‘ReLIC: Reduced Logic Inference for Composition’ for Quantifier Elimination-Based Compositional Reasoning and Verification

Abstract

Formally verifying complex model-based designs has posed a significant challenge for complex systems, primarily due to their sheer scale and the critical nature of safety involved. A common method for tackling this challenge is the divide-and-conquer strategy, which leverages the system model architecture to decompose the verification tasks into smaller subtasks focused on subsystems or components. This approach entails articulating the verification goals as formal property contracts and subsequently verifying each one separately. Once the individual contracts of the subsystems or components are validated, they are integrated through formal reasoning to achieve verification at the system level also represented as a formal property contract. However, the current procedures and tools designed for this type of compositional verification often requires manual postulation of system-level contracts and are susceptible to false alarms in verification outcomes due to over-approximation. In the paper, we introduce our approach to compositional reasoning and verification using quantifier elimination (QE), which automates the derivation of the strongest system-level property given the component-level ones and their connectivity, enabling precise automated analysis for even time-dependent and nonlinear systems. QE serves as the foundation for composition calculus, allowing us to derive the strongest system-level property in a single step. We begin by applying this framework to properties that are time-independent, and subsequently, we expand our approach to encompass the composition of time-dependent properties. For the latter case, we shift the given properties over time to span the time horizon of interest, which we show to be no greater than the total time horizons of the component-level properties. Similarly, we use QE to infer the system-initial-condition from the component-level initial conditions. The automatically inferred strongest system-level property becomes useful in verifying a postulated desired system-level property through induction, involving inferred strongest system-level property and its initial condition. In this regard, we also advance the existing $k$-induction based model-checking by incorporating QE and formulating its base and inductive steps as QE problems. Our composition approach is uniform regardless of the type of composition (cascade/parallel/feedback) and regardless the component properties being composed are time-independent or time-dependent. We also present a prototype verifier called ReLIC (Reduced Logic Inference for Composition), which implements our approach and demonstrate it through several illustrative and practical examples. We also demonstrate the recent integration of our approach into an industrial verification and validation (V&V) tool suite, which allows for augmented static analysis of Simulink models and deep neural networks (DNNs).