K-Induction

K-induction extends standard mathematical induction by using a look-back buffer of k steps to prove safety invariants in complex finite and infinite state systems.

Engineers deploy k-induction to bypass the limitations of simple inductive invariants in hardware and software verification. By assuming a property holds for k consecutive steps (the induction hypothesis) to prove it holds at k+1, tools like CBMC and Kind 2 can verify deep pipeline logic that standard induction fails to capture. This technique effectively unrolls transition systems into SAT or SMT queries: it checks a base case of length k and then attempts to find a counterexample to the inductive step. If the solver returns unsatisfiable, the property is proven for all reachable states. It is a cornerstone of modern model checking, particularly for verifying RTL designs and synchronous controllers where state dependencies span multiple clock cycles.

https://formalverification.github.io/book/Principles/Induction/KInduction.html