Compiler Design/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English

Compiler Design/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English

 How to Quickly Check if a Grammar is LL(1) – Compiler Design Short Trick

LL(1) Grammar is a type of context-free grammar (CFG) used in top-down parsing. To determine whether a given grammar is LL(1), follow this simple short trick based on First and Follow sets.

 Quick Steps to Check if a Grammar is LL(1)

Step 1: Compute First Sets for Each Production

1. FIRST(A) = Set of terminals that appear at the beginning of the derivations of A.
2. If A → ε, then include FOLLOW(A) in FIRST(A).

Step 2: Compute Follow Sets for Each Non-Terminal

1. FOLLOW(A) = Set of terminals that can appear immediately after A in some derivation.
2. If the start symbol is S, then $ (End-of-input marker) is in FOLLOW(S).

Step 3: Apply the LL(1) Condition

For the grammar to be LL(1), it must satisfy the following condition for every non-terminal A:

For two productions A → α | β:
FIRST(α) ∩ FIRST(β) = ∅ (No common terminal symbols)
 If ε ∈ FIRST(α), then FIRST(β) ∩ FOLLOW(A) = ∅

If the condition holds for all non-terminals, the grammar is LL(1).

 Short Trick to Check LL(1) Grammar

Step 1: Compute FIRST & FOLLOW sets.
Step 2: Check if any FIRST sets overlap for a single non-terminal.
Step 3: If a production has ε, ensure FOLLOW(A) and FIRST(A) are disjoint.
Step 4: If all conditions hold, it is LL(1); otherwise, it is NOT LL(1).

 Example to Check LL(1)

Example Grammar:

Step 1: Compute FIRST Sets

• FIRST(S) = {a, b}
• FIRST(A) = {a, ε}
• FIRST(B) = {b}

Step 2: Compute FOLLOW Sets

• FOLLOW(S) = { $ }
• FOLLOW(A) = { $ }
• FOLLOW(B) = { $ }

Step 3: Check LL(1) Condition

• FIRST(A) and FIRST(B) do not overlap
• A → ε, but FIRST(A) ∩ FOLLOW(A) = ∅

 Since all conditions are satisfied, this grammar is LL(1).

 When is a Grammar NOT LL(1)?

 If FIRST(α) ∩ FIRST(β) ≠ ∅, the grammar is not LL(1).
 If ε is in FIRST(A) but FIRST(A) ∩ FOLLOW(A) ≠ ∅, the grammar is not LL(1).

Would you like a practice problem or more examples?

Compiler Design/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English

COMPILER DESIGN (R15A0512)

Here’s a clear and shortcut method (trick) to check whether a given grammar is LL(1) or not, useful for Compiler Design topics in GATE, university exams, and interviews.

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LL(1) Grammar in Compiler Design – Shortcut to Check

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What is LL(1) Grammar?

• L = Scan input Left to right

• L = Produce Leftmost derivation

• 1 = Use 1 token lookahead

LL(1) grammars are top-down parsable with a single lookahead symbol using a predictive parser (like recursive descent).

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Shortcut to Check LL(1) Grammar

To check if a grammar is LL(1), ensure the following:

Condition 1: FIRST/FIRST Conflict

• For every non-terminal with multiple productions,
  → FIRST sets of the alternatives must not intersect.

Check:
If A → α | β
Then: FIRST(α) ∩ FIRST(β) = ∅
→ No common terminals

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Condition 2: FIRST/FOLLOW Conflict (when ε is involved)

• If any production derives ε,
  Then: FIRST(ε-production) ∩ FOLLOW(non-terminal) = ∅

Check:
If A → α | ε,
Then: FIRST(α) ∩ FOLLOW(A) = ∅
→ No overlap between FIRST and FOLLOW

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Step-by-Step Shortcut Method (With Trick)

Step 1: Compute FIRST set for all alternatives

Look at all RHSs of each non-terminal.

Step 2: Check for FIRST/FIRST Conflict

• If same terminal appears in multiple FIRST sets → Not LL(1)

Step 3: Check for ε in FIRST

• If yes, then do:

  • Compute FOLLOW of that non-terminal

  • Check for FIRST/FOLLOW Conflict

Step 4: If no conflicts, grammar is LL(1)

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Example 1: LL(1) Grammar

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S → aA | bB
A → c
B → d


FIRST(S) = {a, b} → disjoint →
No ε → no need to check FOLLOW
LL(1)

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Example 2: Not LL(1) Grammar

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S → aA | aB
A → c
B → d


FIRST(aA) = a, FIRST(aB) = a →
FIRST sets intersect → Not LL(1)
Not LL(1)

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Important Note:

LL(1) If…	Not LL(1) If…
FIRST sets of RHSs are disjoint	FIRST sets overlap
ε in FIRST → check FOLLOW conflict too	FIRST(ε) ∩ FOLLOW(non-terminal) ≠ ∅
One parsing table entry per [Non-Terminal, Terminal]	Multiple entries in parsing table

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Tips to Remember (Exam Trick)

• Same starting symbol in two productions? → Usually NOT LL(1)

• Epsilon involved? → Check FOLLOW

• Intersecting FIRST sets? →

• Parsing Table Conflicts? → Not LL(1)

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Would you like:

• A solved parsing table example?

• A PDF cheat sheet for FIRST/FOLLOW?

• Practice grammar questions for LL(1)?

Let me know!

Compiler Design/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English