Partition Refinement of Component Interaction Automata: Why Structure Matters More Than Size

Abstract: Automata-based modeling languages, like Component Interaction Automata, offer an attractive means to capture and analyze the behavioral aspects of interacting components. At the center of these modeling languages we find finite state machines that allow for a fine-grained description how and when specific service requests may interact with other components or the environment. Unfortunately, automata-based approaches suffer from exponential state explosion, a major obstacle to the successful application of these formalisms in modeling real-world scenarios. In order to cope with the complexity of individual specifications we can apply partition refinement, an abstraction technique to alleviate the state explosion problem. But this technique too exhibits exponential time and space complexity and, worse, does not offer any guarantees for success. To better understand as to why partition refinement succeeds in some cases while it fails in others, we conducted an empirical study on the performance of a partition refinement algorithm for Component Interaction Automata specifications. As a result we have identified suitable predictors for the expected effectiveness of partition refinement. It is the structure, not the size, of a specification that weighs heavier on the outcome of partition refinement. In particular, Component Interaction Automata specifications for real-world systems are capable of producing scale-free networks containing structural artifacts that can assist the partition refinement algorithm not only converge earlier, but also yield a significant state space reduction on occasion.