Symbolic Numeric Planning with Patterns

In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem $Π$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions -- we encode the problem of finding a plan for $Π$ with bound $n$ as a formula with fewer variables and/or clauses than the state-of-the-art rolled-up and relaxed-relaxed-$\exists$ encodings. More importantly, we prove that for any given bound, it is never the case that the latter two encodings allow finding a valid plan while ours does not. On the experimental side, we consider 6 other planning systems -- including the ones which participated in this year's International Planning Competition (IPC) -- and we show that our planner Patty has remarkably good comparative performances on this year's IPC problems.