Consider the following statements: Statement I: LALR parser is more powerful than canonical LR Parser. Statement II: SLR parser is more powerful than LALR Which of the following is correct?
Both Statement I and Statement II false
Understanding Parser Power: LALR, Canonical LR, and SLR
This question asks us to compare the power of different types of LR parsers: LALR, Canonical LR, and SLR. The power of a parser type is determined by the set of grammars it can successfully parse without conflicts. A parser that can handle a larger set of grammars is considered more powerful.
Analyzing Statement I: LALR Parser vs. Canonical LR Parser Power
Statement I says: LALR parser is more powerful than canonical LR Parser.
- Canonical LR (CLR) parsers build items that include the lookahead symbols directly in the state. This allows them to make very precise parsing decisions, resulting in the ability to parse the largest set of LR($k$) grammars among the LR parser family (for a fixed $k$).
- LALR (Look-Ahead LR) parsers are constructed by first building the canonical LR states and then merging states that have identical core items (the production rule and the position of the dot) but possibly different lookahead sets. The lookahead sets from the merged states are combined.
- This merging process in LALR construction reduces the number of states compared to Canonical LR, making the parser table smaller. However, this merging can sometimes introduce reduce/reduce conflicts that were not present in the original Canonical LR automaton, specifically when the merged states had different lookahead sets for the same reduction.
- Because the merging process can introduce conflicts, an LALR parser might fail to parse certain grammars that a Canonical LR parser can handle. Therefore, Canonical LR parsers are generally more powerful than LALR parsers.
Based on this understanding, Statement I, claiming LALR is more powerful than Canonical LR, is false.
Analyzing Statement II: SLR Parser vs. LALR Parser Power
Statement II says: SLR parser is more powerful than LALR.
- SLR (Simple LR) parsers are simpler to construct than LALR or Canonical LR. They use the standard LR(0) item sets (items without lookahead symbols) for states.
- For reduce actions, SLR parsers decide whether to reduce using a production $A \to \alpha$ by checking if the lookahead symbol is in the FOLLOW(A) set. This is a simpler lookahead check compared to the specific lookahead sets computed during the construction of LALR or Canonical LR states.
- The reliance on the general FOLLOW set makes SLR less precise in its decision-making compared to LALR or Canonical LR, which use more specific lookahead information derived from the grammar and state construction.
- Consequently, SLR parsers can encounter conflicts (shift/reduce or reduce/reduce) on certain grammars that LALR parsers can handle. For example, if a state has a reduction $A \to \alpha$ and a shift on terminal $t$, SLR will have a conflict if $t$ is in FOLLOW(A), regardless of whether $t$ is a valid lookahead in that specific state according to LR(1) logic. LALR, with its refined lookahead sets, might resolve this conflict.
- Thus, LALR parsers are generally more powerful than SLR parsers.
Based on this understanding, Statement II, claiming SLR is more powerful than LALR, is false.
Conclusion on Parser Power Statements
Both Statement I (LALR is more powerful than Canonical LR) and Statement II (SLR is more powerful than LALR) are false. The generally accepted hierarchy of power for these LR parser types is:
Canonical LR > LALR > SLR
where '>' means 'is more powerful than' (i.e., can parse a strictly larger set of grammars).
| Parser Type | Power | Number of States (relative) | Lookahead Used for Reduce |
|---|---|---|---|
| SLR | Least Powerful | Fewest (same as LR(0)) | FOLLOW set of LHS |
| LALR | Medium Power | Fewer than CLR (same as LR(0) cores) | Refined lookahead sets (merged) |
| Canonical LR | Most Powerful | Most | Specific lookahead sets per item |
Revision Table: Summary of LR Parser Power Hierarchy
Here is a quick summary of the relative power of these parser types:
- Canonical LR is the most powerful among the three.
- LALR is less powerful than Canonical LR but more powerful than SLR.
- SLR is the least powerful among the three.
The relationship is Canonical LR > LALR > SLR in terms of the set of grammars parsable.
Additional Information: Why LALR is a Practical Choice
While Canonical LR is the most powerful, its main drawback is the large number of states it generates, which can make the parser table very large and inefficient in terms of memory. LALR parsers are specifically designed to address this issue.
- LALR parsers achieve a significant reduction in the number of states compared to Canonical LR. They have the same number of states as the corresponding LR(0) automaton for the grammar, which is often much smaller than the Canonical LR automaton.
- The state reduction is achieved by merging states that have the same core LR(0) items. Even though this merging can sometimes introduce conflicts, many practical programming language grammars are LALR(1), meaning they can be parsed by an LALR parser without conflicts.
- Because LALR offers a good balance between parsing power (being more powerful than SLR) and parser table size (being much smaller than Canonical LR), it is a widely used parser type in practice, especially in parser generators like Yacc/Bison.
Understanding this trade-off between power and table size is key to understanding why LALR is frequently preferred over Canonical LR in compiler construction.
Important Questions from Parser
Given below are two statements
Statement I : LL(1) and LR are examples of Bottom‐up parsers.
Statement II : Recursive descent parser and SLR are examples of Top‐down parsers
In light of the above statements, choose the correct answer from the options given below
Consider the following Grammar G:
S ➝ A | B
A➝ a | c
B➝ b | c
Where {S, A, B} is the set of non-terminals, {a, b, c} is the set of terminals.
Which of the following statement(s) is/are correct?
S 1 : LR(1) can parse all strings that are generated using grammar G.
S 2 : LL(1) can parse all strings that are generated using grammar G.The grammar S → SS | (S)| ϵ is not suitable for predictive parsing because the grammar is:
- Arrange the following parsers in increasing order of their power of handling grammars i.e. from the least powerful parser to the most powerful parser.
A. LR(0)
B. LR(1)
C. LALR(1)
D. LL(0)
E. SLR
Choose the correct answer from the options given below: - Which of the following statements is/are true?
