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

  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},
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… 
One-way quantum finite automata together with classical states
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
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).
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
It is shown that newly introduced 1-way 2-head quantum finite state automaton (1QFA(2)) structure can accept all unary regular languages.
On hybrid models of quantum finite automata
Learning Quantum Finite Automata with Queries
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.
2-tape 1-way Quantum Finite State Automata
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
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.


Hierarchy and equivalence of multi-letter quantum finite automata
Multi-letter Reversible and Quantum Finite Automata
This work introduces a new, quite simple modification of the QFA model (actually even a deterministic reversible FA model) which is able to recognize this language, and completely characterises the set of languages recognizable by the new model FAs, by finding a "forbidden construction" whose presence or absence in the minimal deterministic finite automaton of the language decides the recognizability.
Characterizations of 1-Way Quantum Finite Automata
This paper characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group and shows that piecewise testable sets can be accepted with boundederror by a measure-many quantum finite automaton, introducing new construction techniques for quantum automata in the process.
On the power of quantum finite state automata
It is proved that the class of languages recognizing by linear time, bounded error 2qfa's properly includes the regular languages, and 1-way and 2-way quantum finite state automata are introduced, which are the quantum analogues of deterministic, nondeterministic and probabilistic 1- way and2-way finite state Automata.
1-way quantum finite automata: strengths, weaknesses and generalizations
  • A. AmbainisR. Freivalds
  • Computer Science
    Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
  • 1998
This work constructs a 1-way QFA that is exponentially smaller than any equivalent classical (even randomized) finite automaton, and thinks that this construction may be useful for design of other space-efficient quantum algorithms.
Determining the equivalence for one-way quantum finite automata
An overview of quantum computation models: quantum automata
A basic progress in the research on quantum automata is outlined, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata, and a number of problems to be studied in future are addressed.
Determination of equivalence between quantum sequential machines
Probabilistic ω-automata
This paper addresses closure properties under the Boolean operators union, intersection and complementation and algorithmic aspects, such as checking emptiness or language containment, and provides a comparison of probabilistic ω-automata concerning expressiveness and efficiency.