest here focusses on the following problem: is the convex hull of a Banach-Saks set again Banach-Saks? By means of a comb
We describe convex hulls of the simplest compact space curves, reducible quartics consisting of two circles. When the circles do not meet in complex projective space, their algebraic boundary contains an irrational ruled surface of degree eight whose
High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull construction,