Lectures 15-24 - Lectures 15-18 by Jewelle Diaz Lecture 15...

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Lectures 15-18 by Jewelle Diaz Lecture 15: The Limits of Computing and Artificial Intelligence Can computers solve every problem? o Theoretical Computer Science (or TCS) - Objectives: to make the analysis of these definitions and to draw logical conclusions about computers from them. Question 1 : How many problems concerning arithmetic are there? - The number of all problems concerning arithmetic is finite, but it is not. Is there a value of X which makes the equation X + 1 = 2 true? Is there a value of X which makes the equation X + 1 = 3 true? Is there a value of X which makes the equation X + 1 = 4 true? Is there a value of X which makes the equation X + 1 = 5 true? - Therefore, a single computer program can handle all problems in this class. Question 2: Can a single computer program be written to solve all problems concerning arithmetic? - R eview Alan Turing’s work (lecture 5) - Using his model of computing called Turing Machines Question 3: Which collection of problems concerning arithmetic is larger: the collection of solvable problems or unsolvable problems? - Using Set Theory (mathematical discipline that specifies how such a comparison can be done) - The notion of the Turing Machine o The vast space of problems consists mostly of those that cannot be decided using computers. How much time, how much memory... o Important to know how much “resources” the “best” computer would require to retur n a solution to a given problem. o To deal with the issue of resources (e.g. time and memory): - TCS (developed methods to estimate the “complexity” of a decidable problem and captures the amount of time and memory required - Result: classifies decidable problems as feasible Question 4: Which collection of problems concerning arithmetic is larger: the collection of feasible or non-feasible problems?
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- Disappointing answer: the collection of non-feasible problems is much larger than the collection of feasible problems - Conclude: theoretical point of view, most problems are undecidable and of those which are decidable, most are too complex to be handled by computers. Is all news bad? o Computers (most complex and versatile problem solving tools) o The message is not all that bad: still infinitely many problems that can be efficiently solved with computers - We do reason and do make plans in our everyday activities - We overcome the “computational complexity” of these tasks by incorporating a number of techniques (”tricks”) based on experience and intuition such as reasoning by analogy and default reasoning - We have learnt how to make “good enough” decisions based on incomplete and, sometimes, inconsistent knowledge - It may turn out that our model of computation based on Turing machines is inadequate (although this is not likely) The quest for machine intelligence o 1560, a person watching the Clockwork Prayer in action (the mechanical monk in Lectures 3 and 11) o 60+ years earlier: Leonardo Da Vinci o Robot knight o Possible to advance the designs to create a machine capable of other functions: - speech understanding - reasoning - planning -
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