Q13. Which of the following grammars are ambiguous? -> G1: S1 -> A B C A -> a A la G2: S2 A B C A -> a AI a Bb Bb B -> b BIE C -> a C I ε C -> a C I a G3 S1 -> A B C Α -> α Α Τε Bb Blb C -> a C I a G4: S2 -> A B C A -> a AI a B -> b B l b C -> a C I a

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Hi guys, I was told in the class, you can determine wether the CFG grammar is ambiguous by following the predict recursive decent parser's restriction. Please refer to the images.

for example G1: the First(aA) = {a}

                                   First(a) = {a}

 

 First(aA) intersect  First(a) != empty set, therefore G1 should be ambiguous, but this is wrong, can I get some explanation 

why using this restriction rule is not working on this problem, thanks

Q13. Which of the following grammars are ambiguous?
G1: S1 -> A B C
A -> a Ala
G2: S2 -> A B C
A -> a A la
-> b B | ε
B -> b B I b
B
с -> a CIE
с -> a C 1 a
G3: S1 -> A B C
Α -> α Α Τε
Bb Bl b
Ca C I a
G4: S2 -> A B C
A -> a AI a
Bb Bl b
C a Cla
Transcribed Image Text:Q13. Which of the following grammars are ambiguous? G1: S1 -> A B C A -> a Ala G2: S2 -> A B C A -> a A la -> b B | ε B -> b B I b B с -> a CIE с -> a C 1 a G3: S1 -> A B C Α -> α Α Τε Bb Bl b Ca C I a G4: S2 -> A B C A -> a AI a Bb Bl b C a Cla
The requirement that a predictive parser be able to distinguish between choices in a grammar rule
can be stated in terms of First sets, as follows. Given the grammar rule:
. | an
A → α₁ | 0₂ |
the First sets of any two choices must not have any tokens in common; that is,
First(a.)
First(α;) = Ø for all i ‡ j
(Ø denotes the empty set)
Transcribed Image Text:The requirement that a predictive parser be able to distinguish between choices in a grammar rule can be stated in terms of First sets, as follows. Given the grammar rule: . | an A → α₁ | 0₂ | the First sets of any two choices must not have any tokens in common; that is, First(a.) First(α;) = Ø for all i ‡ j (Ø denotes the empty set)
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