Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-13T11:08:32.524Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

A. Blumensath and E. Grädel, Automatic structures, in Proceedings of the 15th IEEE Symposium on Logic in Computer Science (LICS 2000), IEEE (2000) 51–62.
Chomsky, N., On certain formal properties of grammars. Inform. Control 2 (1959) 137–167. CrossRef
Chandra, A., Kozen, D. and Stockmeyer, L., Alternation. J. ACM 28 (1981) 114–133. CrossRef
A. Carayol and A. Meyer, Context-sensitive languages, rational graphs and determinism. Log. Meth. Comput. Sci. 2 (2006).
D. Giammarresi and A. Restivo, Handbook of Formal Languages, Vol. 3, Chap. Two-dimensional languages. Springer (1996).
B. Khoussainov and A. Nerode, Automatic presentations of structures, in International Workshop on Logical and Computational Complexity (LCC '94), Springer (1995) 367–392.
Kuroda, S., Classes of languages and linear-bounded automata. Inform. Control 7 (1964) 207–223. CrossRef
Latteux, M. and Simplot, D., Context-sensitive string languages and recognizable picture languages. Inform. Comput. 138 (1997) 160–169. CrossRef
Morvan, C., On rational graphs, in Proceedings of the 3rd International Conference on Foundations of Software Science and Computation Structures (FoSSaCS 2000). Lect. Notes Comput. Sci. 1784 (2000) 252–266. CrossRef
Morvan, C. and Rispal, C., Families of automata characterizing context-sensitive languages. Acta Informatica 41 (2005) 293–314. CrossRef
Morvan, C. and Stirling, C., 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. CrossRef
Penttonen, M., One-sided and two-sided context in formal grammars. Inform. Control 25 (1974) 371–392. CrossRef
C. Rispal, The synchronized graphs trace the context-sensitive languages, in Proceedings of the 4th International Workshop on Verification of Infinite-State Systems (INFINITY 2002). Elect. Notes Theoret. Comput. Sci. 68 (2002).