The Search for Minimal Search: A Graph-Theoretic Approach

Abstract

This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set-formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building.