# Multi-letter quantum finite automata: decidability of the equivalence and minimization of states

@article{Qiu2011MultiletterQF, title={Multi-letter quantum finite automata: decidability of the equivalence and minimization of states}, author={Daowen Qiu and Lvzhou Li and Xiangfu Zou and Paulo Mateus and Jozef Gruska}, journal={Acta Informatica}, year={2011}, volume={48}, pages={271-290} }

Multi-letter quantum finite automata (QFAs) can be thought of quantum variants of the one-way multi-head finite automata (Hromkovič, Acta Informatica 19:377–384, 1983). It has been shown that this new one-way QFAs (multi-letter QFAs) can accept with no error some regular languages, for example (a + b)*b, that are not acceptable by QFAs of Moore and Crutchfield (Theor Comput Sci 237:275–306, 2000) as well as Kondacs and Watrous (66–75, 1997; Observe that 1-letter QFAs are exactly measure-once…

## 27 Citations

One-way quantum finite automata together with classical states

- Computer ScienceArXiv
- 2009

A new computing model of 1QFA, namely, one-way quantum finite automata together with classical states (1QFAC for short), is developed, a component of classical states is added, and the choice of unitary evolution of quantum states at each step is closely related to the current classical state.

On equivalence of multi-letter and multi-letter measure-many quantum finite automata

- PhysicsArXiv
- 2012

It is shown that k1-letter QFA A1 and k2-letterQFA A2 over Σ are equivalent if and only if they are (n1 + n 2 2 − 1) + kequivalent, and it is proved that the similar result holds for multi-letter measure-many quantum finite automata (multi-letter MM-QFAs).

Characterizations of one-way general quantum finite automata

- Computer ScienceTheor. Comput. Sci.
- 2012

Ju n 20 20 On equivalence , languages equivalence and minimization of multi-letter and multi-letter measure-many quantum automata 1

- Computer Science
- 2020

This paper shows that for k-letter quantum finite automata, the non-strict cut-point language equivalence problem is undecidable, and comments on existing proofs about the minimization problem of one way quantum finiteAutomata not only because they have been showing great interest in this kind of problem, but also because the problem itself, personally, is a challenge.

1-Way Multihead Quantum Finite State Automata

- Computer Science
- 2016

It is shown that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages.

Learning Quantum Finite Automata with Queries

- Computer ScienceArXiv
- 2021

The purpose is to initiate the study of learning QFA with queries (naturally it may be termed as quantum model learning), and the main results are regarding learning two basic one-way QFA: a learning algorithm for measure-once oneway QFA (MO-1QFA) with query complexity of polynomial time.

Promise problems solved by quantum and classical finite automata

- Computer ScienceTheor. Comput. Sci.
- 2017

2-tape 1-way Quantum Finite State Automata

- Computer Science, PhysicsArXiv
- 2016

It is established that 2-tape 1-way quantum finite state automaton (2T1QFA(2)) can accept all regular languages and it is shown that a language which cannot be accepted by any multi-head deterministic finite automaton can be acceptedBy exploiting the superposition property of quantum automata.

On the power of two-way multihead quantum finite automata

- Computer ScienceRAIRO Theor. Informatics Appl.
- 2019

It has been proved that a language which cannot be recognizing by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite Automata with two heads and it has been investigated that quantum variant of two- way deterministic multihead finite automaton takes less number of heads to recognize a language containing of all words whose length is a prime number.

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