We consider the problem of computing a lightest derivation of a global
structure using a set of weighted rules. A large variety of inference problems
in AI can be formulated in this framework. We generalize A* search and
heuristics derived from abstractions to a broad class of lightest derivation
problems. We also describe a new algorithm that searches for lightest
derivations using a hierarchy of abstractions. Our generalization of A* gives a
new algorithm for searching AND/OR graphs in a bottom-up fashion. We discuss
how the algorithms described here provide a general architecture for addressing
the pipeline problem --- the problem of passing information back and forth
between various stages of processing in a perceptual system. We consider
examples in computer vision and natural language processing. We apply the
hierarchical search algorithm to the problem of estimating the boundaries of
convex objects in grayscale images and compare it to other search methods. A
second set of experiments demonstrate the use of a new compositional model for
finding salient curves in images