Groebner basis in Boolean rings is not polynomial-space

TL;DR

This paper demonstrates that the size of Groebner bases in Boolean rings can grow exponentially, showing that their computation is not bounded by polynomial space relative to input size.

Contribution

It provides a specific example proving that Groebner basis sizes in Boolean rings are not polynomially bounded, challenging assumptions about their computational complexity.

Findings

Groebner basis size can be exponential in Boolean rings

Polynomial bounds do not hold for Groebner basis in Boolean rings

Implications for computational complexity of algebraic algorithms

Abstract

We give an example where the number of elements of a Groebner basis in a Boolean ring is not polynomially bounded in terms of the bitsize and degrees of the input.