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Limits

Limits. How fast and how far?. Limits. P hysical limitations The physics of the real world impose constraints on speed. L imits imposed by algorithm performance The intrinsic nature of certain problems presents limitations on what can be computed. A lgorithm computability

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Limits

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  1. Limits How fast and how far?

  2. Limits • Physical limitations • The physics of the real world impose constraints on speed. • Limits imposed by algorithm performance • The intrinsic nature of certain problems presents limitations on what can be computed. • Algorithm computability • Some problems cannot be solved with computers.

  3. Physical Limitations • Lloyd, Seth. “Ultimate Limits to Computation”, Nature, August 31, 2000. • Analysis based on quantum theory • Theoretical limit: • ~1032 operations per sec. on 1016 bits • Current laptop: • speed: ~109 operations per sec. • memory: ~1010 bits • This is a very theoretical discussion from a physicist who bases his consideration on electronics, and the nuclei of solid matter. The speed of light, Plank’s reduced constant, Boltzmann’s constant, the constant of gravitation, quantum mechanics and thermodynamics all play a role. The consideration is the “ultimate laptop” - a 1 kg. machine. • Over 100 years to reach this limit at Moore’s Law rate.

  4. over 1 yr. for today’s supercomputers about 1 yr. for Lloyd’s ultimate computer Algorithm Performance 2 chars.26 sec. 3 chars40 sec. 4 chars174 min. 5 chars731 hrs. (est.) 6 chars21 yrs. 8 chars1.4M yrs. 15 chars1.0 x 1023 yrs. Note that 731 hrs == 30 days. Assuming that supercomputers are about 100,000 times faster than my laptop, they still require about 14 years to crack an 8-char password with this algorithm. Some algorithms are not feasible because they take too long to execute. Password cracking by testing all possibilities:

  5. Algorithm Performance • What kind of algorithms are infeasible? • Algorithms that consider all possible combinations or permutations for a significant number of values. • Examples: • Play chess by analyzing all possible boards throughout all possible games. • Play cards by considering all possible hands throughout all possible games. • Generate all possible DNA sequences to discover some new drug. • Guess passwords by generating all possible passwords of length 20 or smaller.

  6. HaltChecker any program if (HaltChecker says this program halts) then while (true) { //do something; } else Halt; doesn’t halt halts Computability Does this program halt or not? • Consider the "Halting Problem". Can a program tell me if a program will ever halt? • Assume that we could write a program that could analyze any program code and tell us whether or not the program halts (stops).

  7. The Metaphysical Alan Turing Are computers intelligent? Turing Test (1950) Computer or person in hidden room. Which is it?

  8. Human Behavior Intelligent Behavior More about the Turing Test Criticisms: Sometimes humans are not intelligent. Some intelligent behavior is not human behavior. Unintelligent human behavior Intelligent non-human behavior Turing test What about lying and bluffing? Turing predicts: test passed by 2000 Loebner Prize: no pass by 2009 CAPTCHA -- a reverse Turing test?

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