Ambiguity in CFL Parsing

The String:

The Grammar:

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The String:

The Grammar:

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HW Due Sept 29: Are Context Free Grammars sufficent to capture the usual precedence rules for $\QTR{Large}{+}$ and $\QTR{Large}{\ast }$ without ambiguity?

In particular, means and not , which does require " $\QTR{Large}{()}$ ".

Hint: Try by introducing two new nonterminals, $\QTR{Large}{M}$ and $\QTR{Large}{A}$ ,to capture the precedence rules for multiplication and addition. Now modify the second grammar above. $\QTR{Large}{\ }$