Analysis of partial order reduction techniques for automated planning Abstract: Automated planning is an area of Artiﬁcial Intelligence (AI) that is closely related to decision making. Given a planning problem which is described as an initial state (i.e. a start conﬁguration of the problem) a set of actions and a goal description a planning algorithm is concerned with ﬁnding a sequence of actions or a strategy for achieving the goal conditions from the initial state. Planning in all its variations is a hard problem. Classical planning is one of the simplest forms of planning. Despite its simplicity it is still computationally intractable. Therefore planning problems cannot be solved by brute force algorithms but rather by goal directed algorithms that tackle the complexity of planning. Planning as heuristic search is a prominent technique that has been considered in the area of automated planning. However recent research has shown that planning as heuristic search needs the aid of orthogonal techniques. Partial order reduction is a well known and reliable approach that has originally been introduced in the area of computer aided veriﬁcation to tackle the state explosion problem. It is usually used for explicit state space search to reduce the size of the generated state space. There are two categories of partial order reduction techniques: State reduction and transition reduction techniques. The former are specialized to prune some states that are guaranteed to be uncritical for reaching some ﬁnal states (e.g. goal states in planning) while the latter are designed to prune only redundant states. Later new partial order reduction techniques have been proposed for optimal planning algorithms. However the formal relationships between the previous and later techniques were unclear and furthermore some of the novel techniques were faulty. In the context of classical planning we investigate two variants of a powerful state reduction technique from the area of model checking called stubborn sets. Furthermore we propose a new deﬁnition of stubborn sets for Fully Observable Non Deterministic planning (FOND). For classical planning we show that stubborn sets are completeness and optimality preserving whereas for FOND planning we show that they are at least completeness preserving. In addition we compare between stubborn sets and previous partial order reduction techniques proposed for optimal planning. Moreover we study a transition reduction technique from the area of model checking called sleep ...