Reactive Synthesis for Golog Specifications in the Propositional Situation Calculus

Golog programs over Situation Calculus action theories were introduced as a specification of desired agent behavior, very much like temporally extended goals in planning, but with a focus on procedural aspects typical of programs. In the words of the original paper: "Golog allows the programmer to strike a compromise between the often computationally infeasible classical planning task, in which a plan must be deduced entirely from scratch, and detailed programming, in which every little step must be specified." In this paper, we study temporal synthesis with Golog programs as specifications over nondeterministic propositional action theories. We show that Golog has the same expressive power as linear dynamic logics on finite traces (LDLf), namely that of regular languages or monadic second-order logic (MSO) over finite traces, while exhibiting a markedly lower synthesis complexity: synthesis can be performed by constructing a polynomial-size program graph and taking its cross-product with the domain, whereas LDLf synthesis requires building a deterministic automaton of worst-case doubly exponential size. This advantage is confirmed experimentally.