Infinite-State Liveness Checking with rlive

Alessandro Cimatti, Alberto Griggio, Christopher Johannsen, Kristin Yvonne Rozier, Stefano Tonetta

Abstract:

rlive is a recently-proposed SAT-based liveness model checking algorithm that showed remarkable performance compared to other state-of-the-art approaches, both in absolute terms (solving more problems overall than other engines on standard benchmark sets) as well as in relative terms (solving several problems that none of the other engines could solve). rlive proves or disproves properties of the form FGq, by trying to show that
can be visited only a finite number of times via an incremental reduction to a sequence of reachability queries. A key factor in the good performance of rlive is the extraction of “shoals” from the inductive invariants of the reachability queries to block states that can reach
a bounded number of times.

In this paper, we generalize rlive to handle infinite-state systems, using the Verification Modulo Theories paradigm. In contrast to the finite-state case, liveness cannot be simply reduced to finding a bound on the number of occurrences of
on paths. We propose therefore a solution leveraging predicate abstraction and termination techniques based on well-founded relations. In particular, we show how we can extract shoals that take into account the well-founded relations. We implemented the technique on top of the open source VMT engine IC3ia and we experimentally demonstrate how the new extension maintains the performance advantages (both absolute and relative) of the original rlive, thus significantly contributing to advancing the state of the art of infinite-state liveness verification.