Reducing an Operational Supervisory Control Problem by Decomposition for Deterministic Pushdown Automata

The purpose of Supervisory Control Theory (SCT) is to synthesize a controller for a plant and a specification such that the desired closed-loop behavior is enforced. Effective solvers have been constructed in the past for the setting of plants and specifications modeled by Deterministic Finite Automata (DFA). We extend the domain of the specification to Deterministic Pushdown Automata (DPDA) and verify an effective solver (up to two basic building blocks which ensure controllability and blockfreeness, effectively solved for this setting in two companion papers). We verify the enforcement of desired operational criteria, which are, in contrast to the setting of DFA, partly oblivious to the (un)marked language of the closed loop. Our general approach trivially covers the setting of DFA and can be reused and adapted to develop effective solvers for other settings as the realizability of solutions to the supervisory control problem (SCP) is considered on an abstract level.