A Pragmatic Guide to Building Conservative Discrete Abstractions of Cyber-Physical Systems

Abstract

Symbolic model checking is an effective approach for verifying semantically rich temporal-logic properties of cyber-physical systems, but it hinges on discretizing continuous-state dynamics into a finite-state abstraction. To transfer verification guarantees from the abstract model to the concrete CPS, the abstraction must conservatively approximate the concrete state space and behaviors. Hence, model-builders must maintain this soundness while balancing pessimism with tractability. However, they face several common pitfalls such as under-approximating the state space, under-approximating transitions, unsound pruning of "degenerate" behaviors, and improper specification lifting. This tutorial presents a pragmatic, conservative-by-construction workflow for building discrete abstractions of closed-loop dynamical systems. The workflow consists of four modular steps with interchangeable subroutines: (i) state-space partition and abstraction-function design, (ii) conservative transition construction via axis-aligned bounding boxes, polytopes, or sampling with PAC coverage certificates, (iii) mitigation of spurious transitions and self-loops using certified erasure and counterexample-guided abstraction refinement, and (iv) sound lifting of LTL specifications using may-must semantics. We demonstrate the end-to-end pipeline on three case studies and report how these design choices affect abstraction structure, runtime, and verification outcomes.