Abstract. This paper describes a structurally-guided framework for the decomposition of a verification task into subtasks, each solved by a specialized algorithm for overall efficiency. Our contributions include the following: (1) a structural algorithm for computing a bound of a state-transition diagram’s diameter which, for several classes of netlists, is sufficiently small to guarantee completeness of a bounded property check; (2) a robust backward unfolding technique for structural target enlargement: from the target states, we perform a series of compose-based pre-image computations, truncating the search if resource limitations are exceeded; (3) similar to frontier simplification in symbolic reachability analysis, we use induction via don’t cares for enhancing the presented target enlargement. In many practical cases, the verification problem can be discharged by the enlargement process; otherwise, it is passed in simplified form to an arbitrary subsequent solution approach. The presented techniques are embedded in a flexible verification framework, allowing arbitrary combinations with other techniques. Extensive experimental results demonstrate the effectiveness of the described methods at solving and simplifying practical verification problems. 1

Bounded model checking (BMC) has gained widespread industrial use due to its relative scalability. Its exhaustiveness over all valid input vectors allows it to expose arbitrarily complex design flaws. However, BMC is limited to analyzing only a specific time window, hence will only expose those flaws which manifest within that window and thus cannot readily prove correctness. The diameter of a design has thus become an important concept — a bounded check of depth equal to the diameter constitutes a complete proof. While the diameter of a design may be exponential in the number of its state elements, in practice it often ranges from tens to a few hundred regardless of design size. Therefore, a powerful diameter overapproximation technique may enable automatic proofs that otherwise would be infeasible. Unfortunately, exact diameter calculation requires exponential resources, and overapproximation techniques may yield exponentially loose bounds. In this paper, we provide a general approach for enabling the use of structural transformations, such as redundancy removal, retiming, and target enlargement, to tighten the bounds obtained by arbitrary diameter approximation techniques. Numerous experiments demonstrate that this approach may significantly increase the set of designs for which practically useful diameter bounds may be obtained. 1