Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-30T16:30:05.152Z Has data issue: false hasContentIssue false
  • English
  • Français

Structure and properties of strong prefix codes of pictures

Published online by Cambridge University Press:  28 May 2015

MARCELLA ANSELMO ,
DORA GIAMMARRESI  and
MARIA MADONIA
MARCELLA ANSELMO
Affiliation:
Dipartimento di Informatica, Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy Email: anselmo@dia.unisa.it
DORA GIAMMARRESI
Affiliation:
Dipartimento di Matematica, Università di Roma ‘Tor Vergata,’ Via della Ricerca Scientifica, 00133 Roma, Italy Email: giammarr@mat.uniroma2.it
MARIA MADONIA
Affiliation:
Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria 6/a, 95125 Catania, Italy Email: madonia@dmi.unict.it
Get access Rights & Permissions [Opens in a new window]

Abstract

A set X ⊆ Σ** of pictures is a code if every picture over Σ is tilable in at most one way with pictures in X. The definition of strong prefix code is introduced. The family of finite strong prefix codes is decidable and it has a polynomial time decoding algorithm. Maximality for finite strong prefix codes is also studied and related to the notion of completeness. We prove that any finite strong prefix code can be embedded in a unique maximal strong prefix code that has minimal size and cardinality. A complete characterization of the structure of maximal finite strong prefix codes completes the paper.

Information

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 27 , Special Issue 2: Special Issue: XIV ICTCS , February 2017 , pp. 123 - 142
Copyright
Copyright © Cambridge University Press 2015 

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.)

Article purchase

Temporarily unavailable

References

Aigrain, P. and Beauquier, D. (1995). Polyomino tilings, cellular automata and codicity. Theoretical Computer Science, 147 165–180.CrossRefGoogle Scholar
Anselmo, M., Giammarresi, D. and Madonia, M. (2010). Deterministic and unambiguous families within recognizable two-dimensional languages. Fund. Inform. 98 (2–3) 143–166.Google Scholar
Anselmo, M., Giammarresi, D. and Madonia, M. (2013a). Two-dimensional prefix codes of pictures. In: Béal, M.-P. and Carton, O. (eds.) Proceedings of the DLT2013. Springer Heidelberg Lecture Notes in Computer Science 7907 46–57.CrossRefGoogle Scholar
Anselmo, M., Giammarresi, D. and Madonia, M. (2013b). Strong prefix codes of pictures. In: Muntean, T., Poulakis, D. and Rolland, R. (eds.) Proceedings of the CAI2013. Lecture Notes in Computer Science 8080 47–59.CrossRefGoogle Scholar
Anselmo, M., Giammarresi, D. and Madonia, M. (2014). Prefix picture codes: A decidable class of two-dimensional codes. International Journal of Foundations of Computer Science, 25 (8) 1017–1032.CrossRefGoogle Scholar
Anselmo, M., Giammarresi, D., Madonia, M. and Restivo, A. (2006). Unambiguous recognizable two-dimensional languages. RAIRO: Theoretical Informatics and Applications 40 (2) 227–294.Google Scholar
Anselmo, M. and Madonia, M. (2009). Deterministic and unambiguous two-dimensional languages over one-letter alphabet. Theoretical Computer Science 410 (16) 1477–1485. Elsevier.CrossRefGoogle Scholar
Beauquier, D. and Nivat, M. (2003). A codicity undecidable problem in the plane. Theoretical Computer Science 303 417–430.CrossRefGoogle Scholar
Berstel, J., Perrin, D. and Reutenauer, C. (2009). Codes and Automata, Cambridge University Press.CrossRefGoogle Scholar
Bozapalidis, S. and Grammatikopoulou, A. (2006). Picture codes. ITA 40 (4) 537–550.Google Scholar
Giammarresi, D. and Restivo, A. (1992). Recognizable picture languages. International Journal Pattern Recognition and Artificial Intelligence 6 (2–3) 241–256.CrossRefGoogle Scholar
Giammarresi, D. and Restivo, A. (1997). Two-dimensional languages. In: Rozenberg, G. et al. (eds.) Handbook of Formal Languages, volume III, Springer Verlag, 215–268.CrossRefGoogle Scholar
Grammatikopoulou, A. (2005). Prefix picture sets and picture codes. In: Proceedings of the CAI'05, 255–268.Google Scholar
Kolarz, M. and Moczurad, W. (2012). Multiset, set and numerically decipherable codes over directed figures. In: Combinatorial Algorithms, Lecture Notes in Computer Science, volume 7643, Springer, Heidelberg, 224–235.CrossRefGoogle Scholar
Moczurad, M. and Moczurad, W. (2004). Some open problems in decidability of brick (labeled Polyomino) codes. In: Chwa, K.-Y. and Munro, J. I. (eds.) COCOON 2004. Lecture Notes in Computer Science, volume 3106, Springer-Verlag Berlin, 72–81.Google Scholar
Simplot, D. (1991). A characterization of recognizable picture languages by tilings by finite sets. Theoretical Computer Science 218 (2) 297–323.CrossRefGoogle Scholar