Inapproximability of STRIPS Planning

Automated planning involves finding a sequence of actions that changes the world from an initial state to a final state with goals satisfied. The general problem is PSPACE-hard. Nevertheless, many restricted variants are NP-complete or even in P. Existing complexity work focuses mostly on plan existence, or plan with minimal plan length. Little is known about optimization variants that aim to satisfy as many goal conditions as possible. In this paper, we aim to fill this gap by providing a first inapproximability study of goal-maximization using the classical STRIPS formalism. For MAX-PLANSAT and its length-bounded counterpart MAX-PLANSAT(K), we prove tight constant-factor lower bounds. More specifically, through performing L-reductions from MAXE3SAT and MAX3DM, we show several of these problems are inapproximable by a constant factor, unless P = NP.