September 14

September 14 - CSCI 2670 Introduction to Theory of...

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CSCI 2670 Introduction to Theory of Computing September 14, 2005
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Agenda •Yester day –Pump ing lemma •Today – Introduce context-free grammars – Formally define CFG’s – Begin designing CFG’s • Tomorrow – More on designing CFG’s – Chomsky normal form
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Announcement • Quiz tomorrow – Regular expressions –Pump ing lemma
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Context-free grammars • The shortcoming of finite automata is that each state has very limited meaning – You have no memory of where you’ve been – only knowledge of where you are • Context-free grammars are a more powerful method of describing languages –Examp le : {0 n 1 n | n 0} is a CFG
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Example CFG • Context-free grammars use substitution to maintain knowledge S (S) S SS S () • All possible legal parenthesis pairings can be expressed by consecutive applications of these rules • Is this a regular language?
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Example S (S) | SS | () • (()())(()) •S SS (S)(S) (SS)(()) (()())(()) • This sequence of substitutions is called a derivation
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Parse tree S (S) | SS | () S S S S S () () () S ) ( S ()
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September 14 - CSCI 2670 Introduction to Theory of...

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