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Computational limitations of Stochastic Turing machines and Arthur-Merlin games with small space bounds [chapter]

Maciej Liśkiewicz, Rüdiger Reischuk
1997 Lecture Notes in Computer Science  
A Stochastic Turing machine (STM) is a Turing machine that can perform nondeterministic and probabilistic moves and alternate between both types.  ...  Such devices are also called games against nature, Arthur-Merlin games, or interactive proof systems with public coins.  ...  AM 1 Space(CON) ? AM k Space(CON) : From [DwSt92] we know that CENTER does not belong to AM 1 Space(CON) and that there exists a constant space Arthur-Merlin game for this language.  ... 
doi:10.1007/bfb0029952 fatcat:7vnbstfpxngkpooer65mvnr7ne

NP has log-space verifiers with fixed-size public quantum registers [article]

Abuzer Yakaryilmaz, A. C. Cem Say
2012 arXiv   pre-print
In classical Arthur-Merlin games, the class of languages whose membership proofs can be verified by Arthur using logarithmic space (AM(log-space)) coincides with the class P Co89.  ...  language in NP can be verified with any desired error bound.  ...  [AW02] and the Turing machines with both classical and quantum tapes of [Wat03] .  ... 
arXiv:1101.5227v3 fatcat:srg262moynff7jvfrww456gmja

Page 3448 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
Baer (Mill Valley, CA) 99e:68036 68Q05 68Q15 Liskiewicz, Maciej (PL-WROC-C; Wroctaw); Reischuk, Riidiger Computational limitations of stochastic Turing machines and Arthur-Merlin games with small space  ...  Such devices are also called games against nature, Arthur-Merlin games, or interactive proof systems with public coins.  ... 

A Note on the Representational Incompatibility of Function Approximation and Factored Dynamics

Eric Allender, Sanjeev Arora, Michael J. Kearns, Cristopher Moore, Alexander Russell
2002 Neural Information Processing Systems  
Our result applies even to policies which yield a polynomially poor approximation to the optimal value, and highlights interesting connections with the complexity class of Arthur-Merlin games.  ...  More precisely, we give a fixed family of factored MDPs with linear rewards whose optimal policies and value functions simply cannot be represented succinctly in any standard parametric form.  ...  NP corresponds to Arthur-Merlin games where Arthur says nothing, and thus clearly NP AM . Restricting the number of questions seems to put severe limitations on the power of Arthur-Merlin games.  ... 
dblp:conf/nips/AllenderAKMR02 fatcat:phy2pyapgbg3pombtekievdcty

Quantum Computational Complexity [article]

John Watrous
2008 arXiv   pre-print
Other topics in quantum complexity, including quantum advice, space-bounded quantum computation, and bounded-depth quantum circuits, are also discussed.  ...  This article surveys quantum computational complexity, with a focus on three fundamental notions: polynomial-time quantum computations, the efficient verification of quantum proofs, and quantum interactive  ...  The class QMAM may be defined through a similar analogy with classical Arthur-Merlin games.  ... 
arXiv:0804.3401v1 fatcat:upi5d4ax6jejxkprq6snxuup4y

Quantum Computational Complexity [chapter]

John Watrous
2013 Encyclopedia of Complexity and Systems Science  
Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII.  ...  verifier of the answer to some computational problem.  ...  The class QMAM may be defined through a similar analogy with classical Arthur-Merlin games.  ... 
doi:10.1007/978-3-642-27737-5_428-3 fatcat:6djjqj3ppzby5npbzzxa3mwcoy

Quantum Computational Complexity [chapter]

John Watrous
2009 Encyclopedia of Complexity and Systems Science  
Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII.  ...  verifier of the answer to some computational problem.  ...  The class QMAM may be defined through a similar analogy with classical Arthur-Merlin games.  ... 
doi:10.1007/978-0-387-30440-3_428 fatcat:2vkfughherat3cd3vmyrevqkay

Quantum Computational Complexity [chapter]

John Watrous
2012 Computational Complexity  
Definition of the subject and its importance II. Introduction III. The quantum circuit model IV. Polynomial-time quantum computations V. Quantum proofs VI. Quantum interactive proof systems VII.  ...  verifier of the answer to some computational problem.  ...  The class QMAM may be defined through a similar analogy with classical Arthur-Merlin games.  ... 
doi:10.1007/978-1-4614-1800-9_147 fatcat:f7ceslrlqzh3pptlo32pt7barq

Page 2742 of Mathematical Reviews Vol. , Issue 99d [page]

1991 Mathematical Reviews  
over poly- nomial calculus (85-90); Maciej Liskiewicz and Riidiger Reis- chuk, Computational limitations of stochastic Turing machines and Arthur-Merlin games with small space bounds (91-107); Dan Roth  ...  and Georg Schnitger, Com- munication complexity and sequential computation (71-84); Jan Kraji¢éek, Lower bounds for a proof system with an exponen- tial speed-up over constant-depth Frege systems and  ... 

Turing-equivalent automata using a fixed-size quantum memory [article]

Abuzer Yakaryilmaz
2012 arXiv   pre-print
We focus on space-bounded computation, and obtain the following surprising results: Both of them with constant-space are Turing-equivalent.  ...  Both are obtained from their classical counterparts (Arthur-Merlin proof system and alternating Turing machine, respectively,) by augmenting them with a fixed-size quantum register.  ...  We would like to thank Andris Ambainis and A. C. Cem Say for their many helpful comments on some drafts of this paper.  ... 
arXiv:1205.5395v1 fatcat:5urty77smzdc7niatrfiy2q5cu

Why Philosophers Should Care about Computational Complexity [chapter]

2013 Computability  
In particular, I argue that computational complexity theory-the field that studies the resources (such as time, space, and randomness) needed to solve computational problems-leads to new perspectives on  ...  One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance.  ...  Section 5; and to Andy Drucker, Michael Forbes, Dana Moshkovitz, Ronald de Wolf, and Avi Wigderson for their feedback.  ... 
doi:10.7551/mitpress/8009.003.0011 fatcat:sk6y4k62xbfgdn4nytamdeq6my

A generalization of resource-bounded measure, with an application (Extended abstract) [chapter]

Harry Buhrman, Dieter van Melkebeek, Kenneth W. Regan, D. Sivakumar, Martin Strauss
1998 Lecture Notes in Computer Science  
We introduce resource-bounded betting games, and propose a generalization of Lutz's resource-bounded measure in which the choice of next string to bet on is fully adaptive.  ...  We say that D is computable in a class C if every bit of D(y) is computable in C, given y and the index of the bit in binary.  ...  Acknowledgments The authors specially thank Klaus Ambos-Spies, Ron Book (pace), and Jack Lutz for organizing a special Schloss Dagstuhl workshop in July 1996, where preliminary versions of results and  ... 
doi:10.1007/bfb0028558 fatcat:znvngrqenvhthnl42tl4n5hchm

Debates with small transparent quantum verifiers [article]

Abuzer Yakaryilmaz and A. C. Cem Say, H. Gökalp Demirci
2015 arXiv   pre-print
We show that the incorporation of just two qubits to an otherwise classical constant-space verifier raises the class of debatable languages from at most NP to the collection of all Turing-decidable languages  ...  We also show that the quantum model outperforms its classical counterpart when restricted to run in polynomial time, and demonstrate some non-context-free languages which have such short debates with quantum  ...  Acknowledgements We thank the anonymous reviewers of a previous version of this manuscript for their helpful comments.  ... 
arXiv:1405.1655v2 fatcat:i6t2e4n3wvemxigqm43y6usrai

Computational complexity in electronic structure

James Daniel Whitfield, Peter John Love, Alán Aspuru-Guzik
2013 Physical Chemistry, Chemical Physics - PCCP  
Extensions of computer science and information processing exploiting quantum mechanics has led to new ways of understanding the ultimate limitations of computational power.  ...  In this article, the fundamentals of computational complexity will be reviewed and motivated from the vantage point of chemistry.  ...  In the Merlin-Arthur games, the proof verifying the validity of input x is magically (hence non-deterministically) given by a wizard Merlin who is prone to deception.  ... 
doi:10.1039/c2cp42695a pmid:23172634 fatcat:zqscceg3qbeavgo5ogimzdtrxe

Quantum NP - A Survey [article]

Dorit Aharonov, Tomer Naveh
2002 arXiv   pre-print
This survey is the extension of lecture notes taken by Naveh for Aharonov's quantum computation course, held in Tel Aviv University, 2001.  ...  This result raises a rich array of open problems related to quantum complexity, algorithms and entanglement, which we state at the end of this survey.  ...  Acknowledgements One of us (D.A.) wishes to thank Avi Wigderson for insightful comments during Kitaev's first lecture about the subject [9] .  ... 
arXiv:quant-ph/0210077v1 fatcat:6pmfdmjndvh3plfi5q4jcbklka
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