Excerpt from A New Lower Bound Construction for the Word Problem for Commutative Thue Systems Let be a commutative Thue System, 2 Let R denote the polynomial ring q z] where Q is the field of rational numbers. For each rule a 5 6 S, we form the polynomial - a 6 R, and let F5 denote the resulting set of polynomials. The word problem (for commutative Thue systems) is this: Given B) where a, are commutative words over 2, we want to know if a (mods). The ideal membership problem is this: Given (f, f) where F Q R is a finite set of polynomials and f G R, we want to know if f 6 (f) where (f) Q R is the ideal generated by F. As shown in the word problem can be reduced to the ideal membership problem as follows. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.