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October 18

# October 18 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing October 18, 2005

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October 18, 2005 Agenda Last week Decidableproblems involving regular languages, finite automata, and CFG’s Oneundecidablelanguage EQ CFG This week Undecidablelanguages Techniques for showing a languages is not decidable
October 18, 2005 Announcements Quiz tomorrow Enumerators, definition of algorithm, decidable languages Recommended problems 4.6, 4.7, 4.22, 4.25, 4.26

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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 areboth 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 L(G) G is a CFG
October 18, 2005 Relationship of classes of languages Regular Context-free Decidable Turing- recognizable

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October 18, 2005 Group project 1 F DFA = {<A> | A is a DFA and L(A) is finite}
October 18, 2005 Group project 2 PRIME = { n | n is a prime number}

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October 18, 2005 Group project 3 CONN = {<G> | G is a connected graph}
October 18, 2005 Group project 4 L10 DFA = {D | D is a DFA that accepts every string w with | w| = 10}

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October 18, 2005 Group project 5 INT CFG = {<G 1 , G 2 , w> | G 1 and G 2 are CFG’s and w is accepted by both}
October 18, 2005 Group project 6 INTL CFG = L(G 1 G 2 ), whereG 1 and G 2 areCFG’s

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October 18, 2005 Turing machine acceptance problem Consider the following language A TM
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October 18 - CSCI 2670 Introduction to Theory of Computing...

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