A SAT-based algorithm for reparameterization in symbolic simulation

Abstract

Parametric representations used for symbolic simulation of circuits usually use BDDs. After a few steps of symbolic simulation, state set representation is converted from one parametric representation to another smaller representation, in a process called reparameterization. For large circuits, the reparametrization step often results in a blowup of BDDs and is expensive due to a large number of quantifications of input variables involved. Efficient SAT solvers have been applied successfully for many verification problems. This paper presents a novel SAT-based reparameterization algorithm that is largely immune to the large number of input variables that need to be quantified. We show experimental results on large industrial circuits and compare our new algorithm to both SATbased Bounded Model Checking and BDD-based symbolic simulation. We were able to achieve on average 3x improvement in time and space over BMC and able to complete many examples that BDD-based approach could not even finish.

Symbolic Model Checking for Asynchronous Boolean Programs

“…In [30], the authors use a SAT solver to compute a new parametric representation from a set of constraints. The new parametric representation is canonical for a given variable ordering, and thus allows an efficient fix-point detection.…”

Existential Quantification as Incremental SAT

“…Our approach, in comparison, builds on top of an existing SAT library and is therefore both straightforward to implement and will immediately benefit from any improvement to the library itself. Nevertheless, we consider the SAT-based algorithm of McMillan to be an important work that has indeed found application in the predicate abstraction of hardware circuits [13] and post-image computation [12]. A variation on the McMillan algorithm is given by Sheng and Hsiao [37] who apply a success-driven rather than a conflict-driven search for models (recall that DPLL-style algorithms use a conflict-driven search).…”

Efficient Symbolic Simulation via Dynamic Scheduling, Don’t Caring, and Case Splitting

“…In particular, we have found the input reductions enabled by structurally abstracting the netlist through reparameterization [4] to be very beneficial to symbolic simulation, often times improving performance by orders of magnitude. Note that this is complementary to traditional approaches that reparameterize state sets during symbolic simulation [1,5,6,8]. In fact, both these can be combined into a powerful two-step process that reparameterizes the structural sequential netlist, followed by reparameterizing the next-state BDDs at every time-step of the symbolic simulation.…”

“…[4]. This technique has been extended to cycle-based symbolic simulation by reparameterizing unfolded input variables [5,6,8]. Such approaches are complementary to the techniques presented in this paper.…”