A dual graph translation of a problem in ‘life’

Abstract

Conway’s game of Life provides interesting problems in which modelling issues in constraint programming can be explored. The problem of finding a maximum density stable pattern (‘still-life’) is discussed.A formulation of this problem as a constraint satisfaction problem with 0-1 variables and non-binary constraints is compared with its dual graph translation into a binary CSP. The success of the dual translation is surprising, from previously-reported experience, since it has as many variables as the non-binary CSP and very large domains. An important factor is the identification of many redundant constraints: it is shown that these can safely be removed from a dual graph translation if arc consistency is maintained during search.