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Traces of term-automatic graphs

Published online by Cambridge University Press:  03 June 2008

Antoine Meyer
Antoine Meyer*
Affiliation:
LIAFA, Université Paris Diderot – Paris 7 & CNRS, France; ameyer@liafa.jussieu.fr
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Abstract

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.

Keywords

Languagesinfinite automatatermstiling systemscomplexity.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 615 - 630
Copyright
© EDP Sciences, 2008

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