Separation Logic for Verifying Physical Collisions of CNC Programs

2026-05-11

AI Summary

Traditional CNC machining safety verification relies heavily on repetitive simulation, which struggles to accommodate changing requirements and lacks a formal, scalable approach to collision detection. This work proposes a formal verification framework based on separation logic, modeling the physical workspace as a Spatial Heap where occupancy relations are treated as logical resources. By introducing a Parser-Prover Handshake mechanism, the framework decouples kinematic computation from logical reasoning and, for the first time, defines physical collisions as Spatial Data Races in a logical sense. Leveraging concurrent separation logic, it supports ownership-transfer-based verification in collaborative scenarios. The method eliminates the need for geometric simulation and provides a mathematically rigorous, scalable guarantee of collision freedom, establishing a formal safety foundation for autonomous manufacturing.

Abstract

Safety verification in Computer Numerical Control (CNC) machining has traditionally relied on simulation-based methods that require repetitive tests when requirements change. This paper introduces a formal verification framework that conceptualizes the physical CNC workspace as a Spatial Heap, treating physical occupancy as a managed logical resource. Central to our approach is a Parser-Prover Handshake that decouples machine kinematics from formal logic. By mapping tool trajectories and safety buffers into a discrete spatial model prior to evaluation, the framework enables the use of Separation Logic (SL) to verify safety via formal triples. Within this model, physical collisions are redefined as logical Spatial Data Races, detected through the failure of the separating conjunction to establish disjointness. Furthermore, we extend the methodology to collaborative environments using Concurrent Separation Logic (CSL), where physical hand-offs are verified as formal ownership transfers. This approach provides a scalable, mathematically grounded alternative to geometric simulation, offering a foundation for autonomous, zero-collision manufacturing.

Problem

• CNC safety verification
• physical collision
• formal verification
• Separation Logic
• spatial reasoning

Innovation

• Separation Logic
• Spatial Heap
• Parser-Prover Handshake
• Spatial Data Race
• Concurrent Separation Logic