1. 1 Efficient Parsing and Ambiguity

2. Ambiguity A grammar G is ambiguous if – There exists w ∊ L(G) such that – There are two parse trees for w Allows multiple interpretations of meaning of w Removing ambiguity: not always possible Inherently Ambiguous: – L is inherently ambiguous if – For all grammars G such that L(G) = L – G is ambiguous s-grammars are always unambiguous 2

3. 3 Simple Grammar (s-grammar) G = (V,T,S,P) is a simple grammar if All rules in G are of the form A -> ax – A  V – a  T – x  V* For each A  V and each a  T there is at most one A -> ax rule.

4. 4 Parsing Given a grammar G and string w find derivation of w in G (if it exists.) Brute force parsing – Go through all possibilities of a left-most derivation until the derivation of w is found.

5. Example G = ({S,E,A,I}, {a,b}, P, S), where P contains S -> ES | E E -> aIb | A A -> aA | bA | a | b I -> b | Is aabb  L(G)? 5

6. 6 Creating Parse Tree-Backtracking S ES ab I Stuck, backtrack one step

7. 7 Creating Parse Tree-Backtracking S ES A Stuck, backtrack one step aA aA bA bA

8. 8 Creating Parse Tree-Backtracking S ES A Stuck, backtrack one step aA aA bA b ES A No other choices, backtrack another step

9. 9 Creating Parse Tree-Backtracking S ES A Stuck, backtrack one step aA aA bA b No other choices, backtrack another step E A

10. 10 Creating Parse Tree-Backtracking S Stuck, backtrack one step E ab I

11. 11 Creating Parse Tree-Backtracking S E A aA aA bA b

12. 12 Efficient Parsing Backtracking – Runtime is exponential in length of string Can improve to polynomial time (with degree 3) if in special form (Normal Forms) Can improve to linear time with simple grammar.