Verification of Dynamic Linear Lists for All Numbers of Processes

In real-world design and verification 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 finite 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 on..