PLTL-partitioned model checking for reactive systems under fairness assumptions

We are interested in verifying dynamic properties of finite state reactive systems under fairness assumptions by model checking. The systems we want to verify are specified through a top-down refinement process.In order to deal with the state explosion problem, we have proposed in previous works to partition the reachability graph and to perform the verification on each part separately. Moreover, we have defined a class, called B<inf><i>mod</i></inf>, of dynamic properties that are <i>verifiable by parts</i>, whatever the partition. We decide if a property <i>P</i> belongs to B<inf><i>mod</i></inf> by looking at the form of the Büchi automaton that accepts ¬<i>P</i>. However, when a property <i>P</i> belongs to B<inf><i>mod</i></inf>, the property <i>f</i> ⇒ <i>P</i>, where <i>f</i> is a fairness assumption, does not necessarily belong to B<inf><i>mod</i></inf>.In this paper, we propose to use the refinement process in order to build the parts on which the verification has to be performed. We then show that with such a partition, if a property <i>P</i> is verifiable by parts and if <i>f</i> is the expression of the fairness assumptions on a system, then the property <i>f</i> ⇒ <i>P</i> is still verifiable by parts.This approach is illustrated by its application to the chip card protocol T = 1 using the <i>B</i> engineering design language.

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