Reachability and safety in queue systems

Abstract

We look at a model of a queue system M that consists of the following components: 1. Two nondeterministic finite-state machines W and R, each augmented with finitely many reversal-bounded counters (thus, each counter can be incremented or decremented by 1 and tested for zero, but the number of alternations between nondecreasing mode and nonincreasing mode is bounded by a fixed constant). W or R (but not both) can also be equipped with an unrestricted pushdown stack. 2. One unrestricted queue that can be used to send messages from W (the “writer”) to R (the “reader”). There is no bound on the length of the queue. When R tries to read from an empty queue, it receives an “empty-queue” signal. When this happens, R can continue doing other computation and can access the queue at a later time. W and R operate at the same clock rate, i.e., each transition (instruction) takes one time unit. There is no central control. Note that since M is nondeterministic there are, in general, many computation paths starting from a given initial configuration. We investigate the decidable properties of queue systems. For example, we show that it is decidable to determine, given a system M, whether there is some computation in which R attempts to read from an empty queue. Other verification problems that we show solvable include (binary, forward, and backward) reachability, safety, invariance, etc. We also consider some reachability questions concerning machines operating in parallel.