Deduplication on Finite Automata and Nested Duplication Systems

摘要

Motivated by work on bio-operations on DNA sequences, a string duplication system S consists of an initial string over ∑ and a set of duplication functions that iteratively generate new strings from existing strings in the system. As the main result we introduce the concept of a deduplication—a reverse function of duplication—on an nondetermin-istic finite-state automaton (NFA) and propose the deduplication operation on an NFA that transforms a given NFA to a smaller NFA while generating the same language in the string duplication system. Then, we introduce a nested duplication, which is similar to tandem duplication but depends on the information of the nested duplication in the previous step. We propose an NFA construction for an arbitrary nested duplication system, analyze its properties and present an algorithm that computes the system capacity.