Automata on Directed Graphs : Edge Versus Vertex Marking
Dietmar Berwanger, David Janin, Dietmar Berwanger, David Janin · 2006
Abstract. We investigate two models of finite-state automata that operate on rooted directed graphs by marking either vertices (V-automata) or edges (E-automata). Runs correspond to locally consistent markings and acceptance is defined by means of regular conditions on the paths emanating from the root. Comparing the expressive power of these two notions of graph acceptors, we first show that E-automata are more expressive than V-automata. Moreover, we prove that E-automata are at least as expressive as the µ-calculus. However, to achieve this expressiveness, the usual infinitary acceptance conditions such as parity, Street, Rabin, or Muller conditions, do not suffice, and more general ω-regular conditions are necessary. Our main result implies that every MSO-definable tree language can be recognised by E-automata with uniform runs, that is, runs that do not distinguish between isomorphic subtrees.