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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.
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...
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...
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.
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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