Automata on Directed Graphs : Edge versus Vertex Marking

Dietmar Berwanger (1) , David Janin (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We investigate two models of finite-state automata that op- erate 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 ?-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.

Domaines: Autre [cs.OH]

Dietmar Berwanger, David Janin. Automata on Directed Graphs : Edge versus Vertex Marking. ICGT, Sep 2006, Brazil. pp.46--60. ⟨hal-00306378⟩