We introduce the bound-decreasing duplication operation, a new variant of tandem duplication operation, that has restrictions on the position and the maximum size of the duplication segment in a target string. Then, we examine the bound-decreasing duplication system that iteratively generates strings from an initial string using the bound-decreasing duplication operation. We show that there exists a nondeterministic finite-state automaton (NFA) accepting all strings generated by the bound-decreasing duplication system when an initial input is a single string; in other words, the bound-decreasing duplication system produces a regular language. This helps us to calculate the system capacity based on the corresponding NFA. Furthermore, we revisit a deduplication operation—a reverse process of duplication—on an NFA that transforms a given NFA to a smaller NFA while generating the same language by the string duplication system.
Bibliographical noteFunding Information:
Cho was supported by Labex DigiCosme ( ANR-11-LABEX-0045-DIGICOSME ) operated by ANR as part of the program “Investissement d'Avenir” Idex Paris-Saclay (ANR-11-IDEX-0003-02), Han was supported by the Basic Science Research Program through NRF ( 2018R1D1A1A09084107 ) and Kim was supported in part by the NIH grant R01 GM109459 .
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)