Latticed k-Induction with an Application to Probabilistic Programs

Abstract 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 , which (i) generalizes classical k -induction for verifying transition systems, (ii) Park induction bounding points monotonic maps on lattices, (iii) extends from naturals to transfinite ordinals $$\kappa $$ κ thus yielding . The lattice-theoretic understanding BMC enables us apply both techniques fully automatic infinite-state probabilistic programs prototypical implementation manages automatically verify non-trivial specifications taken literature that—using existing techniques—cannot be verified without synthesizing a stronger inductive invariant first.