Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-19T19:50:01.875Z Has data issue: false hasContentIssue false
  • English
  • Français

Picture codes

Published online by Cambridge University Press:  08 November 2006

Symeon Bozapalidis  and
Archontia Grammatikopoulou
Symeon Bozapalidis
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece; bozapali@math.auth.gr; arxontia@math.auth.gr
Archontia Grammatikopoulou
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece; bozapali@math.auth.gr; arxontia@math.auth.gr
Get access

Abstract

We introduce doubly-ranked (DR) monoids in order to study picture codes. We show that a DR-monoid is free iff it is pictorially stable. This allows us to associate with a set C of pictures a picture code B(C) which is the basis of the least DR-monoid including C. A weak version of the defect theorem for pictures is established. A characterization of picture codes through picture series is also given.

Keywords

Picture codespicture series.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 4 , October 2006 , pp. 537 - 550
Copyright
© EDP Sciences, 2006

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

Aigrain, P. and Beauquier, D., Polyomino Tiling, Cellular Automata and Codicity. Theoret. Comput. Sci. 147 (1995) 165–180. CrossRef
Beauquier, D. and Nivat, M., Codicity Undecidable Problem, A in the Plane. Theoret. Comput. Sci. 303 (2003) 417–430. CrossRef
J. Berstel and D. Perrin. Theory of Codes. Academic Press, New York (1985).
Bozapalidis, S. and Grammatikopoulou, A., Recognizable Picture Series. J. Automat. Combin. 10 (2005) 159–183.
D. Giammarresi and A. Restivo. Two-Dimensional Languages, in Handbook Formal Languages, Beyond Words, edited by G. Rozenberg and A. Salomaa. Springer 3 (1997) 215–267,
Hashiguchi, K., Kundi, T. and Jimbo, S., Finite Codes over Free Binoids. J. Automat. Languages Combin. 7 (2002) 505–518.
Latteux, M. and Simplot, D., Context-Sensitive String Languages and Recognizable Picture Languages. Inform. Comput. 138 (1997) 160–169. CrossRef
Latteux, M. and Simplot, D., Recognizable Picture Languages and Domino Tiling. Theoret. Comput. Sci. 178 (1997) 275–283. CrossRef
O. Matz, Regular Expressions and Context-free Grammars for Picture Languages, in Proc. STACS'97-LNCS. Springer-Verlag 1200 (1997) 283–294.
O. Matz, On Piecewise Testable, Starfree and Recognizable Picture Languages, in Foundations of Software Science and Computation Structures, edited by M. Nivat. Springer-Verlag, Berlin 1378 (1998).
Reinhard, K., On some Recognizable Picture-languages, in Mathematical Foundations of Computer Science edited by L. Brim, J. Gruska and J. Zlatuška. Lect. Notes Comput. Sci. 1450 (1998) 760–770. CrossRef
Simplot, D., Characterization, A of Recognizable Picture Languages by Tilings by Finite Sets. Theoret. Comput. Sci. 218 (1999) 297–323. CrossRef
Siromoney, R., Dare, V.R. and Subramanian, K.G., Infinite Arrays and Infinite Computations. Theoret. Comput. Sci. 24 (1983) 195–205. CrossRef
Siromoney, R., Subramanian, K.G. and Dare, V.R., Infinite Arrays and Controlled Deterministic Table 0L Array Systems. Theoret. Comput. Sci. 33 (1984) 3–11. CrossRef
T. Wilke, Star-free Picture Expressions Are Strictly Weaker Than First-order Logic, in Proc. ICALP'97-LNCS. Springer-Verlag (1997) 1256 347–357.