Topologies for error-detecting variable-length codes.

Given a finite alphabet A and a quasi-metric d over A ⁎ , we introduce the relation τ d , k ⊆ A ⁎ × A ⁎ such that (x , y) ∈ τ d , k holds whenever d (x , y) ≤ k. The error detection capability of variable-length codes is expressed in term of conditions over τ d , k. 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. [ABSTRACT FROM AUTHOR]