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Short trick method to find First of any grammar- Compiler Design

Short trick method to find First of any grammar- Compiler Design

https://www.gyanodhan.com/video/7B2.%20GATE%20CSEIT/Compiler%20Design/274.%20Short%20trick%20method%20to%20find%20First%20of%20any%20grammar-%20Compiler%20Design.mp4

Short Trick to Find FIRST of Any Grammar (Compiler Design)

In Compiler Design, computing the FIRST set is essential for parsing table construction in LL(1) parsers. Here’s a short trick method with rules to find the FIRST set quickly and accurately.


What is FIRST?

The FIRST(X) set is the set of terminals that begin the strings derivable from symbol X (where X can be a terminal, non-terminal, or ε).


Short Trick Rules to Find FIRST

Rule 1: For terminals

If X is a terminal, then:

bash
FIRST(X) = { X }

Rule 2: For ε (epsilon)

bash
FIRST(ε) = { ε }

Rule 3: For non-terminals (A → α1 α2 α3…)

To find FIRST(A):


Shortcut Flow (for A → α):

α is… FIRST(A) contains…
Terminal a a
ε ε
Non-terminal B FIRST(B), and if ε ∈ FIRST(B), check next symbol
Sequence B C D... FIRST(B), and if ε ∈ FIRST(B), add FIRST(C), and so on

Example 1:

less
SA B
Aa | ε
Bb

Step-by-step:


Example 2:

css
S → A B
A → ε
B → ε

Then:


Example 3:

less
SA b
Ac | ε

Tips & Tricks Recap:

Go left to right in RHS
If you see a terminal, add it and stop
If you see ε, skip and check next
If all symbols can derive ε, then add ε to FIRST
Don’t forget to union all FIRSTs if multiple rules exist


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Short trick method to find First of any grammar- Compiler Design

LECTURE NOTES ON COMPILER DESIGN

compiler design lecture notes