Counter-Example Generation Procedure For Path-Based Equivalence Checkers

Path-based equivalence checkers (PBECs) have been successfully applied for verification of programmes from diverse domains and from various stages of high-level synthesis. In the case of non-equivalence, PBEC provides very little information which is not sufficient for further investigation of the two programmes being compared by some human expert. In this work, the authors show how a counter-trace (cTrace) can be generated in the case of non-equivalence reported by the PBEC. Using this cTrace, they also present a procedure to find suitable initialisation values for input variables which reveal the non-equivalence (i.e. counter-example) by using off-the-shelf satisfiability modulo theories (SMT) solvers. To aid the human expert, they also show that how they can visualise this cTrace in the control and data-flow graph of the programmes using the graph visualisation software - Graphviz. This counter-example and visual representation of the corresponding cTrace will be helpful in debugging the root cause of the non-equivalence. The experimental results are encouraging.