Symbolic pattern planning

In this paper, we propose a novel approach for solving automated planning problems, called Symbolic Pattern Planning. Given a deterministic planning problem Π, we propose to compute a plan by first fixing a pattern –defined as an arbitrary sequence of actions– and then define a formula encoding the state resulting from the sequential execution of the actions in the pattern, starting from an arbitrary initial state. By allowing each action in the pattern to be executed consecutively zero, one or possibly more times, and by imposing the conditions on the initial and goal states, we can check whether the pattern allows determining a valid plan or whether the pattern needs to be extended and the procedure iterated. We ground our proposal in the numeric planning setting, we prove the correctness and also the completeness of the procedure (provided at each iteration the pattern is extended with a complete sequence of actions), and we define procedures for the pattern selection and for computing quality plans. When exploiting the planning as satisfiability approach, we show that our encoding allows to determine a valid plan in a number of iterations which is never higher than the one needed by the state-of-the-art rolled-up or relaxed-relaxed-∃ symbolic encodings. On the experimental side, we run an extensive analysis which included the problems and systems involved in the numeric track of the 2023 International Planning Competition, showing that the results validate the theoretical findings and that our planner PATTY has remarkably good comparative performances.