Prove whether the grammar below is LL(1) or not: S-aSbS| bSaS |ɛ
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
Problem 1PE
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Step 1
To check the grammar whether it is LL(1) or not. you need to know first and follow of the grammar. There are some rules which are used to find first and follow.
Rules to find First of the grammar
- For the production rule X->∈, First(X)={∈}
- For the any terminal symbol a, the First(a)={a}
- For the production rule X->Y1Y2Y3
Calculating the First(X)
- If ∈∉First(Y1), then the First(X)=First(Y1)
- If ∈ ∈ First(Y1), then the First(X)={First(Y1) – ∈}∪First(Y2Y3)
Calculating the first (Y2Y3)
- If ∈ ∉ First(Y2), then the First(Y2Y3)=First(Y2)
- If ∈ ∈ First(Y2), then the First(Y2Y3)={First(Y2) –∈}∪First(Y3)
Rules to find Follow of the grammar:-
- For the start symbol S, place the $ in the Follow(S).
- For the any production rule A->αB, then the Follow(B)=Follow(A)
For the any production rule A->αBβ,
- If the ∈ ∉ First(β), then the Follow(B)=First(β)
- If ∈ ∈ First(β), then the Follow(B)={First(β)– ∈}∪Follow(A)
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