Topologies for Error-Detecting Variable-Length Codes

09/05/2023

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by   Jean Néraud, et al.

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Given a finite alphabet A, a quasi-metric d over A^*, and a non-negative integer k, 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.