Testing for cycles in infinite graphs with periodic structure

A k-dimensional dynamic graph is obtained by repeating a basic: cell in a kdimensional orthogonal grid. The nodses in each cell are connected to a finite number of nodes in other cells, and, furthermore, the pattern of the inter-cell connections is the same for each cell. Thus, a dynamic gra.ph is a finitely described infinite graph, w:ith a periodic structure. In this paper we study the problem of deciding whether a given twodimensional dynamic graph has a directed cycle.