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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    $$\kappa $$  κ , thus yielding    $$\kappa $$  κ -induction .  The lattice-theoretic understanding of  k -induction and BMC enables us to apply both techniques to the  fully automatic verification of infinite-state 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.

Latticed k-Induction with an Application to Probabilistic Programs