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Time-space tradeoffs for two-way finite automata [article]

Shenggen Zheng, Daowen Qiu, Jozef Gruska
<span title="2016-03-19">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
deterministic finite automata is Ω(n^2), (2) a time-space tradeoff upper bound for recognition of the languages L_INT(n) on two-way finite automata with quantum and classical states (2QCFA): TS= O(n^3  ...  We prove: (1) a time-space tradeoff upper bound for recognition of the languages L_EQ(n) on two-way probabilistic finite automata (2PFA): TS= O(n n), whereas a time-space tradeoff lower bound on two-way  ...  T S = O(n log n), whereas a time-space tradeoff lower bound on two-way determinis- tic finite automata is Ω(n2 ); (2) a time-space tradeoff upper bound  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.01346v2">arXiv:1507.01346v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rgel6tnjpnc45opahfeb4ghe2y">fatcat:rgel6tnjpnc45opahfeb4ghe2y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200912163922/https://arxiv.org/pdf/1507.01346v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d3/ac/d3accb89478fcc0a4490b28a2b4ff3a7ed655678.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.01346v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Quantum finite automata: survey, status and research directions [article]

Amandeep Singh Bhatia, Ajay Kumar
<span title="2019-01-23">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Quantum computing is concerned with computer technology based on the principles of quantum mechanics, with operations performed at the quantum level.  ...  This article seeks to provide a comprehensive and systematic analysis of quantum finite automata models, quantum finite automata models with density operators and quantum finite automata models with classical  ...  Acknowledgments Amandeep Singh Bhatia was supported by Maulana Azad National Fellowship (MANF), funded by Ministry of Minority Affairs, Government of India.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.07992v1">arXiv:1901.07992v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yoxwrd6e55gh3heapwy3w5uuhm">fatcat:yoxwrd6e55gh3heapwy3w5uuhm</a> </span>
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Lower bounds on the size of semi-quantum finite automata [article]

Lvzhou Li, Daowen Qiu
<span title="2015-10-03">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Specifically, we present a uniform method that gives a lower bound on the size of the three existing main models of semi-quantum automata, and this bound shows that semi-quantum automata can be at most  ...  In the literature, there exist several interesting hybrid models of finite automata which have both quantum and classical states. We call them semi-quantum automata.  ...  Acknowledgements The authors are thankful to Dr. Shenggen Zheng for his useful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.02839v2">arXiv:1502.02839v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xkfjz6yiffau7clrhjwow6ldyy">fatcat:xkfjz6yiffau7clrhjwow6ldyy</a> </span>
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Page 2872 of Mathematical Reviews Vol. , Issue 2003d [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
In this paper the author contributes a new upper bound for branching program size in terms of formula size.  ...  on the succinctness of deterministic, nondeterministic, probabilistic and quantum finite automata.  ... 
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Nonuniform Families of Polynomial-Size Quantum Finite Automata and Quantum Logarithmic-Space Computation with Polynomial-Size Advice [article]

Tomoyuki Yamakami
<span title="2021-04-16">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For two-way quantum finite automata equipped with flexible garbage tapes, we show a close relationship between the nonuniform state complexity of the family of such polynomial-size quantum finite automata  ...  The state complexity of a finite(-state) automaton intuitively measures the size of the description of the automaton.  ...  Notice that, by our definition of one-wayness, 1-way finite automata halt exactly in |x| + 2 steps for any given input x.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1907.02916v4">arXiv:1907.02916v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zyrhfdioc5drzcsujcgpjj3bfa">fatcat:zyrhfdioc5drzcsujcgpjj3bfa</a> </span>
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Bounds on the speedup in quantum signaling

Pablo Arrighi, Vincent Nesme, Reinhard F. Werner
<span title="2017-01-26">2017</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/z3u6fzrh4fdvhnzujueyvzipwi" style="color: black;">Physical Review A</a> </i> &nbsp;
Given a discrete reversible dynamics, we can define a quantum dynamics, which acts on basis states like the classical one, but also allows for superpositions of them.  ...  In a run of many steps the quantum propagation neighborhood can only increase by a constant fringe, so there is no asymptotic increase in speed.  ...  They would also like to warmly thank Jarkko Kari for showing them what amazing little things cellular automata are, especially how the neighbourhood and the inverse neighbourhood depend so little on each  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physreva.95.012331">doi:10.1103/physreva.95.012331</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/weqjemon3zf2dn7mqh62ml7j3q">fatcat:weqjemon3zf2dn7mqh62ml7j3q</a> </span>
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Optimal lower bounds for quantum automata and random access codes [article]

Ashwin Nayak
<span title="1999-09-07">1999</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It was shown by Ambainis, Nayak, Ta-Shma and Vazirani that while this language is accepted by a deterministic finite automaton of size O(n), any one-way quantum finite automaton (QFA) for it has size 2  ...  This was based on the fact that the evolution of a QFA is required to be reversible. When arbitrary intermediate measurements are allowed, this intuition breaks down.  ...  Acknowledgements I would like to thank Dorit Aharonov for suggesting the possibility of enhanced models of quantum finite automata, which motivated much of this work, Andris Ambainis for useful comments  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/quant-ph/9904093v3">arXiv:quant-ph/9904093v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ej4tcnx7mrekrejrpihrxexazq">fatcat:ej4tcnx7mrekrejrpihrxexazq</a> </span>
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Automata and Quantum Computing [article]

Andris Ambainis, Abuzer Yakaryılmaz
<span title="2018-07-04">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Keywords: quantum finite automata, probabilistic finite automata, nondeterminism, bounded error, unbounded error, state complexity, decidability and undecidability, computational complexity  ...  Besides full-scale quantum computers, more restricted models such as quantum versions of finite automata have been studied.  ...  Cem Say and John Watrous for their helpful comments on the subject matter of this chapter.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1507.01988v2">arXiv:1507.01988v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ww2rhgjp6bfevcgasu4e4xant4">fatcat:ww2rhgjp6bfevcgasu4e4xant4</a> </span>
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Page 8043 of Mathematical Reviews Vol. , Issue 2003j [page]

<span title="">2003</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
This work similarly determines provable upper bounds on the sizes of the two key parameters in the DSA for which the system can be broken.  ...  For the structure of feedforward inverse finite automata with delay 2, Zhu first gave a characterization; from a result on mutual invertibility of finite automata, the result mentioned above also leads  ... 
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From Quantum Query Complexity to State Complexity [chapter]

Shenggen Zheng, Daowen Qiu
<span title="">2014</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
State complexity of quantum finite automata is one of the interesting topics in studying the power of quantum finite automata.  ...  On the other hand, if the communication protocols are easy enough, then they can be simulated by finite automata and obtain new state complexity results (upper bounds) for finite automata.  ...  Acknowledgements The first author would like to thank Jozef Gruska for having a most constructive influence on him, teaching him how to think and write in a clear way, and for continuous support during  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-13350-8_18">doi:10.1007/978-3-319-13350-8_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5sk2v3j63fcbtk6coar4odzbmm">fatcat:5sk2v3j63fcbtk6coar4odzbmm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190302020426/http://pdfs.semanticscholar.org/94f9/999aa91f2357d815ac376f6100a27a630035.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/f9/94f9999aa91f2357d815ac376f6100a27a630035.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-13350-8_18"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Research report: State complexity of operations on two-way quantum finite automata [article]

Daowen Qiu
<span title="2008-07-03">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give an instance to show that the upper bound of the state number for the simulation of one-way deterministic finite automata by two-way reversible finite automata is not tight in general.  ...  This paper deals with the size complexity of minimal two-way quantum finite automata (2qfa's) necessary for operations to perform on all inputs of each fixed length.  ...  Tomoyuki Yamakami for helpful discussion regarding qfa's and this report was motivated by the discussion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0807.0476v1">arXiv:0807.0476v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oegmu56yvbbrxdny4vyscpbcjy">fatcat:oegmu56yvbbrxdny4vyscpbcjy</a> </span>
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Dense quantum coding and quantum finite automata

Andris Ambainis, Ashwin Nayak, Amnon Ta-Shma, Umesh Vazirani
<span title="2002-07-01">2002</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r72grtxx6jad5hjzl7fxcunwhi" style="color: black;">Journal of the ACM</a> </i> &nbsp;
It was known that there are languages that are recognized by quantum finite automata with sizes exponentially smaller than those of corresponding classical automata.  ...  This motivates the study of quantum computation with restricted memory and no reinitialization, that is, of quantum finite automata.  ...  We would like to thank Ike Chuang for showing us the 3-into-1 quantum encoding; Dorit Aharonov, Ike Chuang, Michael Nielsen, Steven Rudich, and Avi Wigderson for many interesting discussions; and the anonymous  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/581771.581773">doi:10.1145/581771.581773</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qsrhki7q4vatrd7hlzqimxmb6i">fatcat:qsrhki7q4vatrd7hlzqimxmb6i</a> </span>
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Page 6383 of Mathematical Reviews Vol. , Issue 99i [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Further, let IAFA(k) and 2AFA(k) denote the classes of languages accepted by one-way and two-way al- ternating k-head finite automata, respectively.  ...  The complexity bounds depend on the word-size of the PRAM but not on the multiprefix operations or the instruction set of the processors.” 991:68034 68Q05 68Q15 81P99 Watrous, John (1-WI-C; Madison, WI  ... 
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Nature computes: Information processing in quantum dynamical systems

Karoline Wiesner
<span title="">2010</span> <i title="AIP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jh7idzebgzcuffjreetqux4374" style="color: black;">Chaos</a> </i> &nbsp;
On the basis of this framework we discuss upper and lower bounds for intrinsic information storage in a quantum dynamical system.  ...  The amount of matter and energy in the system puts a limit on the amount of computation it can perform and at what speed.  ...  To lay the foundations for a computational perspective on quantum dynamical systems a class of quantum mechanical finite-state automata was introduced. 8 These automata generate a process language in  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.3491238">doi:10.1063/1.3491238</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/20887080">pmid:20887080</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3hykwtqpmjhwldvuw7ss4qp3o4">fatcat:3hykwtqpmjhwldvuw7ss4qp3o4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812193748/http://www.idt.mdh.se/~gdc/work/ARTICLES/2014/3-CiE-journal/Background/Nature-computes-Wiesner-Chaos_20_037114.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/67/14/6714570483e84f38a23c10b19a2c2f48a7fc317c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1063/1.3491238"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Language recognition power and succinctness of affine automata

Marcos Villagra, Abuzer Yakaryılmaz
<span title="2017-11-07">2017</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6zolbg3dcjdt3edqtvzmiiuuim" style="color: black;">Natural Computing</a> </i> &nbsp;
Then, we initiate a study on the succintness of affine automata.  ...  In particular, we show that an infinite family of unary regular languages can be recognized by 2-state affine automata but the state numbers of quantum and probabilistic automata cannot be bounded.  ...  For details on the models of probabilistic and quantum automata, we recommend references [15] , [19] , and [5] . Let Σ be a finite alphabet.  ... 
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