Latticed $k$-Induction with an Application to Probabilistic Programs

Kevin Batz, Mingshuai Chen, Benjamin Lucien Kaminski, Joost-Pieter Katoen, Christoph Matheja, Philipp Schröer
We revisit two well-established verification techniques, k-induction and bounded model checking (BMC), in the more general setting of fixed point theory over complete lattices. Our main theoretical contribution is latticed k-induction, which (i) generalizes classical k-induction for verifying transition systems, (ii) generalizes Park induction for bounding fixed points of monotonic maps on complete lattices, and (iii) extends from naturals k to transfinite ordinals κ, thus yielding κ-induction.
more » ... The lattice-theoretic understanding of k-induction and BMC enables us to apply both techniques to the fully automatic verification of infinitestate probabilistic programs. Our prototypical implementation manages to automatically verify non-trivial specifications for probabilistic programs taken from the literature that-using existing techniques-cannot be verified without synthesizing a stronger inductive invariant first.
doi:10.18154/rwth-2021-06838 fatcat:crgow7jbazbjxprdh3rsypexiy