Parameterisation of Three-Valued Abstractions

Abstract

T hree-valued abstraction is an established technique in software m odelchecking. It proceeds by generating a state space m odelover the values true, false and unknown, where the latter value is used to represent the loss of inform ation due to abstraction. T em p orallogic properties can then be evaluated on such m odels. In case of an unknown result, the abstraction is iteratively refined. In this paper, we introduce parameterised three-valued model checking. In our new type of m odels, unknown parts can be either associated with the constant value unknown or with expressions over boolean param eters. O ur param eterisation is an alternative way to state that the truth value of certain predicates or transitions is actually not known and that the checked property has to yield the sam e result under each possible param eter instantiation. A novel feature of our approach is that it allows for establishing logical connections between param eters: W hile unknown parts in pure three-valued m odels are never related to each other, our param eterisation approach enables to represent facts like 'a certain pair of transitions has unknown but com plem entary truth values', or 'the value of a predicate is unknown but rem ains constant along all states of a certain path'. W e dem onstrate that such facts can be autom atically derived from the system to be verified and that covering these facts in an abstract m odel can be crucial for the success and efficiency of checking tem poral logic properties. M oreover, we introduce an autom atic verification fram ework based on counterexam ple-guided abstraction refinem ent and param eterisation.