On Verifying Designs With Incomplete Specification

Abstract: Incompleteness of a specification $\mathit{Spec}$ creates two problems. First, an implementation $\mathit{Impl}$ of $\mathit{Spec}$ may have some $\mathit{unwanted}$ properties that $\mathit{Spec}$ does not forbid. Second, $\mathit{Impl}$ may break some $\mathit{desired}$ properties that are not in $\mathit{Spec}$. In either case, $\mathit{Spec}$ fails to expose bugs of $\mathit{Impl}$. In an earlier paper, we addressed the first problem above by a technique called Partial Quantifier Elimination (PQE). In contrast to complete QE, in PQE, one takes out of the scope of quantifiers only a small piece of the formula. We used PQE to generate properties of $\mathit{Impl}$ i.e. those $\mathit{consistent}$ with $\mathit{Impl}$. Generation of an unwanted property means that $\mathit{Impl}$ is buggy. In this paper, we address the second problem above by using PQE to generate false properties i.e those that are $\mathit{inconsistent}$ with $\mathit{Impl}$. Such properties are meant to imitate the missing properties of $\mathit{Spec}$ that are not satisfied by $\mathit{Impl}$ (if any). A false property is generated by modifying a piece of a quantified formula describing 'the truth table' of $\mathit{Impl}$ and taking this piece out of the scope of quantifiers. By modifying different pieces of this formula one can generate a "structurally complete" set of false properties. By generating tests detecting false properties of $\mathit{Impl}$ one produces a high quality test set. We apply our approach to verification of combinational and sequential circuits.