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Define parse tree. Why parse tree construction is only possible for CFG ?

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By Dipali Umre

A parse tree is like a family tree for a sentence in a programming language or any other formal language. It shows how the sentence is constructed according to the rules of a Context-Free Grammar (CFG). Here’s why parse tree construction is only possible for CFG:

  1. Clear Structure: A parse tree follows a specific structure where each node represents a part of the sentence, either a terminal (like a word or symbol) or a non-terminal (like a rule or production). This structure aligns well with the rules of CFG.
  2. Start Symbol as Root: In a parse tree, the root node always represents the start symbol of the grammar (usually denoted as ‘S’). This aligns perfectly with CFG, where the start symbol is the initial point for constructing valid sentences.
  3. Terminal and Non-terminal Labels: Every node in a parse tree is labeled either as a terminal (actual word or symbol in the language) or a non-terminal (a rule or production of the grammar). This labeling system is inherent to CFG as well.
  4. Production Rules as Branches: The branches of the parse tree correspond to the production rules of the CFG. Each non-terminal node expands into its production rules, showing how smaller parts combine to form larger structures.
  5. Terminal Symbols at Leaves: Terminal symbols, which are the actual words or symbols in the language, are always found at the leaves of the parse tree. This corresponds to the fact that in CFG, terminal symbols are the ultimate building blocks of sentences.
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