Realizability of Concurrent Recursive Programs

摘要

We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multi-stack visibly pushdown automata and Zielonka's asynchronous automata towards a model with an undecidable emptiness problem. However, a reasonable restriction allows us to lift Zielonka's Theorem to this recursive setting and permits a logical characterization in terms of a suitable monadic second-order logic. Building on results from Mazurkiewicz trace theory and work by La Torre, Madhusudan, and Parlato, we thus develop a framework for the specification, synthesis, and verification of concurrent recursive processes.