{"id":2808,"date":"2025-06-06T14:05:28","date_gmt":"2025-06-06T14:05:28","guid":{"rendered":"https:\/\/diznr.com\/?p=2808"},"modified":"2025-06-06T14:05:28","modified_gmt":"2025-06-06T14:05:28","slug":"compiler-design-short-trick-to-find-the-given-grammar-is-ll1-or-not-in-compiler-design-english-in","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/compiler-design-short-trick-to-find-the-given-grammar-is-ll1-or-not-in-compiler-design-english-in\/","title":{"rendered":"Compiler Design\/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English"},"content":{"rendered":"

Compiler Design\/ Short trick to find the given grammar is (LL1) or not in Compiler Design In English<\/p>\n

[fvplayer id=”123″]<\/p>\n

\u00a0How to Quickly Check if a Grammar is LL(1) \u2013 Compiler Design Short Trick<\/strong><\/h3>\n

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

\u00a0Quick Steps to Check if a Grammar is LL(1)<\/strong><\/h3>\n

Step 1: Compute First Sets for Each Production<\/strong><\/h3>\n
    \n
  1. FIRST(A)<\/strong> = Set of terminals that appear at the beginning of the derivations of A.<\/li>\n
  2. If A \u2192 \u03b5<\/strong>, then include FOLLOW(A)<\/strong> in FIRST(A)<\/strong>.<\/li>\n<\/ol>\n

    Step 2: Compute Follow Sets for Each Non-Terminal<\/strong><\/h3>\n
      \n
    1. FOLLOW(A)<\/strong> = Set of terminals that can appear immediately after<\/strong> A in some derivation.<\/li>\n
    2. If the start symbol is S<\/strong>, then $ (End-of-input marker) is in FOLLOW(S)<\/strong>.<\/li>\n<\/ol>\n

      Step 3: Apply the LL(1) Condition<\/strong><\/h3>\n

      For the grammar to be LL(1), it must satisfy the following condition for every non-terminal A<\/strong>:<\/p>\n

      For two productions A \u2192 \u03b1 | \u03b2:<\/strong>
      FIRST(\u03b1) \u2229 FIRST(\u03b2) = \u2205<\/strong> (No common terminal symbols)
      \u00a0If \u03b5 \u2208 FIRST(\u03b1)<\/strong>, then FIRST(\u03b2) \u2229 FOLLOW(A) = \u2205<\/strong><\/p>\n

      If the condition holds for all non-terminals, the grammar is LL(1).<\/strong><\/p>\n

      \u00a0Short Trick to Check LL(1) Grammar<\/strong><\/h3>\n

      Step 1:<\/strong> Compute FIRST & FOLLOW<\/strong> sets.
      Step 2:<\/strong> Check if any FIRST sets overlap<\/strong> for a single non-terminal.
      Step 3:<\/strong> If a production has \u03b5<\/strong>, ensure FOLLOW(A) and FIRST(A) are disjoint<\/strong>.
      Step 4:<\/strong> If all conditions hold, it is LL(1); otherwise, it is NOT LL(1).<\/strong><\/p>\n

      \u00a0Example to Check LL(1)<\/strong><\/h3>\n

      Example Grammar:<\/strong><\/p>\n

      \n
      S<\/span> \u2192 aA<\/span> | bB<\/span>
      \nA<\/span> \u2192 a<\/span> | \u03b5
      \nB<\/span> \u2192 b<\/span>
      \n<\/code><\/div>\n<\/div>\n

      Step 1: Compute FIRST Sets<\/strong><\/h3>\n