Algorithmical Aspects of Some Bio Inspired Operations

TL;DR

This thesis explores formal models of biologically inspired string operations, including duplication and completion, revealing their computational properties and applications in genetic sequence analysis.

Contribution

It introduces bounded duplication operations, analyzes their language classes, and proposes new methods for detecting complex repetitive structures in DNA sequences.

Findings

Bounded duplication generates context-sensitive languages.

Prefix-suffix-square completion produces infinite square-rich words.

Extended methods for detecting gapped repeats and palindromes.

Abstract

This thesis investigates three biologically inspired operations: prefix-suffix duplication, bounded prefix-suffix duplication, and prefix-suffix-square completion. Duplication, a common genetic mutation, involves repeating DNA sequences and is modeled here as formal operations on words. The prefix-suffix duplication generates non-context-free languages, even from simple initial words. To better reflect biological processes, we propose a bounded variant that limits duplication length, resolving unsolved problems and aligning with biochemical realities. We also introduce the prefix-suffix-square completion operation, which generates squares at sequence ends. This operation enables the generation of infinite words such as Fibonacci, Period-doubling, and Thue-Morse, which contain squares but avoid higher exponent repetitions, highlighting unique structural properties. In contrast, prefix-suffix duplication cannot generate certain infinite words, such as Thue-Morse, but can produce cube-free words. Additionally, we address the detection of gapped repeats and palindromes-structures important in DNA and RNA analysis. These involve repeating or reversed factors flanking a central gap. Previous studies imposed constraints on gap length or arm-gap relationships; we extend this by solving the problem in three novel settings. This work advances theoretical insights into biologically inspired operations and their computational applications in genetic modeling.