# Verification Components for Hybrid Systems

 Title: Verification Components for Hybrid Systems Author: Jonathan Julian Huerta y Munive (jjhuertaymunive1 /at/ sheffield /dot/ ac /dot/ uk) Submission date: 2019-09-10 Abstract: These components formalise a semantic framework for the deductive verification of hybrid systems. They support reasoning about continuous evolutions of hybrid programs in the style of differential dynamics logic. Vector fields or flows model these evolutions, and their verification is done with invariants for the former or orbits for the latter. Laws of modal Kleene algebra or categorical predicate transformers implement the verification condition generation. Examples show the approach at work. Change history: [2020-12-13]: added components based on Kleene algebras with tests. These implement differential Hoare logic (dH) and a Morgan-style differential refinement calculus (dR) for verification of hybrid programs. BibTeX: @article{Hybrid_Systems_VCs-AFP, author = {Jonathan Julian Huerta y Munive}, title = {Verification Components for Hybrid Systems}, journal = {Archive of Formal Proofs}, month = sep, year = 2019, note = {\url{https://isa-afp.org/entries/Hybrid_Systems_VCs.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: KAD, KAT_and_DRA, Ordinary_Differential_Equations, Transformer_Semantics Used by: Matrices_for_ODEs