Verifying Networks of Timed ProcessesParosh

Over the last years there has been an increasing research eeort directed towards the automatic veriication of innnite state systems, such as timed automata, hybrid automata, data-independent systems, rela-tional automata, Petri nets, and lossy channel systems. We present a method for deciding reachability properties of networks of timed processes. Such a network consists of an arbitrary set of identical timed automata, each with a single real-valued clock. Using a standard reduction from safety properties to reachability properties, we can use our algorithm to decide general safety properties of timed networks. To our knowledge, this is the rst decidability result concerning ver-iication of systems that are innnite-state in \two dimentions": they contain an arbitrary set of (identical) processes, and they use innnite data-structures, viz. real-valued clocks. We illustrate our method by showing how it can be used to automatically verify Fischer's protocol , a timer-based protocol for enforcing mutual exclusion among an arbitrary number of processes. Finally, we show the undecidability of temporal logics, such as PTL and CTL, for timed networks. To do that we rst prove the undecid-ability of the recurrent state problem: given a state in a timed network, check whether there is a computation of the network visiting the state innnitely often. The undecidability result follows immediately, since the recurrent state problem is expressible in these logics.