# Parallel Algorithms for Computing Hilbert Bases

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## Abstract

Given a homogeneous system of linear equations A x = 0, a Hilbert basis is a unique finite minimal set of non-negative solutions from which every non-negative solution of the system can be generated. Computing Hilbert bases is a fundamental problem encountered in various areas in computer science and mathematics, for instance in decision procedures for arithmetic theories, the verification of infinite-state systems and pure combinatorics. In this project. we plan to revisit an approach to computing Hilbert bases described in [1] that is highly parallelizable. With the ubiquity of multi-core architectures, it seems conceivable that, with proper engineering, this approach will outperform existing approaches. The goal of this project is to deliver an implementation of the algorithm of [1] and benchmark it against competing tools. If successful, an integration into the SageMath platform could be envisioned. [1] https://pdfs.semanticscholar.org/6e84/f9ccfdaa37cb33cfc2024aec1dc7d13964c7.pdfPrerequisites: good knowledge of concurrent programming and data structures, and linear algebra