The following grammar is S →A a A b / B b B a A →εB →ε(A) LL (1) (B) Not LL (1) (C) Recursive (D

step 1 The following grammar is its choice A, which is LL1. Now, LL1 stands for left to right, leftmost

The following grammar is S →A a A b / B b B a A →εB →ε(A) LL...

Key Concepts

LL(1) Parsing

LL(1) parsing is a top?down parsing strategy that uses a single token of lookahead to make parsing decisions. A grammar is considered LL(1) if, for every nonterminal, the parser can decide which production to use by looking only at the next input symbol. This requires that, for each production alternative, the FIRST sets must be disjoint and that if any alternative derives ? (epsilon), its FIRST set must be disjoint from the FOLLOW set of the nonterminal.

FIRST and FOLLOW Sets

The FIRST and FOLLOW sets are fundamental tools used in determining the LL(1) property of a grammar. The FIRST set of a production comprises the set of terminal symbols that begin the strings derivable from that production. The FOLLOW set of a nonterminal consists of the terminals that can appear immediately to the right of that nonterminal in some derivation. These sets help in ensuring that no two rules for the same nonterminal conflict when making parsing decisions based on a single lookahead symbol.

Ambiguity in Grammars

A context?free grammar is said to be ambiguous if there exists at least one string for which the grammar provides two or more distinct parse trees (or derivations). Ambiguity leads to uncertainty in the structure of the parsed string and can complicate parsing, particularly in the design of deterministic parsers such as LL(1) parsers which require unambiguous grammars.

Epsilon (Empty) Productions

Epsilon productions are rules in a grammar where a nonterminal can derive the empty string (?). These productions introduce special considerations in parsing because they can cause a nonterminal to be 'nullable' and affect the construction of FIRST and FOLLOW sets. Their proper management is critical for determining whether a grammar meets the LL(1) criteria.

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