A Generalization of Sleep Sets Based on Operator Sequence Redundancy

Abstract

Pruning techniques have recently been shown to speed up search algorithms by reducing the branching factor of large search spaces. One such technique is sleep sets, which were originally introduced as a pruning technique for model checking, and which have recently been investigated on a theoretical level for planning. In this paper, we propose a generalization of sleep sets and prove its correctness. While the original sleep sets were based on the commutativity of operators, generalized sleep sets are based on a more general notion of operator sequence redundancy. As a result, our approach dominates the original sleep sets variant in terms of pruning power. On a practical level, our experimental evaluation shows the potential of sleep sets and their generalizations on a large and common set of planning benchmarks.

Sleep Sets Meet Duplicate Elimination

“…In the literature (Godefroid and Wolper 1992;Godefroid, Holzmann, and Pirottin 1993;Godefroid 1996;Holte, Alkhazraji, and Wehrle 2015) To avoid operators to be propagated in case a cycle is closed, the second step (ii) is restricted to be performed only if σo does not yield a state that is already on the search stack (Godefroid, Holzmann, and Pirottin 1993).…”

“…, σ n ) := ss(σ n ). This variant has been proposed for planning (Holte, Alkhazraji, and Wehrle 2015) within IDA * and cycle detection. Holte et al provide a more general definition of sleep sets that allows for more pruning.…”

“…For our investigations, we need some more terminology. Following Holte et al (2015), orderings < O on the set O of operators induce a lexicographical ordering on the set of operators sequences: for operator sequences σ − 1, and o i = o i . For an ordering defined on O, we will use the same symbol for the induced lexicographical ordering on operator sequences when the meaning is clear from the context.…”

“…State space search is a popular approach to solve search and planning tasks. To tackle the state explosion problem, techniques like move pruning (Burch and Holte 2012;Holte and Burch 2014) and sleep sets (Godefroid and Wolper 1992;Godefroid 1996;Wehrle and Helmert 2012;Holte, Alkhazraji, and Wehrle 2015) have been investigated. Both move pruning and sleep sets are path-dependent pruning techniques that preserve the reachability of all reachable states.…”

“…A state s is a partial state with vars(s) = V. We assume a given initial state s 0 and a partial goal state s . We will denote Holte et al (2015). Let < ss be a total order on the set of operators O.…”