Solving degree, last fall degree, and related invariants
This work addresses the complexity estimation problem for researchers in computational algebra and cryptography, offering incremental theoretical connections between known invariants.
The paper tackles the problem of estimating the complexity of solving polynomial systems via Gröbner bases by relating invariants like solving degree, last fall degree, degree of regularity, and Castelnuovo-Mumford regularity, providing a rigorous framework for such analysis.
In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of solving a system of polynomial equations via Groebner bases methods. Our main results include a connection between the solving degree and the last fall degree and one between the degree of regularity and the Castelnuovo-Mumford regularity.