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**Unformatted text preview: **1.1 pressure… – solved via largescale simulation with lots of math dictating behavior of “cells” based on adjacent cells. turn crank, see what happens.
– as moments increase, accuracy decreases Problems
Problems
Computational Complexity Running time of an algorithm is a function of input size
Some functions grow faster than others
WAY faster
For some problems, we have efficient algorithms (functions that grow moderately). For others, the best known algorithms have running times that grow so fast that they are impractical, and always will be.
Some problems provably cannot be solved with a faster algorithm Spreadsheet of running times
Spreadsheet of running times and execution times at 1 billion steps/sec exercise: create columns for n, n2, n3, 2n, 3n, n!
compute running times for n=10,20,… UNCOMPUTABLE problems
UNCOMPUTABLE problems previous category were problems that could be solved, but known methods took too long this category are problems for which we know: THEY CANNOT BE SOLVED BY ANY ALGORITHM WHATSOEVER History
History Hilbert’s “program” Gödel’s undecidability theorem Turing’s halting problem Natu...

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