IC3 with Internal Signals

IC3 is a highly-effective algorithm for formal hardware verification. It cleverly uses a SAT solver to compute an inductive invariant, an over-approximation of reachable states, of a hardware design. The invariant is computed in CNF as a conjunction of lemmas. This CNF representation over state variables, although efficient, leads to an obvious deficiency: IC3 is not effective for designs that do not have a concise CNF invariant over state variables. We show how to remedy this deficiency by extending traditional IC3 to learn invariants not only in terms of state variables, but also in terms of internal signals of the design. Our proposed method can learn significantly more compact invariants than IC3, while maintaining a highly-efficient CNF representation. We evaluate our technique on several industrial sequential equivalence checking (SEC) problems from IBM, SEC problems derived from designs in the Hardware Model Checking Competition (HWMCC) and SEC problems from academia. In addition, we evaluate it on HWMCC benchmarks. IC3 with internal signals is efficient for SEC and outperforms traditional IC3 on an important class of benchmarks.