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ACAS Xu is an air-to-air collision avoidance system designed for unmannedaircraft that issues horizontal turn advisories to avoid an intruder aircraft.Due the use of a large lookup table in the design, a neural network compressionof the policy was proposed. Analysis of this system has spurred a significantbody of research in the formal methods community on neural networkverification. While many powerful methods have been developed, most workfocuses on open-loop properties of the networks, rather than the main point ofthe system -- collision avoidance -- which requires closed-loop analysis.  In this work, we develop a technique to verify a closed-loop approximation ofthe system using state quantization and backreachability. We use favorableassumptions for the analysis -- perfect sensor information, instant followingof advisories, ideal aircraft maneuvers and an intruder that only fliesstraight. When the method fails to prove the system is safe, we refine thequantization parameters until generating counterexamples where the original(non-quantized) system also has collisions.

Neural Network Compression of ACAS Xu Early Prototype is Unsafe: Closed-Loop Verification through Quantized State Backreachability