Progressive Expansions
Patrick Dehornoy · Birkhäuser Basel eBooks · 2000
In this chapter, we deepen our study of left self-distributivity and, describing the geometry of the terms Ó k t more closely, we prove partial results about the convergence of the Polish Algorithm and the Embedding Conjecture. The Polish Algorithm is a natural syntactic method for deciding LD-equivalence of terms, and the question of whether it always converges is one of the most puzzling open questions about left self-distributivity. The Embedding Conjecture claims that the monoid M LD embeds in the group G LD . The main technical notion in the chapter is the notion of a progressive LD-expansion, a particular kind of LD-expansion where self-distributivity is applied to positions that move from from left to right only. Its interest lies in the uniqueness properties it entails. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.