Computable Approximations of Semicomputable Graphs
Vedran \v{C}a\v{c}i\'c, Matea \v{C}elar, Marko Horvat, Zvonko Iljazovi\'c
TL;DR
This paper investigates the computability of topological graphs formed by connecting arcs and rays, demonstrating that semicomputable graphs can be approximated arbitrarily closely by computable subgraphs with computable endpoints.
Contribution
It introduces methods to approximate semicomputable topological graphs with computable subgraphs, advancing understanding of their computability properties.
Findings
Semicomputable graphs can be approximated by computable subgraphs with arbitrary precision.
Every semicomputable graph in a computable metric space admits such an approximation.
The approach bridges the gap between semicomputability and computability in topological graph structures.
Abstract
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.
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