Invariant Synthesis via Convex Optimization

This chapter focuses on the computation of invariant for a discrete dynamical system collecting semantics. Invariants or collecting semantics properties are properties preserved along all executions of a system and verified in all reachable states. A subset of these invariants are defined as inductive. Inductive invariants are properties, or relationships between variables, that are inductively preserved by one transition of considered systems. Intuitively, it is not required to consider a reachable state and all (or part of) its past while arguing about the validity of the invariant, but only the single state. Applying the induction principle, this chapter obtains that any state satisfying the property is mapped to a next state preserving that same property.