LOApr 2
Computable Approximations of Semicomputable Graphs
arXiv:2411.1367243.5h-index: 12
AI Analysis
This addresses a theoretical problem in computable analysis for researchers in mathematical logic and topology, but it appears incremental as it builds on existing concepts of computability.
The paper tackles the problem of approximating semicomputable graphs in computable metric spaces, proving that they can be approximated with arbitrary precision by computable subgraphs with computable endpoints.
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with arbitrary precision, by its computable subgraph with computable endpoints.