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Kochenderfer, Katz, Corso & Moss, 2026

Algorithms for
Validation

How do you prove an autonomous system is safe? From falsification to reachability analysis, from importance sampling to runtime monitoring. The complete validation toolkit.

12
Chapters
40+
Simulations
100+
Quizzes
Foundations
Chapter 1

Introduction

What is validation? History, societal consequences, the validation framework.

Chapter 2

System Modeling

Model building, probability, parameter learning, agent models.

Chapter 3

Property Specification

Metrics, composite metrics, temporal logic, reachability specifications.

Falsification
Chapter 4

Falsification through Optimization

Direct sampling, disturbances, fuzzing, objective functions, CMA-ES.

Chapter 5

Falsification through Planning

Shooting methods, tree search, heuristic search, MCTS, RL.

Failure Analysis
Chapter 6

Failure Distribution

Rejection sampling, MCMC, probabilistic programming for failures.

Chapter 7

Failure Probability Estimation

Importance sampling, adaptive IS, sequential Monte Carlo, multilevel splitting.

Reachability
Chapter 8

Reachability for Linear Systems

Forward reachability, set propagation, zonotopes, polytopes, LP.

Chapter 9

Reachability for Nonlinear Systems

Interval arithmetic, Taylor models, neural network verification.

Chapter 10

Reachability for Discrete Systems

Graph reachability, SAT, probabilistic reachability, state abstractions.

Deployment
Chapter 11

Explainability

Feature importance, surrogate models, counterfactuals, failure modes.

Chapter 12

Runtime Monitoring

ODD monitoring, uncertainty quantification, conformal prediction.