Ricerc@Sapienza

We introduce and study Regular Decision Processes (RDPs), a new, compact, factored model for domains with non-Markovian dynamics and rewards. In RDPs, transition and reward functions are specified using formulas in linear dynamic logic over finite traces, a language with the expressive power of regular expressions. This allows specifying complex dependence on the past using intuitive and compact formulas, and provides a model that generalizes MDPs and k-order MDPs.

In this paper, we investigate non-Markovian Nondeterministic Fully Observable Planning Domains (NMFONDs), variants of Nondeterministic Fully Observable Planning Domains (FONDs) where the next state is determined by the full history leading to the current state. In particular, we introduce TFONDs which are NMFONDs where conditions on the history are succinctly and declaratively specified using the linear-time temporal logic on finite traces LTLf and its extension LDLf. We provide algorithms for planning in TFONDs for general LTLf/LDLf goals, and establish tight complexity bounds w.r.t.