Relation between XL algorithm and Gröbner Bases Algorithms.
誠 杉田, Mitsuru Kawazoe, Hideki Imai · 2004
We clarify a relation between the XL algorithm and Grobner bases algorithms. The XL algorithm was proposed to be a more efficient algorithm to solve a system of equations with a special assumption without trying to calculate a whole Grobner basis. But in our result, it is shown that the XL algorithm is also a Grobner bases algorithm which can be represented as a redundant version of a Grobner bases algorithm F4 under the assumption in XL.