Verification in Queue-Connected Multicounter Machines

We look at a model of a queue system which consists of two nondeterministic finite-state machines, each augmented with "reversal-bounded" counters, connected by an unbounded queue. One machine (the "writer") can send messages to the other (the "reader") via the queue. There is no central control, but the machines operate synchronously and share the same global clock. Unlike in the traditional model, the writer can make conditional moves that test the emptiness of the queue. We investigate the decidability of various verification problems, e.g., (binary, forward, backward) reachability, safety, and blocking. We also look at extensions of the model: allowing the writer to also test for queue emptiness, adding a pushdown stack to one or both of the machines, allowing multiple queues or two-way communication, etc. Finally, we consider some reachability questions concerning machines operating in parallel.