Psvn: a V Ector 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 e ciently 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 de nition of the original space In PSVN a state is a xed length vector of labels and abstrac tions are generated by simply mapping the set of labels to another smaller set of labels domain abstraction A domain abstraction on labels in duces a state space abstraction and this abstract space preserves important properties of the origi nal space while usually being signi cantly 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 e ciently obtained by applying the domain map on the labels We explore im portant properties of state spaces de ned in PSVN and abstractions generated by domain maps De spite its simplicity PSVN is capable to de ne all nitely generated permutation groups and such benchmark problems as Rubik s Cube the sliding tile puzzles and the Blocks World