论文标题
平面凸代码是可决定的
Planar convex codes are decidable
论文作者
论文摘要
我们表明，平面中可通过紧凑型集实现的每个凸代码都承认由多边形组成的实现，并且平面中的每个开放式凸代码都可以通过多边形的室内设计来实现。我们对形成此类实现所需的顶点数量给出了阶乘型界限。因此，我们证明有一种算法可以确定凸代码是在飞机上允许封闭还是开放实现的算法。
We show that every convex code realizable by compact sets in the plane admits a realization consisting of polygons, and analogously every open convex code in the plane can be realized by interiors of polygons. We give factorial-type bounds on the number of vertices needed to form such realizations. Consequently we show that there is an algorithm to decide whether a convex code admits a closed or open realization in the plane.
