Affine Disjunctive Invariant Generation with Farkas' Lemma

Invariant generation is the classical problem that aims at automated generation of assertions that over-approximates the set of reachable program states in a program. We consider the problem of generating affine invariants over affine while loops (i.e., loops with affine loop guards, conditional branches and assignment statements), and explore the automated generation of disjunctive affine invariants. Disjunctive invariants are an important class of invariants that capture disjunctive features in programs such as multiple phases, transitions between different modes, etc., and are typically more precise than conjunctive invariants over programs with these features. To generate tight affine invariants, existing constraint-solving approaches have investigated the application of Farkas' Lemma to conjunctive affine invariant generation, but none of them considers disjunctive affine invariants.