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Computational Complexity of Probabilistic Turing Machines

John Gill
1977 SIAM journal on computing (Print)  
Abstraeto A probabilistic Turing machine is a Turing machine with the ability to make decisions based on the outcomes of unbiased coin tosses.  ...  With this definition, only partial recursive functions are probabilistically computable. The run time and tape of probabilistic machines are defined.  ...  Some of the results appear in the author's doctoral dissertation, supervised by Manuel Blum and supported by National Science Foundation Grant GJo708 at the University of California, Berkeley.  ... 
doi:10.1137/0206049 fatcat:3nf4y3zaerekpixd6tga7kupdy

Computational complexity of probabilistic Turing machines

John T. Gill
1974 Proceedings of the sixth annual ACM symposium on Theory of computing - STOC '74  
Abstraeto A probabilistic Turing machine is a Turing machine with the ability to make decisions based on the outcomes of unbiased coin tosses.  ...  With this definition, only partial recursive functions are probabilistically computable. The run time and tape of probabilistic machines are defined.  ...  Some of the results appear in the author's doctoral dissertation, supervised by Manuel Blum and supported by National Science Foundation Grant GJo708 at the University of California, Berkeley.  ... 
doi:10.1145/800119.803889 dblp:conf/stoc/Gill74 fatcat:zgw66ohg7fe5xad6pxda7li42m

Minimal nontrivial space complexity of probabilistic one- way turing machines [chapter]

Jānis Kaņeps, Rūsiņš Freivalds
Lecture Notes in Computer Science  
Languages recognizable in o(log log n) space by probabilistic one -w a y Turing machines are proved to be regular. This solves an open problem in [4]. .  ...  The set of states is denoted by Q, and it includes states q accept and q reject- The probabilistic one -way Turing machine differs from the deterministic one only in the additional ability to perform random  ...  The abovementioned definition of the space complexity is the most popular in the papers on complexity of probabilistic machines.  ... 
doi:10.1007/bfb0029629 dblp:conf/mfcs/KanepsF90 fatcat:rf6xnaok3rbtdfou5nnr3jobu4

Page 609 of Mathematical Reviews Vol. 57, Issue 2 [page]

1979 Mathematical Reviews  
Gill, John 4616 Computational complexity of probabilistic Turing machines. SIAM J.  ...  It is shown first that the class of partial functions computed by probabilistic Turing machines is precisely the class of partial recursive functions.  ... 

Multihead two-way probabilistic finite automata [chapter]

Ioan I. Macarie
1995 Lecture Notes in Computer Science  
Partially based on this relation, we find an apparently easier logspace complete problem for PL (the class of languages recognized by logspace unbounded-error probabilistic Turing machines), and we discuss  ...  machines.  ...  Our goal is to study properties of multihead two-way probabilistic finite automata in connection with logspace probabilistic Turing machines.  ... 
doi:10.1007/3-540-59175-3_103 fatcat:l37vry5hunb3nk5dghikepjwia

Rūsiņš Mārtiņš Freivalds: Academic Genealogy and Selected Publications

Rūsiņš Mārtiņš Freivalds, Solvita Zariņa
2016 Baltic Journal of Modern Computing  
Freivalds: Space and reversal complexity of probabilistic one-way Turing machines. "Annals of Discrete Mathematics", 1985, vol. 24, pp. 39-50 110. R.  ...  Freivalds: Space and reversal complexity of probabilistic one-way Turing machines. "Lecture Notes in Computer Science", Springer, 1983, vol. 158, pp. 159-170 111. R.  ... 
doi:10.22364/bjmc.2016.4.4.02 fatcat:i6z5ncr4ivcznhq3qdl65z4lnq

Space-bounded hierarchies and probabilistic computations

Walter L. Ruzzo, Janos Simon, Martin Tompa
1984 Journal of computer and system sciences (Print)  
We study three aspects of the power of space-bounded probabilistic Turing machines.  ...  by a log n spacebounded probabilistic Turing machine with small error probability; this is a generalization of Gill's result that any language in NSPACE (log n) can be recognized by such a machine.  ...  INTRODUCTION This paper studies the power of space-bounded probabilistic Turing machines.  ... 
doi:10.1016/0022-0000(84)90066-7 fatcat:bvcg33bozrbc7beb5fusesbngu

Computational Power of the Quantum Turing Automata

Sina Jafarpour, Mohammad Ghodsi, Keyvan Sadri, Zuheir Montazeri
2007 Fourth International Conference on Information Technology (ITNG'07)  
We introduce a new form of Turing machine based on the concepts of quantum mechanics and investigate the domain of this novel definition for computation.  ...  In next chapter we introduce quantum complexity featuring Quantum Turing Machines and discuss its relationship to classical complexity.  ...  Complexity of Quantum Turing machines Having proven that a quantum computer can compute exactly the same set of languages as a classical computer, we now examine quantum complexity.  ... 
doi:10.1109/itng.2007.56 dblp:conf/itng/JafarpourGSM07 fatcat:nem6vhnxq5hhlmy6hkm2yyrgqu

On Probabilistic Machines, Bounded Rationality and Average-Case Complexity [chapter]

Nimrod Megiddo
1994 Essays in Game Theory  
It is shown that probabilistic machines are more powerful than probability distributions over deterministic ones, that best response may sometimes requires randomization, and that if nature's choices are  ...  computable then there exists a deterministic best response.  ...  Acknowledgments: Thanks to Nathan Linial and other attendees of the IMSSS Summer Workshop on Bounded Rationality, for stimulating discussions on the material in the paper.  ... 
doi:10.1007/978-1-4612-2648-2_9 dblp:conf/birthday/Megiddo94 fatcat:q7ldhrbgfjemhi3mejpr7pw5eq

Page 1683 of Mathematical Reviews Vol. 51, Issue 5 [page]

1976 Mathematical Reviews  
of states; if L is a stochastic language accepted by a probabilistic automaton of complexity L(n), then L is e-approximable by a Turing machine of tape complexity max(log, n, L(log,+k)).  ...  A is of complexity L(m), then the corresponding probabilistic event is e-approximable by a Turing machine of tape complexity max(log, n, L(log, n+k)), where k is a constant depending on « and the number  ... 

On Halting Process of Quantum Turing Machine

Takayuki Miyadera, Masanori Ohya
2005 Open systems & information dynamics  
We, hence, can not avoid the notion of halting to be probabilistic in Quantum Turing Machine.  ...  We prove that there is no algorithm to tell whether an arbitrarily constructed Quantum Turing Machine has same time steps for different branches of computation.  ...  In [1] Myers pointed out that there exists a problem in case different branches of quantum computation on a Quantum Turing Machine (QTM) take different numbers of steps to complete their calculation.  ... 
doi:10.1007/s11080-005-0923-2 fatcat:voi3bsnwfrcghnhc2bsefnkucy

Cumulative subject index volumes 68–71

1986 Information and Control  
analysis, 68, 105 for computing properties and functions of n-node forest stored in processor mesh, 69, 168 deterministic, applications to optimal parallel list ranking, 70, 32 network resource allocation  ...  , probabilistic analysis, 68, 47 optimally data-efficient, for isomorphism inference:  ...  , 70, 97 synchronization tree, for non-deterministic programs and specifications, 68, 254 M Machines for attribute grammars, description, 69, 41 Turing, see Turing machines Models higher type  ... 
doi:10.1016/s0019-9958(86)80014-6 fatcat:hkligygazvcyvdgrhtvhrefpj4

Parameterized Analogues of Probabilistic Computation [chapter]

Ankit Chauhan, B. V. Raghavendra Rao
2015 Lecture Notes in Computer Science  
Our definition uses the machine based characterization of the parameterized complexity class W[P] obtained by Chen et.al [TCS 2005].  ...  We study structural aspects of randomized parameterized computation. We introduce a new class W[P]-PFPT as a natural parameterized analogue of PP.  ...  Acknowledgements We thank anonymous reviewers for their comments on an earlier version of this paper which helped in improving the presentation of the article.  ... 
doi:10.1007/978-3-319-14974-5_18 fatcat:73zawyw5trftjgkbpbpjkr6vbe

Parameterized Analogues of Probabilistic Computation [article]

Ankit Chauhan, B. V. Raghavendra Rao
2014 arXiv   pre-print
Our definition uses the machine based characterization of the parameterized complexity class W[P] obtained by Chen et.al [TCS 2005].  ...  We study structural aspects of randomized parameterized computation. We introduce a new class W[P]- PFPT as a natural parameterized analogue of PP.  ...  Acknowledgements We thank anonymous reviewers for their comments on an earlier version of this paper which helped in improving the presentation of the article.  ... 
arXiv:1409.7790v1 fatcat:asy7frwdinhafnd33l2hewxoo4

Page 1963 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
Many important complexity classes are defined in terms of fixed properties of #accy,(x), the number of accepting paths of a non- deterministic polynomial-time Turing machine (NPTM) on input x (eg., the  ...  The paper presents results for logspace Turing machines and multi- head finite automata with probabilistic and with both probabilistic and nondeterministic states.  ... 
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