Watson-Crick Quantum Finite Automata

TL;DR

This paper introduces Watson-Crick quantum finite automata, a novel model combining DNA-inspired complementarity with quantum automata, significantly enhancing their computational power to accept all regular languages and some beyond.

Contribution

The paper proposes Watson-Crick quantum finite automata, integrating DNA complementarity with quantum automata, and demonstrates their increased computational capabilities over traditional models.

Findings

Accept all regular languages

Accept some non-regular languages like ww

Non-determinism from complementarity enhances power

Abstract

1-way quantum finite automata are deterministic and reversible in nature, which greatly reduces its accepting property. In fact the set of languages accepted by 1-way quantum finite automata is a proper subset of regular languages. In this paper we replace the tape head of 1-way quantum finite automata with DNA double strand and name the model Watson-Crick quantum finite automata. The non-injective complementarity relation of Watson-Crick automata introduces non-determinism in the quantum model. We show that this introduction of non-determinism increases the computational power of 1-way Quantum finite automata significantly. We establish that Watson-Crick quantum finite automata can accept all regular languages and that it also accepts some languages not accepted by any multihead deterministic finite automata. Exploiting the superposition property of quantum finite automata we show that Watson-Crick quantum finite automata accept the language L=ww where w belongs to {a,b}*.