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.
Mots-clés : two-dimensional languages, unambiguity, complement
@article{ITA_2010__44_4_471_0,
author = {Anselmo, Marcella and Madonia, Maria},
title = {Classes of two-dimensional languages and recognizability conditions},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {471--488},
publisher = {EDP-Sciences},
volume = {44},
number = {4},
year = {2010},
doi = {10.1051/ita/2011003},
mrnumber = {2775407},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita/2011003/}
}
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 SP - 471 EP - 488 VL - 44 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2011003/ DO - 10.1051/ita/2011003 LA - en ID - ITA_2010__44_4_471_0 ER -
%0 Journal Article %A Anselmo, Marcella %A Madonia, Maria %T Classes of two-dimensional languages and recognizability conditions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2010 %P 471-488 %V 44 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2011003/ %R 10.1051/ita/2011003 %G en %F ITA_2010__44_4_471_0
Anselmo, Marcella; Madonia, Maria. Classes of two-dimensional languages and recognizability conditions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 44 (2010) no. 4, pp. 471-488. doi : 10.1051/ita/2011003. http://www.numdam.org/articles/10.1051/ita/2011003/
[1] and , Deterministic and unambiguous two-dimensional languages over one-letter alphabet. Theoret. Comput. Sci. 410 (2009) 1477-1485. | Zbl
[2] and , 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.
[3] , , and . Unambiguous recognizable two-dimensional languages. RAIRO-Theor. Inf. Appl. 40 (2006) 227-294. | Numdam | Zbl
[4] , and , From determinism to non-determinism in recognizable two-dimensional languages, in Proc. DLT 07. Lect. Notes Comput. Sci. 4588 (2007) 36-47. | Zbl
[5] , and , Framed versus unframed two-dimensional languages, in Proc. SOFSEM 09. Lecture Notes in Comput. Sci. 5404 (2009) 79-92. | Zbl
[6] , and , Deterministic and unambiguous families within recognizable two-dimensional languages. Fund. Inform. 98 (2010) 143-166. | Zbl
[7] , and , The complexity of unary tiling-recognizable picture languages. Fund. Inform. 90 (2009) 231-249. | Zbl
[8] , Intersection and union of regular languages and state complexity. Inform. Proces. Lett. 43 (1992) 185-190. | Zbl
[9] , Bidimensional pictures: reconstruction, expression and encoding, Ph.D. thesis. http://www.dsi.unifi.it/DRIIA/RaccoltaTesi/Brocchi.pdf
[10] , Langages de figures, Rapport de stage, ENS Lyon (1997).
[11] , Automata, Languages and Machines, Vol. A. Academic Press (1974). | Zbl
[12] , 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] and , Recognizable picture languages. Int. J. Pattern Recogn. Artif. Intell. 6 (1992) 241-256.
[14] and , Two-dimensional languages, Handbook of Formal Languages, Vol. III. G. Rozenberg et al., Eds. Springer Verlag (1997), 215-268.
[15] and , 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.
[16] and , 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] , , A lower bound technique for the size of nondeterministic finite automata. Inform. Process. Lett. 59 (1996) 75-77. | Zbl
[18] , Communication Complexity and Parallel Computing. Springer (1997). | Zbl
[19] , , , and , Communication complexity method for measuring nondeterminism in finite automata. Inform. Comput. 172 (2002) 202-217. | Zbl
[20] and , 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.
[21] , 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). | Zbl
[22] , Dot-depth and monadic quantifier alternation over pictures, Ph.D. thesis Technical Report 99-08, RWTH Aachen (1999). | Zbl
[23] , Dot-depth, monadic quantifier alternation, and first-order closure over grids and pictures, Theoret. Comput. Sci. 270 (2002) 1-70. | Zbl
[24] , Characterizations of Recognizable Picture Series, Ph.D. thesis, Universität Leipzig, Institut für Informatik, Abteilung Automaten und Sprachen (2007). | Zbl
[25] , and , Nondeterminism versus determinism of finite automata over directed acyclic graphs. Bull. Belgian Math. Soc. 1 (1994) 285-298. | Zbl
[26] , The #a = #b Pictures are recognizable, in Proc. 18th STACS 2001. Lect. Notes Comput. Sci. 2010 (2001) 527-538. | Zbl
Cité par Sources :
