Ivy: Interactive Verification of Parameterized Systems via Effectively Propositional Reasoning

The design and implementation of parametric systems can be very tricky even for experienced researchers. We describe an interactive system — Ivy — for interactively verifying parameterized systems. Ivy is based on the following principles: (i) Ivy first attempts to locate counterexamples by bounding the number of protocol actions and symbolically searching for (unbounded) bad inputs. (ii) Invariants in Ivy are expressed as universal formulas in relational first-order logic. Their inductiveness check reduces to unsatisfiability checks in Effectively Propositional Logic (EPR). This guarantees that the tool can always decide whether an invariant is inductive or not. Furthermore, our use of universal formulas guarantees that counterexamples to induction can be presented graphically, allowing inspection by humans. (iii) This allows users to guide the verification process by suggesting candidate local invariants, whose conjunction comprises a global inductive invariant. All user interactions are performed using graphical models, easing the user’s task. We describe our initial experience with some protocols.