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Finite completion of comma-free codes. Part 2

Nguyen Huong Lam — 2004

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.

Finite completion of comma-free codes. Part 1

Nguyen Huong Lam — 2004

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended...

Finite Completion of comma-free codes Part 1

Nguyen Huong Lam — 2010

RAIRO - Theoretical Informatics and Applications

This paper is the first step in the solution of the problem of finite completion of comma-free codes. We show that every finite comma-free code is included in a finite comma-free code of particular kind, which we called, for lack of a better term, canonical comma-free code. Certainly, finite maximal comma-free codes are always canonical. The final step of the solution which consists in proving further that every canonical comma-free code is completed to a finite maximal comma-free code, is intended...

Finite Completion of comma-free codes Part 2

Nguyen Huong Lam — 2010

RAIRO - Theoretical Informatics and Applications

This paper is a sequel to an earlier paper of the present author, in which it was proved that every finite comma-free code is embedded into a so-called (finite) canonical comma-free code. In this paper, it is proved that every (finite) canonical comma-free code is embedded into a finite maximal comma-free code, which thus achieves the conclusion that every finite comma-free code has finite completions.


Unavoidable Set: Extension and Reduction

Phan Trung HuyNguyen Huong Lam — 2010

RAIRO - Theoretical Informatics and Applications

We give an explicit criterion for unavoidability of word sets. We characterize extendible, finitely and infinitely as well, elements in them. We furnish a reasonable upper bound and an exponential lower bound on the maximum leghth of words in a reduced unavoidable set of a given cardinality.

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