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