Detecting Mutex Pairs in State Spaces by Sampling

In the context of state space planning, a mutex pair is a pair of variable-value assignments 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 Missing Mass Method (MMM)—a new efficient and domain-independent method for mutex pair detection, based on sampling reachable states. We exploit a recent result from statistical theory, proven by Berend and Kontorovich in [1], that bounds the probability mass of missing events in a sample of a given size. We tested MMM empirically on various sizes of four standard benchmark domains from the planning and heuristic search literature. In many cases, MMM works perfectly, i.e., finds all and only the mutex pairs. In the other cases, it is near-perfect: it correctly labels all mutex pairs and more than 99.99% of all non-mutex pairs.