Psvn: a Vector Representation for Production Systems Psvn: a Vector Representation for Production Systems

In this paper we present a production system which acts on xed length vectors of labels. Our goal is to automatically generate heuristics to search the state space for shortest paths between states eeciently. The heuristic values which guide search in the state space are obtained by searching for the shortest path in an abstract space derived from the deenition of the original space. In PSVN, a state is a xed length vector of labels and abstractions are generated by simply mapping the set of labels to another smaller set of labels (domain abstraction). A domain abstraction on labels induces a state space abstraction and this abstract space preserves important properties of the original space while usually being signiicantly smaller in size. It is guaranteed that the shortest path between two states in the original space is at least as long as the shortest path between their images in the abstract space. Hence, such abstractions provide admissible heuristics for search algorithms such as A* and IDA*. The mapping of states and operators can be eeciently obtained by applying the domain map on the labels. We explore important properties of state spaces deened in PSVN and abstractions generated by domain maps. Despite its simplicity, PSVN is capable to deene all nitely generated permutation groups and such benchmark problems as Rubik's Cube, the sliding-tile puzzles and the Blocks World.