Classes of two-dimensional languages and recognizability conditions

Marcella Anselmo; Maria Madonia

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2010)

  • Volume: 44, Issue: 4, page 471-488
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Anselmo, Marcella, and Madonia, Maria. "Classes of two-dimensional languages and recognizability conditions." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 44.4 (2010): 471-488. <http://eudml.org/doc/245057>.

@article{Anselmo2010,
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.},
author = {Anselmo, Marcella, Madonia, Maria},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {two-dimensional languages; unambiguity; complement},
language = {eng},
number = {4},
pages = {471-488},
publisher = {EDP-Sciences},
title = {Classes of two-dimensional languages and recognizability conditions},
url = {http://eudml.org/doc/245057},
volume = {44},
year = {2010},
}

TY - JOUR
AU - Anselmo, Marcella
AU - Madonia, Maria
TI - Classes of two-dimensional languages and recognizability conditions
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 2010
PB - EDP-Sciences
VL - 44
IS - 4
SP - 471
EP - 488
AB - 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.
LA - eng
KW - two-dimensional languages; unambiguity; complement
UR - http://eudml.org/doc/245057
ER -

References

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  1. [1] M. Anselmo and M. Madonia, Deterministic and unambiguous two-dimensional languages over one-letter alphabet. Theoret. Comput. Sci. 410 (2009) 1477–1485. Zbl1162.68020
  2. [2] M. Anselmo and M. Madonia, 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. Zbl1256.68095
  3. [3] M. Anselmo, D. Giammarresi, M. Madonia and A. Restivo. Unambiguous recognizable two-dimensional languages. RAIRO-Theor. Inf. Appl. 40 (2006) 227–294. Zbl1112.68085
  4. [4] M. Anselmo, D. Giammarresi and M. Madonia, From determinism to non-determinism in recognizable two-dimensional languages, in Proc. DLT 07. Lect. Notes Comput. Sci. 4588 (2007) 36–47. Zbl1202.68218
  5. [5] M. Anselmo, N. Jonoska and M. Madonia, Framed versus unframed two-dimensional languages, in Proc. SOFSEM 09. Lecture Notes in Comput. Sci. 5404 (2009) 79–92. Zbl1206.68166
  6. [6] M. Anselmo, D. Giammarresi and M. Madonia, Deterministic and unambiguous families within recognizable two-dimensional languages. Fund. Inform. 98 (2010) 143–166. Zbl1196.68117
  7. [7] A. Bertoni, M. Goldwurm and V. Lonati, The complexity of unary tiling-recognizable picture languages. Fund. Inform. 90 (2009) 231–249. Zbl1179.68067
  8. [8] J.-C. Birget, Intersection and union of regular languages and state complexity. Inform. Proces. Lett. 43 (1992) 185–190. Zbl0763.68048
  9. [9] S. Brocchi, Bidimensional pictures: reconstruction, expression and encoding, Ph.D. thesis. http://www.dsi.unifi.it/DRIIA/RaccoltaTesi/Brocchi.pdf 
  10. [10] J. Cervelle, Langages de figures, Rapport de stage, ENS Lyon (1997). 
  11. [11] S. Eilenberg, Automata, Languages and Machines, Vol. A. Academic Press (1974). Zbl0359.94067
  12. [12] 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. 
  13. [13] D. Giammarresi and A. Restivo, Recognizable picture languages. Int. J. Pattern Recogn. Artif. Intell. 6 (1992) 241–256. Zbl1217.68129
  14. [14] D. Giammarresi and A. Restivo, Two-dimensional languages, Handbook of Formal Languages, Vol. III. G. Rozenberg et al., Eds. Springer Verlag (1997), 215–268. 
  15. [15] 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. Zbl1217.68129
  16. [16] 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. 
  17. [17] I. Glaister, J. Shallit, A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59 (1996) 75–77. Zbl0900.68313
  18. [18] J. Hromkovic, Communication Complexity and Parallel Computing. Springer (1997). Zbl0873.68098
  19. [19] J. Hromkovic, J. Karumäki, H. Klauck, G. Schnitger and S. Seibert, Communication complexity method for measuring nondeterminism in finite automata. Inform. Comput. 172 (2002) 202–217. Zbl1009.68067
  20. [20] V. Lonati and M. Pradella, 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. Zbl1250.68168
  21. [21] 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). Zbl1147.68045
  22. [22] O. Matz, Dot-depth and monadic quantifier alternation over pictures, Ph.D. thesis Technical Report 99-08, RWTH Aachen (1999). Zbl0938.68501
  23. [23] O. Matz, Dot-depth, monadic quantifier alternation, and first-order closure over grids and pictures, Theoret. Comput. Sci. 270 (2002) 1–70. Zbl0992.68128
  24. [24] I. Mäurer, Characterizations of Recognizable Picture Series, Ph.D. thesis, Universität Leipzig, Institut für Informatik, Abteilung Automaten und Sprachen (2007). Zbl1164.68016
  25. [25] A. Potthoff, S. Seibert and W. Thomas, Nondeterminism versus determinism of finite automata over directed acyclic graphs. Bull. Belgian Math. Soc. 1 (1994) 285–298. Zbl0803.68032
  26. [26] K. Reinhardt, The #a = #b Pictures are recognizable, in Proc. 18th STACS 2001. Lect. Notes Comput. Sci. 2010 (2001) 527–538. Zbl0976.03044

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