Symbolic image computation is the most fundamental computation in BDD-based sequential system optimization and formal verification. In this paper, we explore the use of over-approximation and BDD minimization with don’t cares during image computation. Our new method, based on the partitioned representation of the transition relation, consists of three phases: First, the model is treated as a set of loosely coupled components, and over-approximate images are computed to minimize the transition relation of each component. A refined overall image is then computed using the simplified transition relation. Finally, the exact image is obtained by a clipping operation that recovers all previous over-approximations. Since BDD minimization employs constraints on the next-state variables of the transition relation, instead of the customary constraints on the present-state variables, we call the resulting method far side image computation. The new method can be implemented on top of any image computation algorithm that is based on the partitioned transition relation. (For example, IWLS95 [21], MLP [17], and Fine-Grain [16].) We demonstrate the effectiveness of our approach by experiments on models ranging from easy to hard: The new method wins significantly over the best known algorithms so far in both CPU time and memory usage, especially on the hard models.

In many computer-aided design tools, binary decision diagrams (BDD's) are used to represent Boolean functions. To increase the efficiency and capability of these tools, many algorithms have been developed to reduce the size of the BDD's. This paper presents heuristic algorithms to minimize the size of the BDD's representing incompletely specified functions by intelligently assigning don't cares to binary values. Experimental results show that new algorithms yield significantly smaller BDD's compared with existing algorithms yet still require manageable run-times. These algorithms are particularly useful for synthesis application where the structure of the hardware/software is derived from the BDD representation of the function to implement because the minimization quality is more critical than the minimization speed in these applications.