Logical Foundations of Cyber-Physical Systems

Cyberphysical Systems: Introduction.- Differential Equations and Domains.- Choice and Control.- Safety and Contracts.- Dynamical Systems and Dynamic Axioms.- Truth and Proof.- Control Loops and Invariants.- Events and Responses.- Reactions and Delays.- Differential Equations and Differential Invariants.- Differential Equations and Proofs.- Ghosts and Differential Ghosts.- Logical Foundations and CPS.- Differential Invariants and Proof Theory.- Verified Models and Verified Runtime Validation.- Hybrid Systems and Games.- Winning Strategies and Regions.- Winning and Proving Hybrid Games.- Game Proofs and Separations.- Virtual Substitution and Real Equations.- Virtual Substitution and Real Arithmetic.- Axioms and Uniform Substitutions.- Differential Axioms and Uniform Substitutions.- Model Checking and Reachability Analysis.- Distributed Systems and Hybrid Systems.

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• Fundamentos da Matemática
• Sistemas de segurança e alarme contra incêndios
• Teoria matemática da computação
• Inteligência artificial
• Lógica matemática
• Engenharia do controlo automático

Cyberphysical Systems (CPS);Differential Equations;Dynamical Systems;Logic;Control Loops;Proofs;Verification;Validation;Hybrid Systems;Hybrid Programs (HP);Games;Model Checking;Safety-Critical Systems;quality control, reliability, safety and risk