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A tradeoff theorem for space and reversal

Jia-Wei Hong
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 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.  ... 
doi:10.1016/0304-3975(84)90033-1 fatcat:zb5lime4kvfnviupdb4f3gi4fe

Time, Space, and Energy in Reversible Computing [article]

Paul Vitanyi (CWI, University of Amsterdam, National ICT Australia)
2005 arXiv   pre-print
with respect to energy-, time- 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.  ... 
arXiv:cs/0504088v1 fatcat:vzx7bmgsvrarzjht44w7f444ei

Time, space, and energy in reversible computing

Paul Vitányi
2005 Proceedings of the 2nd conference on Computing frontiers - CF '05  
with respect to energy-, time-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.  ... 
doi:10.1145/1062261.1062335 dblp:conf/cf/Vitanyi05 fatcat:7nst2y7arjcjbnhn47tt3nuxym

Remote Preparation of Quantum States

C.H. Bennett, P. Hayden, D.W. Leung, P.W. Shor, A. Winter
2005 IEEE Transactions on Information Theory  
Our main result is 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.  ... 
doi:10.1109/tit.2004.839476 fatcat:nishrbydifdb7pztykahq4ooka

Perfect Quantum Error-Correcting Condition Revisited [article]

Tomohiro Ogawa
2005 arXiv   pre-print
We also revisit 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.  ... 
arXiv:quant-ph/0505167v2 fatcat:dtr7cadv45frfmuuxnkd3bxybi

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

Harry Buhrman, John Tromp, Paul Vitányi
2001 Journal of Physics A: Mathematical and General  
We prove 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.  ... 
doi:10.1088/0305-4470/34/35/308 fatcat:fgf5senbcfatpgcsow3smfvc4y

Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

Ryan Williams
2007 Proceedings - IEEE Conference on Computational Complexity  
We prove the first time-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.  ... 
doi:10.1109/ccc.2007.34 dblp:conf/coco/Williams07 fatcat:btbc4jzzcbco7obvgwfmyzkpke

Time-Space Tradeoffs for Counting NP Solutions Modulo Integers

R. Ryan Williams
2008 Computational Complexity  
We prove the first time-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.  ... 
doi:10.1007/s00037-008-0248-y fatcat:ikpmwp4rkrc5dkpvqzpup2qfza

Time and Space Bounds for Reversible Simulation [chapter]

Harry Buhrman, John Tromp, Paul Vitányi
2001 Lecture Notes in Computer Science  
We prove 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.  ... 
doi:10.1007/3-540-48224-5_82 fatcat:y6heionb65cfrnj5dgvwibvj6e

Peak to Average Power Ratio Reduction for Space-Time Codes That Achieve Diversity-Multiplexing Gain Tradeoff [article]

Chung-Pi Lee, Hsuan-Jung Su
2010 arXiv   pre-print
Zheng 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.  ... 
arXiv:1003.0242v1 fatcat:qm5epe7zzffdzbpogjzba7p6rq

Distributed inference networks with costly wires

L R Varshney
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.  ... 
doi:10.1109/acc.2010.5530757 fatcat:odw6ffwccjcmvbsue6hav232li

Quantum and classical tradeoffs

Yaoyun Shi
2005 Theoretical Computer Science  
Intuitively, 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.  ... 
doi:10.1016/j.tcs.2005.03.053 fatcat:clsep7zssbdqxa2k7gizkwuyea

Approximately universal codes over slow-fading channels

S. Tavildar, P. Viswanath
2006 IEEE Transactions on Information Theory  
Our main contribution is 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 .  ... 
doi:10.1109/tit.2006.876226 fatcat:hvnfydhybbcbpfnslvmhzivbva

Reaching and violating thermodynamic uncertainty bounds in information engines [article]

Govind Paneru, Sandipan Dutta, Tsvi Tlusty, Hyuk Kyu Pak
2020 arXiv   pre-print
Here, we examine these bounds, in experiment 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.  ... 
arXiv:1911.09835v3 fatcat:fuux4pjnundqrfovghptsrzvbe
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