Logic optimization and equivalence checking by implication analysis

This paper proposes a new approach to multilevel logic optimization based on automatic test pattern generation (ATPG). It shows that an ordinary test generator for single stuck-at faults can be used to perform arbitrary transformations in a combinational circuit and discusses how this approach relates to conventional multilevel minimization techniques based on Boolean division. Furthermore, effective heuristics are presented to decide what network manipulations are promising for minimizing the circuit. By identifying indirect implications between signals in the circuit, transformations can be derived which are "good" candidates for the minimization of the circuit. A main advantage of the proposed approach is that it operates directly on the structural netlist description of the circuit so that the technical consequences of the performed transformations can be evaluated in an easy way, permitting better control of the optimization process with respect to the specific goals of the designer. Therefore, the presented technique can serve as a basis for optimization techniques targeting nonconventional design goals. This paper only considers area minimization, and our experimental results show that the method presented is competitive with conventional technology-independent minimization techniques. For many benchmark circuits, our tool, the Hannover implication tool, based on learning (HANNIBAL) achieves the best minimization results published to date. Furthermore, the optimization approach presented is shown to be useful in formal verification.