Computing Maximal Error-detecting Capabilities and Distances of Regular Languages

  • Authors:

  • Stavros Konstantinidis;Pedro V. Silva

  • Affiliations:

  • (Correspd.) Department of Mathematics and Computing Science, Saint Mary’s University, Halifax, Nova Scotia, B3H 3C3 Canada. s.konstantinidis@smu.ca;Centro de Matemática, Faculdade de Ciências, Universidade do Porto - R. Campo Alegre 687, 4169-007 Porto, Portugal. pvsilva@fc.up.pt

  • Venue:
  • Fundamenta Informaticae
  • Year:
  • 2010

  • Automata for codes

    CIAA'13 Proceedings of the 18th international conference on Implementation and Application of Automata

Quantified Score

Hi-index 0.00

Visualization

Abstract

A (combinatorial) channel consists of pairs of words representing all possible input-output channel situations. In a past paper, we formalized the intuitive concept of “largest amount of errors” detectable by a given language L, by defining the maximal error-detecting capabilities of L with respect to a given class of channels, and we showed how to compute all maximal error-detecting capabilities (channels) of a given regular language with respect to the class of rational channels and a class of channels involving only the substitution-error type. In this paper we resolve the problem for channels involving any combination of the basic error types: substitution, insertion, deletion. Moreover, we consider the problem of finding the inverses of these channels, in view of the fact that L is error-detecting for γ if and only if it is error-detecting for the inverse of γ. We also discuss a natural method of reducing the problem of computing (inner) distances of a given regular language L to the problem of computing maximal error-detecting capabilities of L.