State Complexity of Boolean Operations on Graph-Walking Automata

Abstract

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 [Formula: see text] and [Formula: see text] states, with [Formula: see text], operating on graphs with [Formula: see text] labels of edge end-points, is representable by a GWA with [Formula: see text] states, and at least [Formula: see text] states are necessary in the worst case. For the intersection, the upper bound is [Formula: see text] and the lower bound is [Formula: see text]. The upper bound for the complementation is [Formula: see text], and the lower bound is [Formula: see text].