1. Lecture 15 Ambiguous Grammars Topics: Context Free Grammars Language generated by a grammar Proofs with L(G) Ambiguous grammars October 20, 2008 CSCE 355 Foundations of Computation

2. – 2 – CSCE 355 Fall 2008 Last Time: Adversarial game revisited Regular or not Grammars: definitions, derivations, parse trees, languages generated by grammars, L(G)New: Language generated by a grammar Proofs with L(G) Ambiguous grammarsHomework 1. 5.1.2 b,c 2. 5.1.7b* {a b c | i != j or j != k} 3. { w in {0,1}* | w is of the form xx} 4. …

3. – 3 – CSCE 355 Fall 2008 Review: Sentential forms: Leftmost Derivations, Parse Trees  E  E+E | E*E | (E) | id  α is a sentential form if

4. – 4 – CSCE 355 Fall 2008 References and example real grammars  http://en.wikipedia.org/wiki/Context-free\_grammar  http://en.wikipedia.org/wiki/Programming\_language  Grammar for Lisp expression ::= atom | list atom ::= number | symbol number ::= [+-]?['0'-'9']+ symbol ::= ['A'-'Z''a'-'z'].* list ::= '(' expression* ')'  http://marvin.cs.uidaho.edu/~heckendo/CS445S07/c- Grammar.pdf

5. – 5 – CSCE 355 Fall 2008 Language generated by a grammar L(G)

6. – 6 – CSCE 355 Fall 2008 L = {0 n 1 n | n >= 1}

7. – 7 – CSCE 355 Fall 2008 L = { w ε {0,1} * | w has same number of zeroes and ones }

8. – 8 – CSCE 355 Fall 2008 Proofs about L(G), the language generated by a grammar To prove a language L is the language generated by a grammar G we need to show that  L(G) is a subset of L  L is a subset of L(G)

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