Traces of term-automatic graphs

Antoine Meyer

RAIRO - Theoretical Informatics and Applications (2008)

  • Volume: 42, Issue: 3, page 615-630
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Meyer, Antoine. "Traces of term-automatic graphs." RAIRO - Theoretical Informatics and Applications 42.3 (2008): 615-630. <http://eudml.org/doc/250366>.

@article{Meyer2008,
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. },
author = {Meyer, Antoine},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Languages; infinite automata; terms; tiling systems; complexity.; graphs defined by term transducers; formal languages},
language = {eng},
month = {6},
number = {3},
pages = {615-630},
publisher = {EDP Sciences},
title = {Traces of term-automatic graphs},
url = {http://eudml.org/doc/250366},
volume = {42},
year = {2008},
}

TY - JOUR
AU - Meyer, Antoine
TI - Traces of term-automatic graphs
JO - RAIRO - Theoretical Informatics and Applications
DA - 2008/6//
PB - EDP Sciences
VL - 42
IS - 3
SP - 615
EP - 630
AB - 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.
LA - eng
KW - Languages; infinite automata; terms; tiling systems; complexity.; graphs defined by term transducers; formal languages
UR - http://eudml.org/doc/250366
ER -

References

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  10. C. Morvan and C. Rispal, Families of automata characterizing context-sensitive languages. Acta Informatica41 (2005) 293–314.  Zbl1067.68086
  11. C. Morvan and C. Stirling, Rational graphs trace context-sensitive languages, in Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science (MFCS 2001). Lect. Notes Comput. Sci.2136 (2001) 548–559.  Zbl0999.68107
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