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October 12 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing October 12, 2005
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October 12, 2005 2 Agenda • Yesterday – Enumerators • Equivalence of enumerators and TM’s – Definition of algorithm • Church-Turing thesis – Decidable languages • Today – More on DFA’s and decidability • Tomorrow – CFG’s and decidability
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October 12, 2005 3 Decidable languages A language is decidable if some Turing machine decides it Every string in Σ * is either accepted or rejected Not all languages can be decided by a Turing machine
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October 12, 2005 4 Some decidable languages • A DFA = {<B,w> | B is a DFA that accepts input string w} • A NFA = {<B,w> | B is an NFA that accepts input string w} • A REX = {<R,w> | R is a regular expression that generates string w}
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October 12, 2005 5 Emptiness testing problem Consider the language E DFA = {<A> | A is a DFA and L(A) = } Theorem: E DFA is a decidable language Proof: Consider the following TM, T T = “On input string <A>, where A is a DFA 1. Mark the start state 2. Repeat until no new states get marked ¾ Mark any state that has a transition coming
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