Verifying Reliability Properties Using the Hyperball Abstract Domain

Abstract

Modern systems are increasingly susceptible to soft errors that manifest themselves as bit flips and possibly alter the semantics of an application. We would like to measure the quality degradation on semantics due to such bit flips, and thus we introduce a Hyperball abstract domain that allows us to determine the worst-case distance between expected and actual results. Similar to intervals, hyperballs describe a connected and dense space. The semantics of low-level code in the presence of bit flips is hard to accurately describe in such a space. We therefore combine the Hyperball domain with an existing affine system abstract domain that we extend to handle bit flips, which are introduce as disjunctions. Bit-flips can reduce the precision of our analysis, and we therefor introduce the Scale domain as a disjunctive refinement to minimize precision loss. This domain bounds the number of disjunctive elements by quantifying the over-approximation of different partitions and uses submodular optimization to find a good partitioning (within a bound of optimal). We evaluate these domains to show benefits and potential problems. For the application we examine here, adding the Scale domain to the Hyperball abstraction improves accuracy by up to two orders of magnitude. Our initial results demonstrate the feasibility of this approach, although we would like to further improve execution efficiency.