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

1997
*
Lecture Notes in Computer Science
*

A

doi:10.1007/bfb0029952
fatcat:7vnbstfpxngkpooer65mvnr7ne
*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. ...##
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NP has log-space verifiers with fixed-size public quantum registers
[article]

2012
*
arXiv
*
pre-print

In classical

arXiv:1101.5227v3
fatcat:srg262moynff7jvfrww456gmja
*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] . ...##
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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

2002
*
Neural Information Processing Systems
*

Our result applies even to policies which yield a polynomially poor approximation to the optimal value,

dblp:conf/nips/AllenderAKMR02
fatcat:phy2pyapgbg3pombtekievdcty
*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*. ...##
###
Quantum Computational Complexity
[article]

2008
*
arXiv
*
pre-print

Other topics in quantum complexity, including quantum advice,

arXiv:0804.3401v1
fatcat:upi5d4ax6jejxkprq6snxuup4y
*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*. ...##
###
Quantum Computational Complexity
[chapter]

2013
*
Encyclopedia of Complexity and Systems Science
*

Definition

doi:10.1007/978-3-642-27737-5_428-3
fatcat:6djjqj3ppzby5npbzzxa3mwcoy
*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*. ...##
###
Quantum Computational Complexity
[chapter]

2009
*
Encyclopedia of Complexity and Systems Science
*

Definition

doi:10.1007/978-0-387-30440-3_428
fatcat:2vkfughherat3cd3vmyrevqkay
*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*. ...##
###
Quantum Computational Complexity
[chapter]

2012
*
Computational Complexity
*

Definition

doi:10.1007/978-1-4614-1800-9_147
fatcat:f7ceslrlqzh3pptlo32pt7barq
*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*. ...##
###
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*...##
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Turing-equivalent automata using a fixed-size quantum memory
[article]

2012
*
arXiv
*
pre-print

We focus on

arXiv:1205.5395v1
fatcat:5urty77smzdc7niatrfiy2q5cu
*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. ...##
###
Why Philosophers Should Care about Computational Complexity
[chapter]

2013
*
Computability
*

In particular, I argue that

doi:10.7551/mitpress/8009.003.0011
fatcat:sk6y4k62xbfgdn4nytamdeq6my
*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. ...##
###
A generalization of resource-bounded measure, with an application (Extended abstract)
[chapter]

1998
*
Lecture Notes in Computer Science
*

We introduce resource-

doi:10.1007/bfb0028558
fatcat:znvngrqenvhthnl42tl4n5hchm
*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*...##
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Debates with small transparent quantum verifiers
[article]

2015
*
arXiv
*
pre-print

We show that the incorporation

arXiv:1405.1655v2
fatcat:i6t2e4n3wvemxigqm43y6usrai
*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. ...##
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Computational complexity in electronic structure

2013
*
Physical Chemistry, Chemical Physics - PCCP
*

Extensions

doi:10.1039/c2cp42695a
pmid:23172634
fatcat:zqscceg3qbeavgo5ogimzdtrxe
*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. ...##
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Quantum NP - A Survey
[article]

2002
*
arXiv
*
pre-print

This survey is the extension

arXiv:quant-ph/0210077v1
fatcat:6pmfdmjndvh3plfi5q4jcbklka
*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] . ...
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