A reduction of 3-SAT problem to Buchberger algorithm

TL;DR

This paper demonstrates a reduction from the NP-complete 3-SAT problem to the problem of constructing a Gröbner basis via the Buchberger algorithm, establishing their computational equivalence.

Contribution

It provides the first known reduction showing that constructing a Gröbner basis is NP-hard, linking it to the 3-SAT problem.

Findings

Reduction from 3-SAT to Buchberger algorithm established

Shows that computing Gröbner bases is NP-hard

Links algebraic computation to NP-complete problems

Abstract

There is a number of known NP class problems, and majority of them have been shown to be equivalent to others. In particular now it is clear that construction of a Gr\"{o}bner basis (or Buchberger algorithm) must be one of equivalent problems, but there was no example. In the following paper the reduction is constructed.