Geodesic
Automaton mappings of words that propagate distortions in Hamming and Levenshte\u\i n metrics no more than $K$ times
Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 78-94

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Let $I$ and $O$ be finite alphabets. For a finite alphabet $\Omega$, let $\Omega^*$ denote the set of all words of finite lengths over the alphabet $\Omega$. In this paper we give a complete description of all automaton mappings of the set $I^*$ into $O^*$ which multiply symbol replacement errors in words by a factor not exceeding $K$. We give a complete description of injective automaton mappings of the set $I^*$ into $O^*$ which multiply symbol skip errors by a factor no greater than $K$. A similar result is obtained for the deletion and insertion metric. 
@article{DM_2002_14_3_a8,
     author = {A. V. Babash},
     title = {Automaton mappings of words that propagate distortions in {Hamming} and {Levenshte\u\i} n metrics no more than $K$ times},
     journal = {Diskretnaya Matematika},
     pages = {78--94},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2002_14_3_a8/}
}
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A. V. Babash. Automaton mappings of words that propagate distortions in Hamming and Levenshte\u\i n metrics no more than $K$ times. Diskretnaya Matematika, Tome 14 (2002) no. 3, pp. 78-94. http://geodesic.mathdoc.fr/item/DM_2002_14_3_a8/