Widen Narrow and Relax

We apply results from linear programming to show that the relaxation of model checking over integers to reals is accurate i e yields a full test of temporal properties for a large class of concurrent systems We de ne abstractions similar to widening and narrowing that accelerate least and greatest xpoint computations in model checking over integers or reals We show that these abstractions are accurate in the same sense Preliminary experimental results e g safety for the ticket algorithm liveness of a parameterized elevator program indicate the potential usefulness of our abstraction techniques