We present an optimization method and al gorithm designed for three objectives: physi cal data independence, semantic optimization, and generalized tableau minimization. The method relies on generalized forms of chase and "backchase" with constraints (dependen cies). By using dictionaries (finite functions) in physical schemas we can capture with con straints useful access structures such as indexes, materialized views, source capabilities, access support relations, gmaps, etc. The search space for query plans is defined and enumerated in a novel manner: the chase phase rewrites the original query into a "universal" plan that integrates all the access structures and alternative pathways that are allowed by appli cable constraints. Then, the backchase phase produces optimal plans by eliminating various combinations of redundancies, again according to constraints. This method is applicable (sound) to a large class of queries, physical access structures, and semantic constraints. We prove that it is in fact complete for "path-conjunctive" queries and views with complex objects, classes and dictio naries, going beyond previous theoretical work on processing queries using materialized views.