A mutex pair in a state space is a pair of assignments of values to state variables that does not occur in any reachable state. Detecting mutex pairs is a problem that has been addressed frequently in the planning literature. In this paper, we present the Coarse Abstraction (CA) method, a new efficient method for detecting mutex pairs in state spaces represented with multi-valued variables. CA detects mutex pairs based on exhaustive search in a collection of very small abstract state spaces. While in general CA may miss some mutex pairs, we provide a formal guarantee that CA finds all mutex pairs under a simple and quite natural condition. Using this formal guarantee, we prove that these properties hold for a range of common benchmark domains. We also show that CA can find all mutex pairs even if the formal guarantee is not satisfied. Finally, we show that CA's effectiveness depends on how the domain is represented, and that it can fail to find mutex pairs in some domains and representations.

Mutex groups are defined in the context of STRIPS planning as sets of facts out of which, maximally, one can be true in any state reachable from the initial state. The importance of computing and exploiting mutex groups was repeatedly pointed out in many studies. However, the theoretical analysis of mutex groups is sparse in current literature. This work provides a complexity analysis showing that inference of mutex groups is as hard as planning itself (PSPACE-Complete) and it also shows a tight relationship between mutex groups and graph cliques. This result motivates us to propose a new type of mutex group called a fact-alternating mutex group (fam-group) of which inference is NP-Complete. Moreover, we introduce an algorithm for the inference of fam-groups based on integer linear programming that is complete with respect to the maximal fam-groups and we demonstrate how beneficial fam-groups can be in the translation of planning tasks into finite domain representation. Finally, we show that fam-groups can be used for the detection of dead-end states and we propose a simple algorithm for the pruning of operators and facts as a preprocessing step that takes advantage of the properties of fam-groups. The experimental evaluation of the pruning algorithm shows a substantial increase in a number of solved tasks in domains from the optimal deterministic track of the last two planning competitions (IPC 2011 and 2014).