Invariant Logic: A Calculus for Problem Reformulation

Symmetries abound in nature. Observing symmetries often provides the key to discovering internal structure. In problem solving, observing and reasoning about symmetries is a powerful tool for shifting viewpoints on a problem. A calculus for reasoning about problem symmetries has been developed, called Invariant Logic. Invariant Logic is partially implemented in STRATA, a system which synthesizes algorithms through problem reformulation. In STRATA, Invariant Logic is used to reason about generalized problem symmetries for several purposes. The first purpose is as a calculus for generating expressions denoting problem symmetries. The second purpose is problem abstraction generating abstract problem descriptions which denote models in which the problem symmetries have been collapsed. The third purpose is problem reduction specializing a problem description by adding constraints in order to realize performance gains.