Characteristic invariants in Hennessy\u2013Milner logic

Abstract

In this paper, we prove that Hennessy–Milner Logic (HML), despite its structural limitations, is sufficiently expressive to specify an initial property varphi _0 and a characteristic invariant upchi _{_I} for an arbitrary finite-state process P such that varphi _0 wedge mathbf{AG }(upchi _{_I}) is a characteristic formula for P. This means that a process Q, even if infinite state, is bisimulation equivalent to P iff Q models varphi _0 wedge mathbf{AG }(upchi _{_I}). It follows, in particular, that it is sufficient to check an HML formula for each state of a finite-state process to verify that it is bisimulation equivalent to P. In addition, more complex systems such as context-free processes can be checked for bisimulation equivalence with P using corresponding model checking algorithms. Our characteristic invariant is based on so called class-distinguishing formulas that identify bisimulation equivalence classes in P and which are expressed in HML. We extend Kanellakis and Smolka’s partition refinement algorithm for bisimulation checking in order to generate concise class-distinguishing formulas for finite-state processes.