Yves Lecerf, Machines de Turing reversibles. R'ecursive insolubilit'e en nfflN de l"equation u = ` n ou ` est un "isomorphism de codes". Comptes Rendus de L'Academie Francaise des Sciences, Vol. 257, 2597-2600 (1963).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....f(x) i. End Fourier twice Note that the (deterministic) computation of (x; f(x) from x in time T f (n) in step 2 can always be made reversible (and hence unitary) at the cost of only a constant factor in the number of computation steps. This is due to a result obtained independently by Lecerf ([L]) and Bennett ( B] Suppose f is 1 to 1. Then after each performance of Fourier twice, all the possible configurations j(y; f(x) i in the superposition will be distinct, and their amplitudes will therfore all be 2 Gamman , up to phase. Their probabilities will therefore each be 2 Gamma2n ....

Yves Lecerf, Machines de Turing reversibles. R'ecursive insolubilit'e en nfflN de l"equation u = ` n ou ` est un "isomorphism de codes". Comptes Rendus de L'Academie Francaise des Sciences, Vol. 257, 2597-2600 (1963).

.... interest in the notion of reversibility was sparked by the prospect of quantum computers, whose observationfree computational steps are intrinsically reversible [De85, Sh94, Br95] Early strategies to make a Turing machine reversible were terribly wasteful in terms of space: Lecerf s method [Le63], rediscovered by Bennett [Be73] required space T to simulate a T (n) time S(n) space machine reversibly in time O(T ) Bennett then greatly improved on this by reducing the space to O(S log T ) at the expense of an increase in time to T 1 ffl [Be89] Levine and Sherman refined the analysis of ....

.... the same time and space bounds if the time is neither linear nor exponential in the space [FrAm97] It is interesting to compare our result with the equivalence of deterministic time and reversible time, which is simply shown by storing the whole computational history on a separate write only tape [Le63, Be89]. It is remarkable that this is the very same construction which proves the equivalence of nondeterministic time and symmetric 5 time [LePa82] This duality of the pairs nondeterminism versus symmetry and determinism versus reversibility is tied to the question of whether transitions can be ....

Y. Lecerf, Machines de Turing r'eversibles. Insolubilit'e r'ecursive en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes", Comptes Rendus 257 (1963), pp. 2597--2600.

....Turing machines, RAMs, or circuits, allow logically irreversible operations. To reflect physical reality they must be replaced by completely reversible computational models, for example by universal simulation. Simulation of irreversible Turing machines by reversible ones goes back to Lecerf [12] and Bennett [1] The original methods required an amount of memory proportional to the amount of computation time, since the step by step reproducibility of the history was achieved by remembering it during most of the computation. It was recognized later that keeping the configuration only of ....

Y. Lecerf, Machines de Turing r'eversibles. R'ecursive insolubilit'e en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes", Comptes Rendus, 257(1963), 2597-2600.

.... circuit technology actually inefficiently generates around 10 8 bits of physical entropy per bit of computational state that is discarded However, irreversible operations and the accompanying production of entropy are actually not required for any computation, as was shown by Lecerf 63 [11] and independently by Bennett 73 [1] Unfortunately, it seems that computations that produce no entropy may, at least in some cases, require either more computational space or more time (by an unboundedly large factor) than their counterparts in (nonphysical) models in which unwanted information ....

Y. Lecerf. Machines de Turing r'eversibles. Insolubilit'e r'ecursive en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes". Comptes Rendus hebdomadaires des seances de l'academie des sciences, 257:2597--2600, 1963.

....used to design computational procedures containing irreversible operations. To perform the intended computations without energy dissipation the related computation procedures need to become completely reversible. Fortunately, all irreversible computations can be simulated in a reversible manner, [11, 1]. All known reversible simulations do not change the computation time significantly, but do require considerable amounts of auxiliary memory space. In this type of simulation one needs to save on space; time is already almost optimal. The reversible simulation in [1] of T steps of an irreversible ....

Y. Lecerf, Machines de Turing r'eversibles. R'ecursive insolubilit'e en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes", Comptes Rendus, 257(1963), 2597-2600.

....used to design computational procedures containing irreversible operations. To perform the intended computations without energy dissipation the related computation procedures need to become completely reversible. Fortunately, all irreversible computations can be simulated in a reversible manner [Lecerf, 1963, Bennett, 1973] All known reversible simulations do not change the computation time significantly, but do require considerable amounts of auxiliary memory space. In this type of simulation one needs to save on space; time is already almost optimal. Consider the standard model of Turing machine. ....

Y. Lecerf, Machines de Turing r'eversibles. R'ecursive insolubilit'e en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes", Comptes Rendus, 257(1963), 2597-2600.

....relevance for adiabatic computing. Reversible computation. Next, we consider irreversibility issues related to reversible computations themselves. Such computations may be directly programmed on a reversible computer or may be a reversible simulation of an irreversible computation. References [Lecerf, 1963, Bennett, 1973] show independently that all computations can be performed logically reversibly at the cost of eventually filling up the memory with unwanted garbage information. This means that reversible computers with bounded memories require in the long run irreversible bit operations, for ....

....used to design computational procedures containing irreversible operations. To perform the intended computations without energy dissipation the related computation procedures need to become completely reversible. Fortunately, all irreversible computations can be simulated in a reversible manner, [Lecerf, 1963, Bennett, 1973] All known reversible simulations of irreversible computations use little overhead in time but large amounts of additional space. Commonly, polynomial time computations are considered as the practically relevant ones. Reversible simulation will not change such a time bound ....

Y. Lecerf, Machines de Turing r'eversibles. R'ecursive insolubilit 'e en n 2 N de l"equation u = ` n , o`u ` est un "isomorphisme de codes", Comptes Rendus, 257(1963), 2597-2600.

....f(x) i. End Fourier twice Note that the (deterministic) computation of (x; f(x) from x in time T f (n) in step 2 can always be made reversible (and hence unitary) at the cost of only a constant factor in the number of computation steps. This is due to a result obtained independently by Lecerf ([Lec]) and Bennett ( Ben] Suppose f is 1 to 1. Then after each performance of Fourier twice, all the possible configurations j(y; f(x) i in the superposition will be distinct, and their amplitudes will therefore all be 2 Gamman , up to phase. Their probabilities will therefore each be 2 ....

Yves Lecerf, Machines de Turing reversibles. R'ecursive insolubilit'e en nfflN de l"equation u = ` n ou ` est un "isomorphism de codes". Comptes Rendus de L'Academie Francaise des Sciences, Vol. 257, 2597-2600 (1963).

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