Part 3. Mathematical models

On changing the minimum glue length for alphabetic faults

P. S. Dergach^a, N. S. Botirova<sup>b

a</sup> Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
^b Tashkent Branch of Lomonosov Moscow State University

Abstract: The purpose of this thesis is to study the nature of the change in the minimum length of gluing for alphabetic coding for various types of faults in circuits. Three types of operations are considered: deletion, addition and replacement of one letter. The main issue studied in the work is to estimate how many times the length of the minimum gluing can change after performing each of the indicated operations. As a result of the study, a criterion for preserving the ambiguity property in terms of the coding scheme was found, and upper and lower bounds were obtained for the rate of change in the length of the minimum gluing in each of the three cases. These estimates are an important practical tool for designing alphabetic encodings, taking into account possible faults in circuits.

Keywords: alphabetic coding, minimum gluing, coding scheme, alphabetic encoding