Efficient Modeling of Linear Circuits to Perform Qualitative Reasoning Tasks

Modeling a system is the first step in reasoning about physical devices. By restricting our domain to linear circuits, we can find an efficient algorithm to do this modeling. The algorithm presented in this article is an efficient implementation of the star-mesh reductions used in Electrical Engineering. By choosing the right representation and based on simple data structures, we can reduce considerably the process of modeling a circuit. The algorithm has three main sources of efficiency gain: An efficient cluster representation reduces the complexity of the produced model; a simple data structure reduces the search for parallel regions; in the last step, we generate a circuit model where the principle of superposition does not need to be applied. Those three points reduce dramatically both, the complexity of the modeling process and the size of the model. The reduction in the size of the model impacts favorably its use in any reasoning task to be performed. Finally, avoiding superposition will allow us to treat this class of circuits more efficiently.