text: In this paper we consider the specification and verification of infinite-state systems using temporal logic. In particular, we describe parameterised systems using a new variety of first-order temporal logic that is both powerful enough for this form of specification and tractable enough for practical deductive verification. Importantly, the power of the temporal language allows us to describe (and verify) asynchronous systems, communication delays and more complex properties such as liveness and fairness properties. These aspects appear difficult for many other approaches to infinite-state verification.
  @cite_28: 
  @cite_16: We propose a new method for the verification of parameterized cache coherence protocols. Cache coherence protocols are used to maintain data consistency in multiprocessor systems equipped with local fast caches. In our approach we use arithmetic constraints to model possibly infinite sets of global states of a multiprocessor system with many identical caches. In preliminary experiments using symbolic model checkers for infinite-state systems based on real arithmetics (HyTech [HHW97] and DMC [DP99]) we have automatically verified safety properties for parameterized versions of widely implemented write-invalidate and write-update cache coherence policies like the Mesi, Berkeley, Illinois, Firefly and Dragon protocols [Han93]. With this application, we show that symbolic model checking tools originally designed for hybrid and concurrent systems can be applied successfully to a new class of infinite-state systems of practical interest.
  @cite_23: We analyze the model-checking problems for safety and liveness properties in parameterized broadcast protocols. We show that the procedure suggested previously for safety properties may not terminate, whereas termination is guaranteed for the procedure based on upward closed sets. We show that the model-checking problem for liveness properties is undecidable. In fact, even the problem of deciding if a broadcast protocol may exhibit an infinite behavior is undecidable.
summary: Constraint based verification using counting abstractions @cite_16 @cite_28 @cite_23 , provides complete procedures for checking safety properties of broadcast protocols. However, such approaches have theoretically non-primitive recursive upper bounds for decision procedures (although they work well for small, interesting, examples) --- in our case the upper bounds are definitely primitive-recursive;