Safety Verification of Asynchronous Pushdown Systems with Shaped Stacks

In this paper, we study the program-point reachability problem of con-current pushdown systems that communicate asynchronously via unbounded andunordered message buffers. Our goal is to relax the common restriction that mes-sages can only be retrieved by a pushdown process when its stack is empty. Weintroduce a new class of asynchronously communicating pushdown systems witha mild shape constraint on the stacks, and show that the program-point cover-ability problem remains decidable: stacks that fit the shape may reach arbitraryheights; further a process may execute any communication action (be it processcreation, message send or retrieval) whether or not its stack is empty. This classextends previous computational models studied in the context of asynchronousprograms, and enables the safety verification of a large class of message passingprograms.