Inductive Validity Cores

Abstract

Symbolic model checkers can construct proofs of properties over very complex models. However, the results reported by the tool when a proof succeeds do not generally provide much insight to the user. It is often useful for users to have traceability information related to the proof: which portions of the model were necessary to construct it. This traceability information can be used to diagnose a variety of modeling problems such as overconstrained axioms and underconstrained properties, and can also be used to measure completeness of a set of requirements over a model. We propose the notion of inductive validity cores (IVCs), which are intended to trace a property to a minimal set of model elements necessary for proof. Such cores are not unique, and algorithms for efficiently producing both single IVC and all IVCs are presented. IVCs can be used for several interesting analyses, including regression analysis for testing/proof, determination of the minimum (as opposed to minimal) number of model elements necessary for proof, the diversity examination of model elements leading to proof, and analyzing fault tolerance.

Specification Quality Metrics Based on Mutation and Inductive Incremental Model Checking

“…Unlike testing, where we can follow the execution trace, the proof process uses the whole model, but many parts of it may not be necessary to prove the properties. This problem has been studied using the following approaches: mutation proof [7], [9], [16], [24] and inductive validity cores [2], [3], [4], [12].…”