By National Research Council, Division on Engineering and Physical Sciences, Computer Science and Telecommunications Board, Committee on the Fundamentals of Computer Science: Challenges and Opportunities
Desktop technology: Reflections at the box, Reflections from the sector presents a concise characterization of key principles that lie on the center of laptop technological know-how (CS) learn. The publication deals an outline of CS learn spotting the richness and variety of the sphere. It brings jointly dozen essays on varied points of CS study, their motivation and effects. by way of describing in available shape laptop science’s highbrow personality, and via conveying a feeling of its vibrancy via a collection of examples, the booklet goals to organize readers for what the long run may possibly carry and aid to motivate CS researchers in its production.
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On the technical side, there is much work to be done. Arthur C. ” Let’s create some more magic! EXPONENTIAL GROWTH, COMPUTABILITY, AND COMPLEXITY 37 COMPUTABILITY AND COMPLEXITY Jon Kleinberg, Cornell University, and Christos Papadimitriou, University of California, Berkeley The Quest for the Quintic Formula One of the great obsessions of Renaissance sages was the solution of polynomial equations: find an x that causes a certain polynomial to evaluate to 0. Today we all learn in school how to solve quadratic equations (polynomial equations of degree two, such as ax2 + bx + c = 0), even though many of us have to look up the formula every time (it’s x = 1 / 2 a−b ± b 2 − 4ac ).
So a demonstration that this single program eventually terminates must implicitly resolve this mathematical conjecture! Could detecting the termination of programs really be as hard as automating mathematics? This thought experiment raises the suggestion that we should perhaps be considering the problem from the other direction, trying to show that it is not possible to build a Universal Termination Detector. Another line of reasoning that might make us start considering such an impossibility result is, as suggested above, the self-referential nature of the universal machine U: U is a Turing machine that can simulate the behavior of any Turing machine.
Viewed from the safe distance of a few centuries, the story is clearly one about computation, and it contains many of the key ingredients that arise in later efforts to model computation: We take a computational process that we understand intuitively (solving an equation, in this case), formulate a precise model, and from the model derive some highly unexpected consequences about the computational power of the process. It is precisely this approach that we wish to apply to computation in general.