Traces of Term-Automatic Graphs

Antoine Meyer (1)

1 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

In formal language theory, many families of languages are defined using either grammars or finite acceptors. For instance, context-sensitive languages are the languages generated by growing grammars, or equivalently those accepted by Turing machines whose work tape's size is proportional to that of their input. A few years ago, a new characterisation of context-sensitive languages as the sets of traces, or path labels, of rational graphs (infinite graphs defined by sets of finite-state transducers) was established. We investigate a similar characterisation in the more general framework of graphs defined by term transducers. In particular, we show that the languages of term-automatic graphs between regular sets of vertices coincide with the languages accepted by alternating linearly bounded Turing machines. As a technical tool, we also introduce an arborescent variant of tiling systems, which provides yet another characterisation of these languages.

Mots clés: languages; infinite automata; terms; tiling systems; complexity

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Antoine Meyer. Traces of Term-Automatic Graphs. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), 2008, 42, p. 615-630. ⟨10.1051/ita:2008018⟩. ⟨hal-00325729⟩