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This open access two-volume set LNCS 12759 and 12760 constitutes the refereed proceedings of the 33rd International Conference on Computer Aided Verification, CAV 2021, held virtually in July 2021. The 63 full papers presented together with 16 tool papers and 5 invited papers were carefully reviewed and selected from 290 submissions. The papers were organized in the following topical sections: Part I: invited papers; AI verification; concurrency and blockchain; hybrid and cyber-physical systems; security; and synthesis. Part II: complexity and termination; decision procedures and solvers; hardware and model checking; logical foundations; and software verification.

Software Engineering --- Mathematical theory of computation --- Artificial intelligence --- Computer programming / software development --- Computer modelling & simulation --- architecture verification --- artificial intelligence --- computer programming --- distributed computer systems --- distributed systems --- embedded systems --- formal logic --- formal methods --- formal verifications --- model checker --- model checking --- signal processing --- software architecture --- software design --- software engineering --- software quality --- Software engineering. --- Machine theory. --- Artificial intelligence. --- Computer science. --- Computer simulation. --- Software Engineering. --- Formal Languages and Automata Theory. --- Artificial Intelligence. --- Computer Science Logic and Foundations of Programming. --- Computer Modelling. --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Informatics --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Fifth generation computers --- Neural computers --- Abstract automata --- Abstract machines --- Automata --- Mathematical machine theory --- Algorithms --- Logic, Symbolic and mathematical --- Recursive functions --- Robotics --- Computer software engineering --- Engineering