Veriication of Dynamic Linear Lists for All Numbers of Processes ? Veriication of Dynamic Linear Lists for All Numbers of Processes 2

In real-world design and veriication of concurrent systems with many identical processes, the number of processes is never a factor in the system correctness. This paper embodies such an engineering reasoning to propose an almost automatic method to safely verify safety properties of such systems. The central idea is to construct a nite collective quotient structure (CQS) which collapses state-space representations for all system implementations with all numbers of processes. The problem is presented as safety bound problem which ask if the number of processes satisfying a certain property exceeds a given bound. Our method can be applied to systems with dynamic linear lists of unknown number of processes. Processes can be deleted from or inserted at any position of the linear list during transitions. We have used our method to develop CQS constructing algorithms for two classes of concurrent systems : (1) untimed systems with a global waiting queue and (2) dense-time systems with one local timer per process. We show that our method is both sound and complete in verifying the rst class of systems. The veriication problem for the second class systems is undecidable even with only one global binary variable. However, our method can still automatically generate a CQS of size no more than 1512 nodes to verify that an algorithm in the class: Fischer's timed algorithm indeed preserves mutual exclusion for any number of processes.