Integration of state machine graphical animation and Maude to facilitate characteristic conjecture: an approach to lemma discovery in theorem proving

State Machine Graphical Animation (called SMGA) is a visualization tool that assists formal methods experts in conjecturing characteristics of a protocol/system. The characteristics guessed by using the tool can be used as lemma candidates to theorem prove that the protocol/system satisfies its desired properties. Because previous work has shown that interaction in SMGA is one promising factor to foster assistance, in this paper, we revise SMGA equipping it with various interactive features in order to help human users in conjecturing lemmas. Moreover, we integrate SMGA and Maude, a declarative language and high-performance tool, so that the revised version of SMGA (called r-SMGA) can use some powerful features of Maude, such as parsing associative-commutative binary operators as well as context-free grammars, reachability analysis, and model checking. We conduct a case study with the Suzuki-Kasami protocol to demonstrate the usefulness of these new features. In the case study, some characteristics are conjectured and confirmed with these features. Based on the guessed characteristics and assistance of r-SMGA, we successfully prove that the protocol enjoys the mutual exclusion property. Finally, we propose guidelines that can help users to conjecture characteristics using r-SMGA. Our result shows that the graphical animation approach is useful for lemma conjecture in theorem proving. The formal verification is a part of the case study.