2-tape 1-way Quantum Finite State Automata

TL;DR

This paper introduces a 2-tape 1-way quantum finite automaton that can accept all regular languages and some non-regular languages, leveraging quantum superposition to enhance computational power beyond classical automata.

Contribution

It proposes a novel 2-tape quantum automaton model that surpasses previous models by accepting all regular languages and certain non-regular languages like ww.

Findings

Accepts all regular languages

Can accept languages not recognizable by multi-head deterministic automata

Utilizes quantum superposition to recognize complex languages like ww

Abstract

1-way quantum finite state automata are 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. We introduce 2-tape 1-way quantum finite state automaton (2T1QFA(2))which is a modified version of 1-way 2-head quantum finite state automaton(1QFA(2)). In this paper, we replace the single tape of 1-way 2-head quantum finite state automaton with two tapes. The content of the second tape is determined using a relation defined on input alphabet. The main claims of this paper are as follows: (1)We establish that 2-tape 1-way quantum finite state automaton(2T1QFA(2)) can accept all regular languages (2)A language which cannot be accepted by any multi-head deterministic finite automaton can be accepted by 2-tape 1-way quantum finite state automaton(2T1QFA(2)) .(3) Exploiting the superposition property of quantum automata we show that 2-tape 1-way quantum finite state automaton(2T1QFA(2)) can accept the language L=ww.