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Computational Complexity of Probabilistic Turing Machines

1977
*
SIAM journal on computing (Print)
*

Abstraeto A

doi:10.1137/0206049
fatcat:3nf4y3zaerekpixd6tga7kupdy
*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. ...##
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Computational complexity of probabilistic Turing machines

1974
*
Proceedings of the sixth annual ACM symposium on Theory of computing - STOC '74
*

Abstraeto A

doi:10.1145/800119.803889
dblp:conf/stoc/Gill74
fatcat:zgw66ohg7fe5xad6pxda7li42m
*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. ...##
###
Minimal nontrivial space complexity of probabilistic one- way turing machines
[chapter]

*
Lecture Notes in Computer Science
*

Languages recognizable in o(log log n) space by

doi:10.1007/bfb0029629
dblp:conf/mfcs/KanepsF90
fatcat:rf6xnaok3rbtdfou5nnr3jobu4
*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*. ...##
###
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]

1995
*
Lecture Notes in Computer Science
*

Partially based on this relation, we find an apparently easier logspace complete problem for PL (the class

doi:10.1007/3-540-59175-3_103
fatcat:l37vry5hunb3nk5dghikepjwia
*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*. ...##
###
Rūsiņš Mārtiņš Freivalds: Academic Genealogy and Selected Publications

2016
*
Baltic Journal of Modern Computing
*

Freivalds: Space and reversal

doi:10.22364/bjmc.2016.4.4.02
fatcat:i6z5ncr4ivcznhq3qdl65z4lnq
*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. ...##
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Space-bounded hierarchies and probabilistic computations

1984
*
Journal of computer and system sciences (Print)
*

We study three aspects

doi:10.1016/0022-0000(84)90066-7
fatcat:bvcg33bozrbc7beb5fusesbngu
*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*. ...##
###
Computational Power of the Quantum Turing Automata

2007
*
Fourth International Conference on Information Technology (ITNG'07)
*

We introduce a new form

doi:10.1109/itng.2007.56
dblp:conf/itng/JafarpourGSM07
fatcat:nem6vhnxq5hhlmy6hkm2yyrgqu
*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*. ...##
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On Probabilistic Machines, Bounded Rationality and Average-Case Complexity
[chapter]

1994
*
Essays in Game Theory
*

It is shown that

doi:10.1007/978-1-4612-2648-2_9
dblp:conf/birthday/Megiddo94
fatcat:q7ldhrbgfjemhi3mejpr7pw5eq
*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. ...##
###
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

2005
*
Open systems & information dynamics
*

We, hence, can not avoid the notion

doi:10.1007/s11080-005-0923-2
fatcat:voi3bsnwfrcghnhc2bsefnkucy
*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. ...##
###
Cumulative subject index volumes 68–71

1986
*
Information and Control
*

analysis, 68, 105 for

doi:10.1016/s0019-9958(86)80014-6
fatcat:hkligygazvcyvdgrhtvhrefpj4
*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 ...##
###
Parameterized Analogues of Probabilistic Computation
[chapter]

2015
*
Lecture Notes in Computer Science
*

Our definition uses the

doi:10.1007/978-3-319-14974-5_18
fatcat:73zawyw5trftjgkbpbpjkr6vbe
*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. ...##
###
Parameterized Analogues of Probabilistic Computation
[article]

2014
*
arXiv
*
pre-print

Our definition uses the

arXiv:1409.7790v1
fatcat:asy7frwdinhafnd33l2hewxoo4
*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. ...##
###
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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