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A tradeoff theorem for space and reversal

1984
*
Theoretical Computer Science
*

in this note, the following result is proved: Let M be an off-line Turing machine, TV the input length, S the l~ork spacit

doi:10.1016/0304-3975(84)90033-1
fatcat:zb5lime4kvfnviupdb4f3gi4fe
*and*R the total number of*reversals*of the work tape heads. ... Then RS = o(n) implies RS = 0( 1). l 03043975/84 S3.00*a*1984, Elsevier Science Publishers B.V. (North-Holland) ... Rackofi*and*Dymond noticed another kind of*tradeoff*phenomenon,*space*versus*reversal*. ...##
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Time, Space, and Energy in Reversible Computing
[article]

2005
*
arXiv
*
pre-print

with respect to energy-, time-

arXiv:cs/0504088v1
fatcat:vzx7bmgsvrarzjht44w7f444ei
*and**space*requirements. ... We survey results of*a*quarter century of work on computation by*reversible*general-purpose computers (in this setting Turing machines),*and*general*reversible*simulation of irreversible computations, ... Therefore, we can exchange*space*use*for*irreversible erasures. Such*a**tradeoff*can be used to reduce the*space*requirements of the*reversible*simulation. ...##
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Time, space, and energy in reversible computing

2005
*
Proceedings of the 2nd conference on Computing frontiers - CF '05
*

with respect to energy-, time-

doi:10.1145/1062261.1062335
dblp:conf/cf/Vitanyi05
fatcat:7nst2y7arjcjbnhn47tt3nuxym
*and**space*requirements. ... We survey results of*a*quarter century of work on computation by*reversible*general-purpose computers (in this setting Turing machines),*and*general*reversible*simulation of irreversible computations, ... Therefore, we can exchange*space*use*for*irreversible erasures. Such*a**tradeoff*can be used to reduce the*space*requirements of the*reversible*simulation. ...##
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Remote Preparation of Quantum States

2005
*
IEEE Transactions on Information Theory
*

Our main result is

doi:10.1109/tit.2004.839476
fatcat:nishrbydifdb7pztykahq4ooka
*a*general method of remote state preparation*for*arbitrary states of many qubits, at*a*cost of 1 bit of classical communication*and*1 bit of entanglement per qubit sent. ... In this "universal" formulation, these ebit*and*cbit requirements are shown to be simultaneously optimal by exhibiting*a*dichotomy. ...*Theorem*13:*For*an AVS , the q.c.t.*tradeoff*curve is given by where is the*tradeoff*of*Theorem*9 as*a*function of cbit rate*and*the ensemble distribution , made explicit. ...##
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Perfect Quantum Error-Correcting Condition Revisited
[article]

2005
*
arXiv
*
pre-print

We also revisit

arXiv:quant-ph/0505167v2
fatcat:dtr7cadv45frfmuuxnkd3bxybi
*a*variant of the no-cloning*and*no-deleting*theorem*based on an information-theoretical*tradeoff*between two parties*for*the*reversibility*of quantum operations,*and*demonstrate that the ... no-cloning*and*no-deleting*theorem*leads to the perfect error-correcting condition on Kraus operators. ... Acknowledgment The author wishes to thank*A*. Fujiwara*for*teaching him the essence of the one-to-one affine parameterization of quantum operations. He is grateful to H. Nagaoka*and*K. ...##
###
Page 1374 of Mathematical Reviews Vol. 56, Issue 4
[page]

1978
*
Mathematical Reviews
*

measures of time

*and**space**and*their relationships,*and*complete problems (*for*computer scientists,*a*slight misapplication of that term). ... The time-*space**tradeoff*, which is never clearly stated in its usual sense, involves the existence of two methods*for*computing the same function, one of which is economical in*space*but expensive in time ...##
###
Time and space bounds for reversible simulation

2001
*
Journal of Physics A: Mathematical and General
*

We prove

doi:10.1088/0305-4470/34/35/308
fatcat:fgf5senbcfatpgcsow3smfvc4y
*a*general upper bound on the*tradeoff*between time*and**space*that suffices*for*the*reversible*simulation of irreversible computation. ... Previously, only simulations using exponential time or quadratic*space*were known. The*tradeoff*shows*for*the first time that we can simultaneously achieve subexponential time*and*subquadratic*space*. ... Optimality*and**Tradeoffs*: The lower bound of*Theorem*2 is optimal in the following sense. ...##
###
Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

2007
*
Proceedings - IEEE Conference on Computational Complexity
*

We prove the first time-

doi:10.1109/ccc.2007.34
dblp:conf/coco/Williams07
fatcat:btbc4jzzcbco7obvgwfmyzkpke
*space**tradeoffs**for*counting the number of solutions to an NP problem modulo small integers,*and*also improve upon the known time-*space**tradeoffs**for*Sat. ... In particular,*for*all distinct primes p*and*q, we prove that at least one of MOD p -Sat*and*MOD q -Sat exhibits*a*time-*space**tradeoff*lower bound, identical to the best known*for*Sat. ... 10 Acknowledgements I am grateful to Virginia Vassilevska, Dieter van Melkebeek,*and*the anonymous referees*for*their helpful comments. ...##
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Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

2008
*
Computational Complexity
*

We prove the first time-

doi:10.1007/s00037-008-0248-y
fatcat:ikpmwp4rkrc5dkpvqzpup2qfza
*space**tradeoffs**for*counting the number of solutions to an NP problem modulo small integers,*and*also improve upon the known time-*space**tradeoffs**for*Sat. ... In particular,*for*all distinct primes p*and*q, we prove that at least one of MOD p -Sat*and*MOD q -Sat exhibits*a*time-*space**tradeoff*lower bound, identical to the best known*for*Sat. ... 10 Acknowledgements I am grateful to Virginia Vassilevska, Dieter van Melkebeek,*and*the anonymous referees*for*their helpful comments. ...##
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Time and Space Bounds for Reversible Simulation
[chapter]

2001
*
Lecture Notes in Computer Science
*

We prove

doi:10.1007/3-540-48224-5_82
fatcat:y6heionb65cfrnj5dgvwibvj6e
*a*general upper bound on the*tradeoff*between time*and**space*that suffices*for*the*reversible*simulation of irreversible computation. ... Previously, only simulations using exponential time or quadratic*space*were known. The*tradeoff*shows*for*the first time that we can simultaneously achieve subexponential time*and*subquadratic*space*. ... Optimality*and**Tradeoffs*: The lower bound of*Theorem*2 is optimal in the following sense. ...##
###
Peak to Average Power Ratio Reduction for Space-Time Codes That Achieve Diversity-Multiplexing Gain Tradeoff
[article]

2010
*
arXiv
*
pre-print

Zheng

arXiv:1003.0242v1
fatcat:qm5epe7zzffdzbpogjzba7p6rq
*and*Tse have shown that over*a*quasi-static channel, there exists*a*fundamental*tradeoff*, known as the diversity-multiplexing gain (D-MG)*tradeoff*. ... This result implies that, instead of designing codes on*a*case-by-case basis, as done by most existing works, there possibly exist general methodologies*for*designing*space*-time codes with low PAPR that ... Here, we use the perfect*space*-CCDF of PAPR*for**a*5 × 5*space*-time code [7] using HNF*and*PLUS approximate cubic shaping. ...##
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Distributed inference networks with costly wires

2010
*
Proceedings of the 2010 American Control Conference
*

*A*natural relaxation is shown to be

*a*

*reverse*convex minimization problem. ... This paper formulates

*and*studies the

*tradeoff*between algebraic notions of inference functionality

*and*algebraic notions of wiring costs. ... This relaxed problem is

*a*

*reverse*convex program. Proof: Follows from Propositions 3

*and*4. ...

##
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Quantum and classical tradeoffs

2005
*
Theoretical Computer Science
*

Intuitively,

doi:10.1016/j.tcs.2005.03.053
fatcat:clsep7zssbdqxa2k7gizkwuyea
*a*reduction in the quantumness requires an increase in the amount of classical computation, hence giving*a*"quantum*and*classical*tradeoff*". ... We propose an approach*for*quantifying*a*quantum circuit's quantumness as*a*means to understand the nature of quantum algorithmic speedups. ... I am also indebted to Serap Savari, Yufan Zhu, Shengyu Zhang*and*Tian Liu*for*useful discussions,*and*to an anonymous reviewer*for*helping me improve the presentation of the paper. ...##
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Approximately universal codes over slow-fading channels

2006
*
IEEE Transactions on Information Theory
*

Our main contribution is

doi:10.1109/tit.2006.876226
fatcat:hvnfydhybbcbpfnslvmhzivbva
*a*precise characterization of codes that are universally*tradeoff*-optimal, i.e., they optimally*tradeoff*the diversity*and*multiplexing gains*for*every statistical characterization ... Performance of reliable communication over*a*coherent slow fading MIMO channel at high SNR is succinctly captured as*a*fundamental*tradeoff*between diversity*and*multiplexing gains. ... We state their construction (see Proposition 9, [20] ),*for*completeness:*Theorem*5.5. Let q be*a*prime power*and*let L ≤ q + 1. Suppose α is*a*primitive element over F q . ...##
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Reaching and violating thermodynamic uncertainty bounds in information engines
[article]

2020
*
arXiv
*
pre-print

Here, we examine these bounds, in experiment

arXiv:1911.09835v3
fatcat:fuux4pjnundqrfovghptsrzvbe
*and*theory, by exploring the entire phase*space*of*a*cyclic information engine operating in*a*non-equilibrium steady state. ... We examine how the interplay of work fluctuation*and*dissipation shapes the information conversion efficiency of the engine,*and*find that dissipation is minimal at*a*finite noise level, where the original ... Indeed, we found that with an appropriate backward protocol, the original TUR is satisfied in*a*wider phase*space**and*the GTURs 2 are satisfied*for*the entire phase*space*of the engine. ...
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