Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-22T23:16:45.074Z Has data issue: false hasContentIssue false
  • English
  • Français

On the classes of languages accepted by limited context restarting automata∗∗∗∗∗∗

Published online by Cambridge University Press:  10 February 2014

Friedrich Otto ,
Peter Černo  and
František Mráz
Friedrich Otto
Affiliation:
Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany. otto@theory.informatik.uni-kassel.de
Peter Černo
Affiliation:
Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Praha 1, Czech Republic; petercerno@gmail.com; mraz@ksvi.ms.mff.cuni.cz
František Mráz
Affiliation:
Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Praha 1, Czech Republic; petercerno@gmail.com; mraz@ksvi.ms.mff.cuni.cz
Get access

Abstract

In the literature various types of restarting automata have been studied that are based on contextual rewriting. A word w is accepted by such an automaton if, starting from the initial configuration that corresponds to input w, the word w is reduced to the empty word by a finite number of applications of these contextual rewritings. This approach is reminiscent of the notion of McNaughton families of languages. Here we put the aforementioned types of restarting automata into the context of McNaughton families of languages, relating the classes of languages accepted by these automata in particular to the class GCSL of growing context-sensitive languages and to the class CRL of Church–Rosser languages.

Keywords

Restarting automatoncontextual rewritingMcNaughton family of languages
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 48 , Issue 1: Non-Classical Models of Automata and Applications (NCMA 2012) , January 2014 , pp. 61 - 84
Copyright
© EDP Sciences 2014

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

S. Basovník, Learning restricted restarting automata using genetic algorithm. Master’s thesis, Charles University. Faculty of Mathematics and Physics, Prague, Czech (2010).
S. Basovník and F. Mráz, Learning limited context restarting automata by genetic algorithms, in Theorietag, edited by J. Dassow and B. Truthe. Otto-von-Guericke-Universität, Magdeburg (2011) 1–4.
Beaudry, M., Holzer, M., Niemann, G. and Otto, F., McNaughton families of languages. Theoret. Comput. Sci. 290 (2003) 1581–1628. Google Scholar
R.V. Book and F. Otto, String-Rewriting Systems. Springer, New York (1993).
Büchi, J.R., Regular canonical systems. Arch. f. Math. Logik Grundlagenf. 6 (1964) 91–111. Google Scholar
G. Buntrock,Wachsende kontext-sensitive Sprachen. Habilitationsschrift. Fakultät für Mathematik und Informatik, Universität Würzburg (1996).
Buntrock, G. and Otto, F., Growing context-sensitive languages and Church-Rosser languages. Inf. Comput. 141 (1998) 1–36. Google Scholar
J. Čejka, Learning correctness preserving reduction analysis. BSc Project, Charles University. Faculty of Mathematics and Physics, Prague, Czech (2003).
Černo, P. and Mráz, F., Clearing restarting automata. Fund. Inf. 104 (2010) 17–54. Google Scholar
P. Černo and F. Mráz, Δ-clearing restarting automata and CFL, in edited by G. Mauri and A. Leporati. DLT 2011, in vol. 6795 of Lect. Notes Comput. Sci. Springer, Berlin (2011) 153–164.
Dahlhaus, E. and Warmuth, M., Membership for growing context-sensitive grammars is polynomial. J. Comput. System Sci. 33 (1986) 456–472. Google Scholar
Hofbauer, D. and Waldmann, J., Deleting string rewriting systems preserve regularity. Theoret. Comput. Sci. 327 (2004) 301–317. Google Scholar
P. Hoffmann, Learning restarting automata by genetic algorithms, in SOFSEM 2002: Student Research Forum, edited by M. Bieliková. Masaryk University, Brno (2002) 15–20.
P. Jančar, F. Mráz, M. Plátek and J. Vogel, Restarting automata, FCT’95, in vol. 965 of Lect. Notes Comput. Sci., edited by H. Reichel. Springer, Berlin (1995) 283–292.
Jančar, P., Mráz, F., Plátek, M. and Vogel, J.. On monotonic automata with a restart operation. J. Autom. Lang. Comb. 4 (1999) 287–311. Google Scholar
D. Knuth and P. Bendix, Simple word problems in universal algebras, in Comput. Problems in Abstract Algebra, edited by J. Leech. Pergamon Press, New York (1970) 263–297.
Leupold, P. and Otto, F., On McNaughton families of languages that are specified by some variants of monadic string-rewriting systems. Fund. Inf. 112 (2011) 219–238. Google Scholar
McNaughton, R., Narendran, P. and Otto, F., Church-Rosser Thue systems and formal languages. J. Assoc. Comput. Mach. 35 (1988) 324–344. Google Scholar
F. Mráz, F. Otto and M. Plátek, Learning analysis by reduction from positive data, in ICGI 2006, in vol. 4201 of Lect. Notes Comput. Sci., edited by Y. Sakakibara, S. Kobayashi, K. Sato, T. Nishino and E. Tomita. Springer, Berlin (2006) 125–136.
Niemann, G. and Otto, F., The Church-Rosser languages are the deterministic variants of the growing context-sensitive languages. Inform. Comput. 197 (2005) 1–21. Google Scholar
G. Niemann and J.R. Woinowski, The growing context-sensitive languages are the acyclic context-sensitive languages, in DLT 2002, in vol. 2295 of Lect. Notes Comput. Sci., edited by W. Kuich, G. Rozenberg and A. Salomaa. Springer, Berlin (2002) 197–205.
Otto, F., On deciding the confluence of a finite string-rewriting system on a given congruence class. J. Comput. System Sci. 35 (1987) 285–310. Google Scholar
F. Otto, Restarting automata, Recent Advances in Formal Languages and Applications, in vol. 25 of Studies in Comput. Intelligence, edited by Z. Ésik, C. Martin-Vide and V. Mitrana. Springer, Berlin (2006) 269–303.
F. Otto, P. Černo and F. Mráz, Limited context restarting automata and McNaughton families of languages, in Fourth Workshop on Non-Classical Models for Automata and Applications (NCMA 2012), Proc., books@ocg.at, Band 290, edited by R. Freund, M. Holzer, B. Truthe and U. Ultes-Nitsche. Oesterreichische Computer Gesellschaft, Wien (2012) 165–180.
Woinowski, J., The context-splittable normal form for Church-Rosser language systems. Inform. Comput. 183 (2003) 245–274. Google Scholar