1-Way Multihead Quantum Finite State Automata

Debayan Ganguly,Kingshuk Chatterjee,Kumar Sankar Ray

doi:10.4236/am.2016.79088

Debayan Ganguly, Kingshuk Chatterjee + Show 1 more

Open Access

https://doi.org/10.4236/am.2016.79088

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Journal: Applied mathematics	Publication Date: Jan 1, 2016
Citations: 19	License type: CC BY 4.0

Affiliation: Indian Statistical Institute

Abstract

1-way multihead quantum finite state automata (1QFA(k)) can be thought of modified version of 1-way quantum finite state automata (1QFA) and k-letter quantum finite state automata (k-letter QFA) respectively. It has been shown by Moore and Crutchfield as well as Konadacs and Watrous that 1QFA can’t accept all regular language. In this paper, we show different language recognizing capabilities of our model 1-way multihead QFAs. New results presented in this paper are the following ones: 1) We show that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages. 2) A language which can’t be accepted by 1-way deterministic 2-head finite state automaton (1DFA((2)) can be accepted by 1QFA(2) with bounded error. 3) 1QFA(2) is more powerful than 1-way reversible 2-head finite state automaton (1RMFA(2)) with respect to recognition of language.

Highlights

Classical finite state automaton is the very basic model of classical finite machine
Whenever we mention one-way quantum finite automata we mean the model described by Konadacs et al It has been shown by Kondacs et al that the languages recognized by 1-way quantum finite automaton (1QFA)’s form a proper subset of the regular languages
We introduce 1-way multihead quantum finite state automaton (1QFA(k)) by introducing multiple heads combined with existing automaton and study its language recognizing capabilities

Summary

Introduction

Classical finite state automaton is the very basic model of classical finite machine. Whenever we mention one-way quantum finite automata we mean the model described by Konadacs et al It has been shown by Kondacs et al that the languages recognized by 1QFA’s form a proper subset of the regular languages. The second model is 2-way quantum finite state automaton (2QFA) [2] In this model,it is easy to simulate any deterministic automaton and some non-regular languages can be recognized as well; this implies that 2QFA’s are strictly more powerful than their classical counterparts. We introduce 1-way multihead quantum finite state automaton (1QFA(k)) by introducing multiple heads combined with existing automaton and study its language recognizing capabilities. It has been shown that this languages is recognized by 1QFA(2)

Quantum Finite Automata

Multihead Quantum Finite Automata

Conclusion