In formal language theory, many families of languages are defined using grammars or finite acceptors like pushdown automata and Turing machines. 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.


Turing Machine Tiling System Input Word Rational Graph Tree Transducer 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Antoine Meyer
    • 1
  1. 1.LIAFA – Université Paris Diderot – Paris 7, Case 7014, 2 place Jussieu, 75251 Paris Cedex 05France

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