Qualitative Synthesis of Configurations for Two-Terminal Systems Based on Desired Behavior

In design, inferring structure from function is a combinatorial generate-and-test problem.Existing methods use prestored domain-specific partial configurations to constrainthe generator. We have found that for certain types of economic and physicalsystems consisting of two-terminal components connected in parallel, it is fruitfulto specify function in terms of desired behavior, and to identify sets of componentswhose resultant behavior matches that desired behavior. In this paper, we present twosynthesis operators called stretch and steepen that operate on qualitatively specifiedpiecewise linear functions that characterize the behavior of components. We are currentlyapplying this model to the domain of financial hedging, where behaviors of thecomponents (stocks, bonds, options, etc.) are specified in terms of two-dimensionalpiecewise linear relationships, and the goal is to synthesize these to produce a constrainedbehavior in response to uncontrollable events.