by Robert Sedgewick · 2 Jan 1992
id vector (bottom). Kosaraju’s method is simple to explain and implement. To find the strong components of a graph, first run DFS on its reverse, computing the permutation of vertices defined by the postorder numbering. (This process constitutes a topological sort if the digraph is a DAG.) Then, run DFS again
by Ray Kurzweil · 14 Jul 2005 · 761pp · 231,902 words
Computing. The Computational Capacity of the Human Brain 113 Accelerating the Availability of Human-Level Personal Computing. Human Memory Capacity. The Limits of Computation 116 Reversible Computing. How Smart Is a Rock? The Limits of Nanocomputing. Setting a Date for the Singularity. Memory and Computational Efficiency: A Rock Versus a Human Brain
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a single chip. We will see chip technology move in this direction as a way of keeping power requirements and heat dissipation in check.47 Reversible Computing. Ultimately, organizing computation with massive parallel processing, as is done in the human brain, will not by itself be sufficient to keep energy levels and
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could be performed using only reversible logical operations.49 A decade later, Ed Fredkin and Tommaso Toffoli presented a comprehensive review of the idea of reversible computing.50 The fundamental concept is that if you keep all the intermediate results and then run the algorithm backward when you've finished your calculation
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and shows the expected reductions in energy input and heat dissipation.56 Fredkin's reversible logic gates answer a key challenge to the idea of reversible computing: that it would require a different style of programming. He argues that we can, in fact, construct normal logic and memory entirely from reversible logic
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we'll use the more conservative estimate.63 As discussed above, 1042 calculations per second could be achieved without producing significant heat. By fully deploying reversible computing techniques, using designs that generate low levels of errors, and allowing for reasonable amounts of energy dissipation, we should end up somewhere between 1042 and
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this amount of computing is estimated to be available for one thousand dollars by 2080. A more conservative but compelling design for a massively parallel, reversible computer is Eric Drexler's patented nanocomputer design, which is entirely mechanical.65 Computations are performed by manipulating nanoscale rods, which are effectively spring-loaded. After
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of using energy will be far greater, which will translate into lower energy requirements. Over the next several decades computing will make the transition to reversible computing. (See "The Limits of Computation" in chapter 3.) As I discussed, the primary energy need for computing with reversible logic gates is to correct occasional
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errors from quantum and thermal effects. As a result reversible computing has the potential to cut energy needs by as much as a factor of a billion, compared to nonreversible computing. Moreover, the logic gates and
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requirements such as energy usage, heat dissipation, internal communication speeds, the composition of matter in the solar system, and many other factors. These designs use reversible computing, but as I pointed out in chapter 3, we still need to consider the energy requirements for correcting errors and communicating results. In an analysis
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and per bit that these trends can continue to the point where nonbiological intelligence is trillions of trillions of times more powerful than biological intelligence. Reversible computing can reduce energy requirements, as well as heat dissipation, by many orders of magnitude. Even restricting computation to "cold" computers will achieve nonbiological computing platforms
by Chris Okasaki · 12 Apr 1998 · 230pp
by Max More and Natasha Vita-More · 4 Mar 2013 · 798pp · 240,182 words
a supercomputer beyond the wildest dreams of Cray, the size of a bacterium! What I didn’t do was pay any attention to “this crazy reversible computing stuff.” Until I did the heat dissipation calculations. The problem is that there really is a fundamental physical limit involved in computation, but it represents
by Robin Hanson · 31 Mar 2016 · 589pp · 147,053 words
now. In addition, it seems that gains will slow even further around 2035, when computer chips must be redesigned to enable reversible computing. (Reversible computing is discussed in Chapter 6, Entropy section.) With reversible computing, gains in making parts smaller, faster, and cheaper have to be split between supporting more operations and running each operation more
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Moore’s law growth rates for active devices (not memory) to slow down by about a factor of two after around 2035 when nearly adiabatic reversible computing becomes important. Historically, the price of energy and cooling has fallen much slower than has the price of computer hardware. It might seem that when
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the energy and cooling that computers need. However knowing the energy usage doesn’t necessarily say how much computing is going on. For example, with reversible computers one could mimic the energy and cooling of a single computing unit via four computing units that run at one-half speed, and thereby produce
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minerals can usually be substituted at modest cost, and there are many promising energy alternatives, such as solar cells, thorium nuclear reactors, or fusion reactors. Reversible computing can allow lots of computing even with rather limited energy. Thus there can be an important early em era where most growth comes from simple
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of each trained em worker, and em workers are less likely to congregate at firm locations, instead of at clan castles. In the limit, very reversible computers must be quantum computers. If quantum computing became feasible on large scales, then a few kinds of important calculations could be done faster and cheaper
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and Generational Differences Over 35 Years.” Journal for the Scientific Study of Religion 54(2): 363–379. Bennett, Charles. 1989. “Time/Space Trade-offs for Reversible Computation.” SIAM Journal of Computing 18(4): 766–776. Benson, Alan. 2014. “Rethinking the Two-Body Problem: The Segregation of Women Into Geographically Dispersed Occupations.” Demography
by Paul Davies · 31 Jan 2019 · 253pp · 83,473 words
heat is produced; there is no rise in entropy. I should stress that today’s computers are very far indeed from the theoretical possibility of reversible computation. But we are dealing here with deep issues of principle, and there is no known reason why the theoretical limit may not one day be
by Paul J. Nahin · 27 Oct 2012 · 229pp · 67,599 words
have the same number of 1s and 0s as do the inputs.6 10.4 THERMODYNAMICS OF LOGIC The reason for our interest in logically reversible computation becomes clear once we ask the following question: for the logically irreversible gates, where does the destroyed information “go”? It appears as heat! An implicit
by Chris Bernhardt · 19 Mar 2019 · 211pp · 57,618 words
a description of this cryptographic protocol. Chapter 6. The chapter starts with standard topics in computation: bits, gates, and logic. Then we briefly look at reversible computation and the ideas of Ed Fredkin. We show that both the Fredkin gate and the Toffoli gate are universal—you can build a complete computer
by Eliezer Yudkowsky · 11 Mar 2015 · 1,737pp · 491,616 words
am still thinking through the exact formalism myself. In thermodynamics, knowledge of logical truths does not count as negentropy; as would be expected, since a reversible computer can compute logical truths at arbitrarily low cost. All this that I have said is true of the logically omniscient: any lesser mind will necessarily
by Jaron Lanier · 6 May 2013 · 510pp · 120,048 words
heat, the randomness. You can create a local shield against entropy, but your neighbors will always pay for it.* *A rare experimental machine called a “reversible” computer never forgets, so that any computation can be run backward as well as forward. Such devices run cool! This is an example of how thermodynamics
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