In this paper, we present the logic of Counter arithmetic with Lambda expressions and Uninterpreted functions (CLU). CLU generalizes the logic of equality with uninterpreted functions (EUF) with constrained lambda expressions, ordering, and successor and predecessor functions. In addition to modeling pipelined processors that EUF has proved useful for, CLU can be used to model many infinite-state systems including those with infinite memories, finite and infinite queues including lossy channels, and networks of identical processes. Even with this richer expressive power, the validity of a CLU formula can be efficiently decided by translating it to a propositional formula, and then using Boolean methods to check validity. We give theoretical and empirical evidence for the efficiency of our decision procedure. We also describe verification techniques that we have used on a variety of systems, including an out-of-order execution unit and the load-store unit of an industrial microprocessor.

We consider the problem of bounded model checking of systems expressed in a decidable fragment of first-order logic. While model checking is not guaranteed to terminate for an arbitrary system, it converges for many practical examples, including pipelined processors. We give a new formal definition of convergence that generalizes previously stated criteria. We also give a sound semidecision procedure to check this criterion based on a translation to quantified separation logic. Preliminary results on simple pipeline processor models are presented.