Exploiting Functional Dependencies in Declarative Problem Specifications

In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed in order to express some of the constraints, or due to precise modelling choices, e.g., to provide multiple viewpoints of the search space in order to increase propagation. In either way, the recognition of dependencies greatly helps solvers, letting them avoid spending search on unfruitful branches, while maintaining the highest degree of declarativeness. By modelling constraint problem specifications as second-order formulae, we provide a characterization of functional dependencies in terms of semantic properties of first-order ones. Additionally, we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies. We present OPL examples of various problems, from bio-informatics, planning and resource allocation fields, and show how in many cases OPL greatly benefits from the addition of such search procedures.