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Unformatted text preview: COMP272: Theory of Computation Unit 1: Motivation and Overview Theory of Computation Mathematical study of computing machines, their fundamental capabilities and their limitations. Q1 : What problems are solvable, in PRACTICE, by computer and what problems are not? Complexity theory (NPhardness) answers these ques tions (see COMP271). Q2 : What problems are solvable, in PRINCIPLE, by computers and what problems are not? Computability theory answers these questions (see COMP 272). 1 Motivation Example 1 A compiler can detect syntax errors in the pro grams you write. Can we write a compiler that will also detect “infinite loops”? No! The problem of whether a program halts under all inputs is an UNSOLVABLE problem. We will see why in this course. Example 2 Given any two programs, determine whether they compute the same function. This problem is also UNSOLVABLE. 2 Motivation What is an unsolvable problem? A problem for which there is no algorithm?...
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This note was uploaded on 09/22/2011 for the course COMP 272 taught by Professor Prof.tai during the Spring '10 term at HKUST.
 Spring '10
 Prof.Tai

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