Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T15:25:23.055Z Has data issue: false hasContentIssue false
  • English
  • Français

On a complete set of operationsfor factorizing codes

Published online by Cambridge University Press:  15 October 2005

Clelia De Felice
Clelia De Felice*
Affiliation:
Dipartimento di Informatica e Applicazioni, Università di Salerno, 84081 Baronissi (SA), Italy; [email protected]
Get access

Abstract

It is known that the class of factorizing codes, i.e.,codes satisfying the factorization conjectureformulated by Schützenberger, isclosed under two operations:the classicalcomposition of codes and substitutionof codes.A natural question which arisesis whethera finite set Oof operations existssuch that each factorizingcode can be obtained by usingthe operations inO and starting with prefix or suffix codes.O is named herea complete setof operations (for factorizing codes).We show that composition and substitutionare not enough in order to obtaina completeset. Indeed, we exhibit a factorizing code over a two-letter alphabet A = {a,b}, precisely a 3-code, which cannot beobtained by decomposition or substitution.

Keywords

Variable length codesformal languagesfactorizations of cyclic groups.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 40 , Issue 1 , January 2006 , pp. 29 - 52
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

M. Anselmo, A Non-Ambiguous Decomposition of Regular Languages and Factorizing Codes, in Proc. DLT'99, G. Rozenberg, W. Thomas Eds. World Scientific (2000) 141–152.
Anselmo, M., Non-Ambiguous De, Acomposition of Regular Languages and Factorizing Codes. Discrete Appl. Math. 126 (2003) 129–165. CrossRef
J. Berstel and D. Perrin, Theory of Codes. Academic Press, New York (1985).
Berstel, J. and Perrin, D., Trends in the Theory of Codes. Bull. EATCS 29 (1986) 84–95.
J. Berstel and C. Reutenauer, Rational Series and Their Languages. EATCS Monogr. Theoret. Comput. Sci. 12 (1988).
J.M. Boë, Une famille remarquable de codes indécomposables, in Proc. Icalp 78. Lect. Notes Comput. Sci. 62 (1978) 105–112.
J.M. Boë, Sur les codes factorisants, in Théorie des Codes, Actes de la 7 e École de Printemps d'Informatique Théorique, edited by D. Perrin. LITP and ENSTA, Paris (1980) 1–8.
Bruyère, V. and De Felice, C., Synchronization and decomposability for a family of codes. Intern. J. Algebra Comput. 4 (1992) 367–393. CrossRef
Bruyère, V. and De Felice, C., Synchronization and decomposability for a family of codes: Part 2. Discrete Math. 140 (1995) 47–77. CrossRef
V. Bruyère and M. Latteux, Variable-Length Maximal Codes, in Proc. Icalp 96. Lect. Notes Comput. Sci. 1099 (1996) 24–47.
M.G. Castelli, D. Guaiana and S. Mantaci, Indecomposable prefix codes and prime trees, in Proc. DLT 97 edited by S. Bozapadilis-Aristotel (1997).
Césari, Y., Sur un algorithme donnant les codes bipréfixes finis. Math. Syst. Theory 6 (1972) 221–225. CrossRef
Y. Césari, Sur l'application du théorème de Suschkevitch à l'étude des codes rationnels complets, in Proc. Icalp 74. Lect. Notes Comput. Sci. (1974) 342–350.
De Felice, C., Construction of a family of finite maximal codes. Theoret. Comput. Sci. 63 (1989) 157–184. CrossRef
De Felice, C., A partial result about the factorization conjecture for finite variable-length codes. Discrete Math. 122 (1993) 137–152. CrossRef
De Felice, C., An application of Hajós factorizations to variable-length codes. Theoret. Comput. Sci. 164 (1996) 223–252. CrossRef
C. De Felice, Factorizing Codes and Schützenberger Conjectures, in Proc. MFCS 2000. Lect. Notes Comput. Sci. 1893 (2000) 295–303.
De Felice, C., On some Schützenberger Conjectures. Inform. Comp. 168 (2001) 144–155. CrossRef
De Felice, C., An enhanced property of factorizing codes. Theor. Comput. Sci. 340 (2005) 240–256. CrossRef
De Felice, C. and Restivo, A., Some results on finite maximal codes. RAIRO-Inform. Theor. Appl. 19 (1985) 383–403. CrossRef
De Felice, C. and Reutenauer, C., Solution partielle de la conjecture de factorisation des codes. C.R. Acad. Sci. Paris 302 (1986) 169–170.
Derencourt, D., A three-word code which is not prefix-suffix composed. Theor. Comput. Sci. 163 (1996) 145–160. CrossRef
L. Fuchs, Abelian groups. Pergamon Press, New York (1960).
Hajós, G., Sur la factorisation des groupes abéliens. Casopis Pest. Mat. Fys. 74 (1950) 157–162.
Krasner, M. and Ranulac, B., Sur une propriété des polynômes de la division du cercle. C.R. Acad. Sci. Paris 240 (1937) 397–399.
Lam, N.H., A note on codes having no finite completions. Inform. Proc. Lett. 55 (1995) 185–188. CrossRef
Lam, N.H., Hajós factorizations and completion of codes. Theor. Comput. Sci. 182 (1997) 245–256. CrossRef
Neraud, J. and Selmi, C., Locally complete sets and finite decomposable codes. Theor. Comput. Sci. 273 (2002) 185–196. CrossRef
M. Nivat, Éléments de la théorie générale des codes, in Automata Theory, edited by E. Caianiello. Academic Press, New York (1966) 278–294.
Perrin, D., Codes asynchrones. Bull. Soc. Math. France 105 (1977) 385–404. CrossRef
D. Perrin, Polynôme d'un code, in Théorie des Codes, Actes de la 7 e École de Printemps d'Informatique Théorique, edited by D. Perrin. LITP and ENSTA, Paris (1980) 169–176.
D. Perrin and M.P. Schützenberger, Un problème élémentaire de la théorie de l'information, Théorie de l'Information, Colloques Internat. CNRS, Cachan 276 (1977) 249–260.
Restivo, A., On codes having no finite completions. Discrete Math. 17 (1977) 309–316. CrossRef
Restivo, A., Codes and local constraints. Theor. Comput. Sci. 72 (1990) 55–64. CrossRef
Restivo, A., Salemi, S. and Sportelli, T., Completing codes. RAIRO-Inf. Theor. Appl. 23 (1989) 135–147. CrossRef
Restivo, A. and Silva, P.V., On the lattice of prefix codes. Theor. Comput. Sci. 289 (2002) 755–782. CrossRef
C. Reutenauer, Sulla fattorizzazione dei codici. Ricerche di Mat. XXXII (1983) 115–130.
Reutenauer, C., Non commutative factorization of variable-length codes. J. Pure Appl. Algebra 36 (1985) 167–186. CrossRef
Sands, A.D., On the factorisation of finite abelian groups. Acta Math. Acad. Sci. Hungaricae 8 (1957) 65–86. CrossRef
M.P. Schützenberger, Une théorie algébrique du codage, Séminaire Dubreil-Pisot 1955–56, exposé No. 15 (1955), 24 p.
Vincent, M., Construction de codes indécomposables. RAIRO-Inf. Theor. Appl. 19 (1985) 165–178.
L. Zhang and C.K. Gu, Two classes of factorizing codes – (p,p)-codes and (4,4)-codes, in Words, Languages and Combinatorics II, edited by M. Ito and H. Jürgensen. World Scientific (1994) 477–483.