Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T19:39:53.729Z Has data issue: false hasContentIssue false
  • English
  • Français

Classes of two-dimensional languages and recognizability conditions

Published online by Cambridge University Press:  28 February 2011

Marcella Anselmo  and
Maria Madonia
Marcella Anselmo
Affiliation:
Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84084 Fisciano (SA), Italy; anselmo@dia.unisa.it
Maria Madonia
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy; madonia@dmi.unict.it
Get access

Abstract

The paper deals with some classes of two-dimensional recognizable languages of “high complexity”, in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages. For such classes we can solve some open questions related to unambiguity, finite ambiguity and complementation. Then we reformulate a necessary condition for recognizability stated by Matz, introducing a new complexity function. We solve an open question proposed by Matz, showing that all the known necessary conditions for recognizability of a language and its complement are not sufficient. The proof relies on a family of languages defined by functions.

Keywords

Two-dimensional languagesunambiguitycomplement
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 44 , Issue 4 , October 2010 , pp. 471 - 488
Copyright
© EDP Sciences, 2011

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

Anselmo, M. and Madonia, M., Deterministic and unambiguous two-dimensional languages over one-letter alphabet. Theoret. Comput. Sci. 410 (2009) 1477–1485. CrossRef
Anselmo, M. and Madonia, M., A note on unambiguity, finite ambiguity and complementation in recognizable two-dimensional languages, in Proc. CAI 09. Lect. Notes Comput. Sci. 5725 (2009) 147–159. CrossRef
Anselmo, M., Giammarresi, D., Madonia, M. and Restivo, A.. Unambiguous recognizable two-dimensional languages. RAIRO-Theor. Inf. Appl. 40 (2006) 227–294. CrossRef
Anselmo, M., Giammarresi, D. and Madonia, M., From determinism to non-determinism in recognizable two-dimensional languages, in Proc. DLT 07. Lect. Notes Comput. Sci. 4588 (2007) 36–47. CrossRef
Anselmo, M., Jonoska, N. and Madonia, M., Framed versus unframed two-dimensional languages, in Proc. SOFSEM 09. Lecture Notes in Comput. Sci. 5404 (2009) 79–92. CrossRef
Anselmo, M., Giammarresi, D. and Madonia, M., Deterministic and unambiguous families within recognizable two-dimensional languages. Fund. Inform. 98 (2010) 143–166.
Bertoni, A., Goldwurm, M. and Lonati, V., The complexity of unary tiling-recognizable picture languages. Fund. Inform. 90 (2009) 231–249.
Birget, J.-C., Intersection and union of regular languages and state complexity. Inform. Proces. Lett. 43 (1992) 185–190. CrossRef
S. Brocchi, Bidimensional pictures: reconstruction, expression and encoding, Ph.D. thesis. http://www.dsi.unifi.it/DRIIA/RaccoltaTesi/Brocchi.pdf
J. Cervelle, Langages de figures, Rapport de stage, ENS Lyon (1997).
S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press (1974).
D. Giammarresi, Two-dimensional languages and recognizable functions, in Proc. DLT 93, edited by G. Rozenberg and A. Salomaa. World Scientific Publishing Co., Singapore (1994), 290–301.
Giammarresi, D. and Restivo, A., Recognizable picture languages. Int. J. Pattern Recogn. Artif. Intell. 6 (1992) 241–256. CrossRef
D. Giammarresi and A. Restivo, Two-dimensional languages, Handbook of Formal Languages, Vol. III. G. Rozenberg et al., Eds. Springer Verlag (1997), 215–268.
D. Giammarresi and A. Restivo, Matrix based complexity functions and recognizable picture languages, in Logic and Automata: History and Perspectives, E. Grader, J. Flum and T. Wilke, Eds. Texts in Logic and Games 2. Amsterdam University Press (2007), 315–337.
D. Giammarresi and A. Restivo, Ambiguity and complementation in recognizable two-dimensional languages, in Proc. Int. Conf. Theoret. Comput. Sci., IFIP, Vol. 273, edited by G. Ausiello, J. Karhumäki, G. Mauri and L. Ong. Springer, Boston (2008), 5–20.
Glaister, I., Shallit, J., A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59 (1996) 75–77. CrossRef
J. Hromkovic, Communication Complexity and Parallel Computing. Springer (1997).
Hromkovic, J., Karumäki, J., Klauck, H., Schnitger, G. and Seibert, S., Communication complexity method for measuring nondeterminism in finite automata. Inform. Comput. 172 (2002) 202–217. CrossRef
Lonati, V. and Pradella, M., Snake-deterministic tiling systems, in Proc. MFCS 2009, 34th International Symposium on Mathematical Foundations of Computer Science. Lect. Notes Comput. Sci. 5734 (2009) 549–560. CrossRef
O. Matz, On piecewise testable, starfree, and recognizable picture languages, in Foundations of Software Science and Computation Structures, Vol. 1378, M. Nivat, Ed. Springer-Verlag, Berlin (1998).
O. Matz, Dot-depth and monadic quantifier alternation over pictures, Ph.D. thesis Technical Report 99-08, RWTH Aachen (1999).
O. Matz, Dot-depth, monadic quantifier alternation, and first-order closure over grids and pictures, Theoret. Comput. Sci. 270 (2002) 1–70. CrossRef
I. Mäurer, Characterizations of Recognizable Picture Series, Ph.D. thesis, Universität Leipzig, Institut für Informatik, Abteilung Automaten und Sprachen (2007).
Potthoff, A., Seibert, S. and Thomas, W., Nondeterminism versus determinism of finite automata over directed acyclic graphs. Bull. Belgian Math. Soc. 1 (1994) 285–298.
Reinhardt, K., The #a = #b Pictures are recognizable, in Proc. 18th STACS 2001. Lect. Notes Comput. Sci. 2010 (2001) 527–538. CrossRef