State Complexity of Boolean Operations on Graph-Walking Automata

Finite automata that traverse graphs by moving along their edges are known as graph-walking automata (GWA). This paper investigates the state complexity of Boolean operations for this model. It is proved that the union of GWA with m and n states, with m <= n, operating on graphs with k labels of edge end-points, is representable by a GWA with 2km + n + 1 states, and at least 2(k - 3)(m - 1) + n - 1 states are necessary in the worst case. For the intersection, the upper bound is (2k + 1)m + n and the lower bound is 2(k - 3)(m - 1) + n - 1. The upper bound for the complementation is 2kn + 1, and the lower bound is 2(k - 3)(n - 1).