Transitive Closures of Regular Relations for Verifying Infinite-State Systems

We consider a model for representing innnite-state and para-meterized systems, in which states are represented as strings over a nite alphabet. Actions are transformations on strings, in which the change can be characterized by an arbitrary nite-state transducer. This program model is able to represent programs operating on a variety of data structures, such as queues, stacks, integers, and systems with a parame-terized linear topology. The main contribution of this paper is an eeective derivation of a general and powerful transitive closure operation for this model. The transitive closure of an action represents the eeect of executing the action an arbitrary number of times. For example, the transitive closure of an action which transmits a single message to a buuer will be an action which sends an arbitrarily long sequence of messages to the buuer. Using this transitive closure operation, we show how to model and automatically verify safety properties for several types of innnite-state and parameterized systems.