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Consider the grammar
S → (S) | a
Let the number of states in SLR(1), LR(1) and LALR(1) parsers for the grammar be n1, n2 and n3 respectively. The following relationship holds good
  • a)
    n1 < n2 < n3
  • b)
    n1 = n3 < n2
  • c)
    n1 = n2 = n3
  • d)
    n1 ≥ n3 ≥ n2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the grammarS → (S) | aLet the number of states in SLR(1...
LALR(1) is formed by merging states of LR(1) (also called CLR(1)), hence no of states in LALR(1) is less than no of states in LR(1), therefore n3 < n2. And SLR(1) and LALR(1) have same no of states, i.e (n1 = n3).
Hence n1 = n3 < n2
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Most Upvoted Answer
Consider the grammarS → (S) | aLet the number of states in SLR(1...
SLR(1), LR(1), and LALR(1) Parsers
SLR(1), LR(1), and LALR(1) are all types of parsers used in compiler design. These parsers are used to analyze the syntax of a programming language and construct a parse tree or abstract syntax tree.

SLR(1) Parser
SLR(1) stands for "Simple LR(1)" parser. It is a type of bottom-up parser that uses a parsing table to parse the input. The SLR(1) parsing table is constructed from the LR(0) items of the grammar. The number of states in an SLR(1) parser is denoted as n1.

LR(1) Parser
LR(1) stands for "Look-Ahead LR(1)" parser. It is also a type of bottom-up parser that uses a more powerful parsing table compared to SLR(1). The LR(1) parsing table is constructed from the LR(1) items of the grammar. The number of states in an LR(1) parser is denoted as n2.

LALR(1) Parser
LALR(1) stands for "Look-Ahead LR(1)" parser. It is a variant of the LR(1) parser that uses a smaller parsing table while still maintaining the same parsing power. The LALR(1) parsing table is constructed from the LR(0) items of the grammar. The number of states in an LALR(1) parser is denoted as n3.

Relationship between n1, n2, and n3
The given relationship states that n1 = n3 = n2, which means that the number of states in the SLR(1) parser is equal to the number of states in the LALR(1) parser, which is also equal to the number of states in the LR(1) parser.

This relationship holds true because both SLR(1) and LALR(1) parsers are derived from the same LR(0) items of the grammar. The only difference between them is the construction of the parsing table. SLR(1) parser uses a simpler and smaller parsing table compared to LALR(1) parser, resulting in fewer states. LALR(1) parser, on the other hand, uses a more compact parsing table that combines similar states, resulting in a smaller number of states compared to LR(1) parser.

Since both SLR(1) and LALR(1) parsers are derived from the same LR(0) items, they will have the same number of states. Similarly, LR(1) parser, which uses more powerful parsing table construction, will have a larger number of states compared to SLR(1) and LALR(1) parsers.

Hence, the correct answer is option 'B' - n1 = n3 = n2.
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