Analysis of Quantum Pattern Matching for Generalized Degenerate Strings
Year: 2026
Type: article
Abstract: This work presents a comprehensive analysis of quantum algorithms for the Generalized Degenerate String Matching (SMGD) problem, which involves finding occurrences of a pattern P of length m in a generalized degenerate text \(\mathcal{T}\) consisting of n sets containing s strings of total length N. The proposed work first explores an algorithm combining existing approaches such as the Aho-Corasick automaton and quantum techniques like Grover search to achieve a query complexity of \(O(m + N + m\sqrt{sHn})\), where H is the maximum number of strings in any set of \(\mathcal{T}\). To demonstrate a definitive quantum advantage over the state-of-the-art classical algorithm which has a running time of O(mn + N) (Ascone et al., WABI 2024), this work extends to a strategy based on alignment-shift that fully exploits the quantum model of computation by simulating parallel shifts. This algorithm achieves a running time of \(\tilde{O}(\sqrt{mnN})\), which represents a sub-linear query complexity and establishes a potential theoretical quantum speed-up for generalized degenerate strings.
Source: Työväentutkimus Vuosikirja
Author: Khan, Md Rabiul Islam
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7199724362