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class2 - Main Question cs3102: Theory of Computation Class...

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cs3102: Theory of Computation Class 2: Problems and Finite Automata Spring 2010 University of Virginia David Evans Main Question What problems can a particular type of machine solve? What is a problem ? What is a machine ? What does it mean for a machine to solve a problem ? Problems Defining Problem A problem is defined by: A description of a set of inputs A description of a set of outputs and the property an output must have A machine solves a problem if for every input it eventually produces a satisfactory output . Finite Problems Problems with a finite number of possible inputs Uninteresting: can be solved by a lookup machine All theoretically interesting problems have infinitely many possible inputs. In the real world lots of interesting problems have finite number of inputs: chess (0 or 1 inputs?), Internet search with bounded-length query, human genome assembly, etc. Outputs How many possible outputs do you need for a problem to be interesting? 2 – “Yes” or “No”
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class2 - Main Question cs3102: Theory of Computation Class...

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