October 19

October 19 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing October 19, 2005
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October 19, 2005 Agenda Yesterday A little more on decidable languages Countable sets Today More on countable sets Diagonalization An undecidable language
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Languages we know are decidable Language Input A DFA <D,w>, D is a DFA, w is a string A NFA <N,w>, N is an NFA, w is a string A REX <R,w>, R is an RE, w is a string E DFA <D>, D is a DFA and L(D) =  EQ DFA L(R) <C,D>, C and D are both DFA’s and L(C) =  L(D) R is a regular expression A CFG <G,w>, G is a CFG, w is a string E CFG <G>, G is a CFG
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October 19, 2005 Comparing the size of infinite sets Given two infinite sets A and B, is there any way  of determining if |A|=|B| or if |A|>|B|? Yes! Functional correspondence can show two infinite  sets have the same number of elements Diagonalization can show one infinite set has  more elements than another
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October 19 - CSCI 2670 Introduction to Theory of Computing...

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