## Time and Space Bounds for Reversible Simulation (2001)

Citations: | 18 - 1 self |

### BibTeX

@MISC{Buhrman01timeand,

author = {Harry Buhrman and John Tromp},

title = {Time and Space Bounds for Reversible Simulation},

year = {2001}

}

### OpenURL

### Abstract

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. The boundary values are the exponential time with hardly any extra space required by the Lange-McKenzie-Tapp method and the (log 3)th power time with square space required by the Bennett method. We also give the first general lower bound on the extra storage space required by general reversible simulation. This lower bound is optimal in that it is achieved by some reversible simulations. 1 Introduction Computer power has roughly doubled every 18 months for the last half-century (Moore's law). This increase in power is due primarily to the continuing miniaturization of the elements of which computers are made, resulting in more and more ele...

### Citations

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Quantum Computation and Quantum Information
- Nielsen, Chuang
- 2000
(Show Context)
Citation Context ...towards implementation of reversible computing on silicon see MIT’s Pendulum Project and linked web pages (http://www.ai.mit.edu/∼cvieri/reversible.html). On a more futuristic note, quantum computing =-=[15, 14]-=- is reversible. Despite its importance, theoretical advances in reversible computing are scarce and far between; all serious ones are listed in the references. Related Work: Currently, almost no algor... |

931 | Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer - Shor - 1994 |

486 |
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Citation Context ...l it has been argued many times that this effect gains in significance to the extent that efficient operation (or operation at all) of future computers requires them to be reversible (for example, in =-=[8, 1, 2, 4, 7, 11, 5]-=-). The mismatch of computing organization and reality will express itself in friction: computers will dissipate a lot of heat unless their mode of operation becomes reversible, possibly quantum mechan... |

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(Show Context)
Citation Context ...efficiency of general reversible simulation of irreversible computation. Suppose the irreversible computation to be simulated uses T time and S space. A first efficient method was proposed by Bennett =-=[3]-=-, but it is space hungry and uses 1 time ST log 3 and space S log T. If T is maximal, that is, exponential in S, then the space use is S 2 . This method can be modelled by a reversible pebble game. Re... |

90 |
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Citation Context ...l it has been argued many times that this effect gains in significance to the extent that efficient operation (or operation at all) of future computers requires them to be reversible (for example, in =-=[8, 1, 2, 4, 7, 11, 5]-=-). The mismatch of computing organization and reality will express itself in friction: computers will dissipate a lot of heat unless their mode of operation becomes reversible, possibly quantum mechan... |

34 | Reversibility and adiabatic computation: Trading time and space for energy
- Li, Vitanyi
- 1996
(Show Context)
Citation Context ...l it has been argued many times that this effect gains in significance to the extent that efficient operation (or operation at all) of future computers requires them to be reversible (for example, in =-=[8, 1, 2, 4, 7, 11, 5]-=-). The mismatch of computing organization and reality will express itself in friction: computers will dissipate a lot of heat unless their mode of operation becomes reversible, possibly quantum mechan... |

29 |
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Citation Context ...tion parameters this method can be tweaked to run in ST 1+ǫ time for every ǫ > 0 at the cost of introducing a multiplicative constant depending on 1/ǫ. The complexity analysis of [3] was completed in =-=[10]-=-. 2steps are intervals of the simulated computation that are bridged by using the exponential simulation method. (It should be noted that embedding Bennett’s pebbling game in the exponential method g... |

28 | Reversible space equals deterministic space
- Lange, McKenzie, et al.
- 2000
(Show Context)
Citation Context ... modelled by a reversible pebble game. Reference [12] demonstrated that Bennett’s method is optimal for reversible pebble games and that simulation space can be traded off against limited erasing. In =-=[9]-=- it was shown that using a method by Sipser [16] one can reversibly simulate using only O(S) extra space but at the cost of using exponential time. Results: Previous results seem to suggest that a rev... |

11 | Reversible simulation of irreversible computation
- LI, VITANYI
- 1996
(Show Context)
Citation Context ... is space hungry and uses 1 time ST log 3 and space S log T. If T is maximal, that is, exponential in S, then the space use is S 2 . This method can be modelled by a reversible pebble game. Reference =-=[12]-=- demonstrated that Bennett’s method is optimal for reversible pebble games and that simulation space can be traded off against limited erasing. In [9] it was shown that using a method by Sipser [16] o... |

10 | Reversibility in optimally scalable computer architectures
- Frank, Knight, et al.
- 1997
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Citation Context |

10 | A 1-tape 2-symbol reversible Turing machine - Morita, Shirasaki, et al. - 1989 |

9 | Separations of reversible and irreversible space-time complexity classes - Frank, Ammer |

7 |
Halting space-bounded computation, Theoret
- Sipser
(Show Context)
Citation Context ...e [12] demonstrated that Bennett’s method is optimal for reversible pebble games and that simulation space can be traded off against limited erasing. In [9] it was shown that using a method by Sipser =-=[16]-=- one can reversibly simulate using only O(S) extra space but at the cost of using exponential time. Results: Previous results seem to suggest that a reversible simulation is stuck with either quadrati... |