13 research outputs found
On the group of a rational maximal bifix code
We give necessary and sufficient conditions for the group of a rational
maximal bifix code to be isomorphic with the -group of , when
is recurrent and is rational. The case where is uniformly
recurrent, which is known to imply the finiteness of , receives
special attention.
The proofs are done by exploring the connections with the structure of the
free profinite monoid over the alphabet of
Topologies for Error-Detecting Variable-Length Codes
Given a finite alphabet , a quasi-metric over , and a
non-negative integer , we introduce the relation such that holds whenever . The
error detection capability of variable-length codes is expressed in term of
conditions over . With respect to the prefix metric, the factor
one, and any quasi-metric associated with some free monoid (anti-)automorphism,
we prove that one can decide whether a given regular variable-length code
satisfies any of those error detection constraints.Comment: arXiv admin note: text overlap with arXiv:2208.1468