# 1-way quantum finite automata: strengths, weaknesses and generalizations

@article{Ambainis19981wayQF, title={1-way quantum finite automata: strengths, weaknesses and generalizations}, author={Andris Ambainis and Rusins Freivalds}, journal={Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)}, year={1998}, pages={332-341} }

We study 1-way quantum finite automata (QFAs). First, we compare them with their classical counterparts. We show that, if an automaton is required to give the correct answer with a large probability (greater than 7/9), then any 1-way QFAs can be simulated by a 1-way reversible automaton. However, quantum automata giving the correct answer with smaller probabilities are more powerful than reversible automata. Second, we show that 1-way QFAs can be very space-efficient. We construct a 1-way QFA…

## 260 Citations

### One-Way Finite Automata with Quantum and Classical States

- Computer ScienceLanguages Alive
- 2012

It is proved that coin-tossing one-way probabilistic finite automata (coin-Tossing 1PFA) and one- way quantum finite Automata with control language (1QFACL) as well as several other models of QFA, can be simulated by 1QCFA.

### Empowering measures for quantum finite automata (QFA)

- Computer Science, Physics2011 3rd International Conference on Computer Research and Development
- 2011

This paper discusses about 1-QFA and 2-Q FA and their drawbacks, and introduces an algorithm by implementing 1-way quantum finite k-counter automata (1-QFk-CA) with multiple scanning of the input string to improve the power of QFAs.

### Characterizations of one-way general quantum finite automata

- Computer ScienceTheor. Comput. Sci.
- 2012

### Quantum Finite Automata : a Language Acceptor Model

- Computer Science, Physics
- 2012

This survey work has drawn a comparison among 1- way QFA, 2-way QFA and 1.5-wayQFA, and discussed about the strengths and weakness of all these QFA models and the power of Quantum Finite State Automata.

### 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 the Weakness of One-Way Quantum Pushdown Automata

- Computer Science2010 Fourth International Conference on Quantum, Nano and Micro Technologies
- 2010

This work focuses on (empty-stack acceptance) one-way quantum pushdown automata, and shows that there exists a regular language which one- way quantum push down automata cannot recognize.

### Two-way finite automata with quantum and classical state

- Computer ScienceTheor. Comput. Sci.
- 2002

### Succinctness of two-way probabilistic and quantum finite automata

- Computer ScienceDiscret. Math. Theor. Comput. Sci.
- 2010

It is proved that two-way probabilistic and quantum finite automata (2PFAs and 2QFAs) can be considerably more concise than both their one-way versions, and two- way nondeterministic finite automaton (2NFAs), and it is shown that 2ZFAs with mixed states can support highly efficient probability amplification.

### Quantum Computing: 1-Way Quantum Automata

- Computer ScienceDevelopments in Language Theory
- 2003

This paper analyzes several models of 1-way quantum finite automata and compares their behaviors with those of measure-once, measure-many and reversible 1- way quantum automata.

### Revisiting the Power and Equivalence of One-Way Quantum Finite Automata

- Computer ScienceICIC
- 2010

A new proof is given for the fact that measure-many one-way quantum finite automata (MM-1QFA) recognize only regular languages with bounded error and generalizes the proof to a broader class of automata that include probabilistic automata and some kinds of quantum finite Automata.

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