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Page 7890 of Mathematical Reviews Vol. , Issue 99k [page]

1999 Mathematical Reviews  
properties of the classes of sets recognized by space-bounded two-dimensional probabilistic Turing machines.  ...  Summary: “This paper investigates closure properties of the classes of sets recognized by space-bounded two-dimensional probabilis- tic Turing machines with error probability less than 4.  ... 

Page 1300 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
homomorphism, and (2) the class of lan- guages recognized by o(loglogn) space-bounded two-way un- bounded error probabilistic Turing machines is not closed under each of the above operations.  ...  ; Ube) Closure property of probabilistic Turing machines and alternating Turing machines with sublogarithmic spaces.  ... 

Remarks on Four-Dimensional Probabilistic Finite Automata

Makoto Sakamoto, Yasuo Uchida, Makoto Nagatomo, Tuo Zhang, Hikaru Susaki, Takao Ito, Tsunehiro Yoshinaga, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani
2014 2014 7th International Conference on Signal Processing, Image Processing and Pattern Recognition  
On the other hand, the class of sets accepted by probabilistic machines have been studied extensively.  ...  As far as we know, however, there is no results concerned with four-dimensional probabilistic machines.  ...  On the other hand, the classes of sets recognized by two-or three-dimensional probabilistic finite automata and probabilistic Turing machines have been studied extensively [3-6, 9, 12-15, 17-19, 25, 28  ... 
doi:10.1109/sip.2014.9 fatcat:q6azultzc5hwbkjfmy45zhwkqq

Remarks on Four-Dimensional Probabilistic Finite Automata

Makoto Sakamoto, Yasuo Uchida, Makoto Nagatomo, Tuo Zhang, Hikaru Susaki, Takao Ito, Tsunehiro Yoshinaga, Satoshi Ikeda, Masahiro Yokomichi, Hiroshi Furutani
2015 International Journal of Software Engineering and Its Applications  
On the other hand, the class of sets accepted by probabilistic machines have been studied extensively.  ...  As far as we know, however, there is no results concerned with four-dimensional probabilistic machines.  ...  On the other hand, the classes of sets recognized by two-or three-dimensional probabilistic finite automata and probabilistic Turing machines have been studied extensively [3-6, 9, 12-15, 17-19, 25, 28  ... 
doi:10.14257/ijseia.2015.9.6.10 fatcat:tglvocqrbrbcfhgjiiddzacucq

Probabilistic rebound Turing machines

Lan Zhang, Katsushi Inoue, Akira Ito, Yue Wang
2002 Theoretical Computer Science  
This paper introduces a probabilistic rebound Turing machine (PRTM), and investigates the fundamental property of the machine.  ...  (o(logn))] denotes the class of languages recognized by o(logn) space-bounded PRTMs with error probability less than 1 2 .  ...  We thank the referees for suggestions for improving the exposition.  ... 
doi:10.1016/s0304-3975(01)00098-6 fatcat:p55iw5ul7ralxhyjrkell644xm

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

Amandeep Singh Bhatia, Ajay Kumar
2019 arXiv   pre-print
Quantum automata can be classified thusly: quantum finite automata, quantum sequential machine, quantum pushdown automata, quantum Turing machine and orthomodular lattice-valued automata.  ...  In light of the current state of quantum computation theory research, a systematic review of the literature seems timely.  ...  Acknowledgments Amandeep Singh Bhatia was supported by Maulana Azad National Fellowship (MANF), funded by Ministry of Minority Affairs, Government of India.  ... 
arXiv:1901.07992v1 fatcat:yoxwrd6e55gh3heapwy3w5uuhm

Space-Efficient Deterministic Simulation of Probabilistic Automata

Ioan I. Macarie
1998 SIAM journal on computing (Print)  
Given a description of a probabilistic automaton (one-head probabilistic nite automaton or probabilistic Turing machine) and an input string x of length n, we ask how much space does a deterministic Turing  ...  machine need in order to decide the acceptance of the input string by that automaton?  ...  Theorem 6 The languages recognized by f(n) 2 o(log log log n) space-bounded probabilistic Turing machines can be recognized by deterministic Turing machines in space O(c f(n) (log n)), where c is a constant  ... 
doi:10.1137/s0097539793253851 fatcat:afmxsmyccfd25ctwpy2mcyn6za

Languages recognized by nondeterministic quantum finite automata [article]

Abuzer Yakaryilmaz, A. C. Cem Say
2010 arXiv   pre-print
We also characterize the class of languages that are recognized necessarily by two-sided error by QFA's.  ...  We prove several closure properties of the related classes. The ramifications of these results about classical and quantum sublogarithmic space complexity classes are examined.  ...  Acknowledgments We are grateful to Andris Ambainis, John Watrous, and Flavio D'Alessandro for their helpful comments on the subject matter of this paper.  ... 
arXiv:0902.2081v2 fatcat:5zgm6qrsr5fr3hvaroscbhacw4

Subject index volumes 1–200

1999 Theoretical Computer Science  
, 265 tape-bounded probabilistic Turing machine, 265 acceptors, 330 transducers, 265 tape-bounded two-dimensional Turing machines, 507 Turing computations, nondeterministic -, 194 tapes, 2107,  ...  , 2390, 2405, 2776 recognizable in polynomial time by probabilistic Turing machines, 255 recognized by finite state automata with multiplicity in semiring K, 227 sets, recursive -. 2214, 2357 definitions  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Classical and quantum computation with small space bounds (PhD thesis) [article]

Abuzer Yakaryilmaz
2011 arXiv   pre-print
Firstly, we consider QTMs in the unbounded error setting: (i) in some cases of sublogarithmic space bounds, the class of languages recognized by QTMs is shown to be strictly larger than that of classical  ...  ones; (ii) in constant space bounds, the same result can still be obtained for restricted QTMs; (iii) the complete characterization of the class of languages recognized by realtime constant space nondeterministic  ...  SUBLINEAR-SPACE REALTIME TURING MACHINES In this chapter, we give space lower bounds of realtime classical Turing machines recognizing nonregular languages.  ... 
arXiv:1102.0378v1 fatcat:qvpqmbn67jbvhlprvlcam2wf24

Parallel computation for well-endowed rings and space-bounded probabilistic machines

A. Borodin, S. Cook, N. Pippenger
1983 Information and Control  
It is shown that a probabilistic Turing acceptor or transducer running within space bound S can be simulated by a time S 2 parallel machine and therefore by a space S 2 deterministic machine.  ...  The method introduces a generalization of the ring of integers, called well-endowed rings. Such rings possess a very efficient parallel implementation of the basic (+, -, ×) ring operations.  ...  Our deterministic space bound S 2 also applies to the simulation of probabilistic Turing transducers bounded by space S.  ... 
doi:10.1016/s0019-9958(83)80060-6 fatcat:dggmyiqzvvhjdi5t5ld6fdjfuq

Dynamical recognizers: real-time language recognition by analog computers

Cristopher Moore
1998 Theoretical Computer Science  
Each class of maps and inequalities, such as quadratic functions with rational coefficients, is capable of recognizing a particular class of languages.  ...  We relate this model to other models of analog computation; in particular, it can be seen as a real-time, constant-space, off-line version of Blum, Shub and Smale's real-valued machines.  ...  and Spootie the Cat for companionship.  ... 
doi:10.1016/s0304-3975(97)00028-5 fatcat:hy3hbmbiijf53a455zn7rk4vve

A Study In Complexity

Kyriakos Sourmelis
2021 Zenodo  
Through the mathematical models and a thorough analysis, the attributes of each complexity class are explained and investigated.  ...  The study goes into weird complexity classes and mathematical equations showcasing how difficult and chaotic the world of algorithms is.  ...  The penultimate class is the Bounded-error Probabilistic Polynomial time class where we use a probabilistic Turing machine (again like ZPP and RP) but in this case, the machine has an error probability  ... 
doi:10.5281/zenodo.6370623 fatcat:ydmry2ghqfaf3ndygtmneld3qi

Extension Complexity of Formal Languages [article]

Hans Raj Tiwary
2019 arXiv   pre-print
We demonstrate the utility of this machine characterization by obtaining upper bounds for polytopes for problems in nondeterministic logspace; lower bounds in streaming models; and upper bounds on extension  ...  This allows us to define the notion of extension complexity of formal languages. We prove several closure properties of languages admitting compact extended formulations.  ...  Acknowledgements The author would like to acknowledge the support of grant GA15-11559S of GA ČR.  ... 
arXiv:1603.07786v5 fatcat:2r2ryix2c5bt7njhfgcqn3magm

Characterizations of one-way general quantum finite automata [article]

Lvzhou Li, Daowen Qiu, Xiangfu Zou, Lvjun Li, Lihua Wu, Paulo Mateus
2010 arXiv   pre-print
We prove that MO-1gQFA recognize, with bounded error, precisely the set of all regular languages. We prove that MM-1gQFA also recognize only regular languages with bounded error.  ...  generally affects the language recognition power of one-way QFA.  ...  Then by the boundedness of S from a finite-dimensional space, from the sequence {ρ x (n) } n∈N , we can extract a Cauchy sequence {ρ x (n k ) , } k∈N , i.e., a convergent subsequence.  ... 
arXiv:0911.3266v3 fatcat:c2g46wqk5bhthei5tqbn22bux4
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