A General Modular Synthesis Problem For Pushdown Systems

The modular synthesis from a library of components (LMS) asks to compose a recursive state machine satisfying a given specification, by modularly controlling a finite set of component instances taken from the library. It combines and subsumes two synthesis problems studied in the literature: the synthesis from libraries of recursive components and the modular strategy synthesis. We consider standard specifications as reachability and safety (expressed by finite automata), and visibly pushdown automata specifications, and show that for all these classes of specifications the Lms problem is EXPTIME-complete.