Improving formal analysis of state machines with particular emphasis on and-cross transitions

Abstract

In this paper, we present an approach to formally encode state machines expressed in Umple for symbolic verification. We illustrate this with a real-world modeling example that encodes and analyzes and-cross transitions. This paper discusses a formal description of our approach to represent state machine systems under analysis (SSUAs); a systematic approach to certifying that SSUAs are deterministic; and an evaluation of performance (memory usage and execution time) on the case study. MethodWe describe a formalization of state machines in Umple that enables their translation to model checking tools and also to code that is consistent with this. We present three alternative modeling solutions for a sample problem and a solution based on the use of and-cross transitions. State machine models corresponding to these solutions are represented in Umple, a model-oriented programming language. These are automatically transformed to SMV, the input language of the nuXmv (or NuSMV) model checker. By cleanly separating concerns, we systematically integrate components of hierarchical state systems as opposed to the traditional flattening approach, yet manage the complexity introduced by concurrency and and-crossing. We then compose and verify a set of requirements (e.g., correctness, safety, liveliness, etc.) on the resulting systems of all the modeling approaches to empirically compare the different modeling alternatives with the use of and-cross transitions. ResultsWe can encode and formally analyse complex state machines with and-cross transition(s). We observed a large reduction in the number of required transitions for encoding the SSUA, as opposed to the alternative approaches. We asserted that solutions derived from the approaches are identical behavior-wise even though each approach models the SSUA differently. Each of the approaches yielded the same result for potentially conflicting pairs which is a false positive (i.e., the SSUAs are deterministic). We observe that each approach maintains the same global state-space irrespective of the variations in their number of transitions. Furthermore, we observe that it is untrue that a more abstract method applied to an SSUA outperforms its less abstract counterpart whenever parameters (such as execution time, memory usage and the number of Binary Decision Diagrams - BDDs) are the factors under consideration. ContributionsA systematic approach to encode state machines with and-cross transitions (including unusual transitions). An enhanced but fully automated approach to discovering nondeterminism in state machines even in the presence of unbounded domains and multiple and-cross transitions within the same enclosing orthogonal state. An empirical study of the impact of abstraction on some performance parameters. We also present an extended formalization of Umple state machines.