Work

Nonexistence of Algorithm Deciding if the Fundamental Group of an Arbitrary Constructive Compact Set is Trivial

Year: 2025

Type: article

Abstract: In this paper, we give an introduction to the compact space under Constructive Mathematics, ultimately showing that there exist no computer programs that can always determine if a fundamental group of a constructive compact topological space is trivial or not. We will begin with the non-halting case of the programs, which shows that the fundamental group of our selected set is trivial. From here, we will explore the halting case of the programs, which can be solved by arbitrarily picking a nontrivial subset of our selected set. The main result of this section is that we can show that the algorithm is decidable due to our initial construction, while realizing its contradiction with our input. We want to show that such an algorithm doesn’t exist by employing the proof-by-contradiction method.

Source: Theoretical and Natural Science

DOI: 10.54254/2753-8818/2025.22661

Authors: Encheng Jin, Yang Li, Xinyang Qian, Kaijing Yao, Siheng Yu

Institutions: New York University, Nanjing Foreign Language School, University of California, Berkeley, East China Normal University

Language: English

Topic: Computability, Logic, AI Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4410129174

FWCI:

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