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Explore safety validation and "stress testing" of autonomous dynamical systems through algorithms presented in the book "Algorithms for Validation" by M. Kochenderfer et al. in this 35-minute conference talk from JuliaCon Global 2025. Learn how to rigorously validate the safety of autonomous systems that increasingly operate in airways, roads, and critical infrastructure through a practical case study of two aircraft on a collision course with a controller attempting to avoid collision. Discover how observation errors can mislead controllers into making dangerous decisions and understand methods for finding rare failure events and estimating their probabilities. Work through interactive Pluto.jl notebooks that demonstrate how Julia can specify system safety properties, efficiently find rare failures by optimizing over system rollouts, estimate failure probabilities through Markov Chain Monte Carlo, and compute reachable sets through set propagation techniques under bounded noise. Utilize key Julia packages including SignalTemporalLogic.jl, NonlinearSolve.jl, Turing.jl, and LazySets.jl while learning how Julia integrates with Python-based Neural Network controllers and black-box simulation environments. Apply these validation techniques beyond aviation to autonomous driving and flight, financial decision making, chemical process control, logistics and transportation, energy grid balancing, and other critical applications where safety validation is essential.