Two-way and one-way quantum and classical automata with advice for online minimization problems

We consider online algorithms. Typically, the model is investigated with respect to the competitive ratio. In this paper, we explore two-way automata and one-way automata as models for online algorithms. We focus on quantum and classical online algorithms. We show that there are problems that can be...

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Bibliographic Details
Published in:Theoretical computer science Vol. 920; pp. 76 - 94
Main Authors: Khadiev, Kamil, Khadieva, Aliya, Ziatdinov, Mansur, Mannapov, Ilnaz, Kravchenko, Dmitry, Rivosh, Alexander, Yamilov, Ramis
Format: Journal Article
Language:English
Published: Elsevier B.V 12.06.2022
Subjects:
Automata
Online algorithms
Online minimization problems
Quantum computation
Streaming algorithms
Two-way automata
Two-way automata
Online algorithms
Streaming algorithms
Quantum computation
Online minimization problems
Automata
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:We consider online algorithms. Typically, the model is investigated with respect to the competitive ratio. In this paper, we explore two-way automata and one-way automata as models for online algorithms. We focus on quantum and classical online algorithms. We show that there are problems that can be solved more efficiently by two-way automata with quantum and classical states than by classical two-way automata in the case of sublogarithmic memory (sublinear size), even if classical automata get advice bits. Additionally, we show that there are problems that can be solved more efficiently by one-way quantum automata than by classical one-way automata in the case of sublogarithmic memory (resp., sublinear size) and in the case of logarithmic memory (resp., linear size) even if classical automata get advice bits.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2022.02.026