Verifying Universal Properties of Parameterized Networks

Kai Baukus1 Yassine Lakhne h2y Karsten Stahl1 1 Institute of Computer S ien e and Applied Mathemati s University of Kiel Preusserstr. 1{9, D-24105 Kiel, Germany fkba, kstg informatik.uni-kiel.de 2 VERIMAG, Centre Equation 2 Av. de Vignate, 38610 Gi eres, Fran e lakhne h imag.fr Abstra t In this paper, we present a method for the veri ation of soalled universal properties of fair parameterized networks of similar pro esses, that is, properties of the form 8p1 : : : pn : , where is a quanti er-free LTL formula. To prove an universal property of a parameterized network, we rst model the in nite family of networks by a single fair WS1S transition system, that is, a transition system whose variables are set (2nd-order) variables and whose transitions are des ribed in WS1S. Then, we abstra t the WS1S system into a nite state system that an be modelhe ked. We present a generi abstra tion relation for verifying universal properties as well as an algorithm for omputing an abstra t system. However, the abstra t system may ontain in nite omputations that have no orresponding fair omputations at the on rete level, and hen e, in ase the property of interest is a progress property, veri ation may fail be ause of this. Therefore, we present methods that allow to synthesize fairness onditions from the parameterized network and dis uss under whi h onditions and how to lift fairness onditions of this network to fairness onditions on the abstra t system. We implemented our methods in a tool, alled pax, and applied it to several examples.