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Difficulty: Very hardMust Be True / Most Strongly Supported

In the field of computational linguistics, any parsing algorithm that efficiently resolves left-branching ambiguities must utilize a dynamic memoization matrix. Furthermore, if a parsing algorithm utilizes a dynamic memoization matrix, it cannot operate strictly in linear time unless it is restricted exclusively to context-free grammars. The newly developed 'Verde' parsing algorithm efficiently resolves left-branching ambiguities, yet it is specifically designed to handle context-sensitive grammars, which are explicitly not context-free. Finally, at least some parsing algorithms that operate strictly in linear time are currently utilized in commercial translation software.

Based on the information provided, which of the following statements must be true? (Select all that apply.)

  1. The Verde algorithm does not operate strictly in linear time.Answer
  2. The Verde algorithm utilizes a dynamic memoization matrix.Answer
  3. C
    Any parsing algorithm that utilizes a dynamic memoization matrix efficiently resolves left-branching ambiguities.
  4. D
    No parsing algorithm that operates strictly in linear time is capable of handling context-sensitive grammars.
  5. E
    The Verde algorithm is not utilized in commercial translation software.

Answer

The statements that must be true are that the Verde algorithm utilizes a dynamic memoization matrix, and that it does not operate strictly in linear time.
The correct statements are direct deductions from chaining the conditional rules. The Verde algorithm is stated to be efficient, triggering the rule that it must use a dynamic memoization matrix. Because it uses this matrix and is explicitly not context-free, it triggers the second rule (using matrix + not context free -> not linear time). Therefore, it must be true that Verde uses a matrix, and it must be true that Verde does not operate in linear time.

Step-by-Step Solution

1
Map the first conditional premise.
If an algorithm efficiently resolves left-branching ambiguities, then it must utilize a dynamic memoization matrix (Efficient -> Matrix).
This establishes the fundamental requirement for parsing efficiency in this context.
2
Map the complex 'unless' conditional premise.
If an algorithm uses a dynamic memoization matrix, then it cannot operate in linear time UNLESS it is restricted to context-free grammars (Matrix + Not Context-Free -> Not Linear Time).
The word 'unless' introduces a necessary exception. If the exception is not met, the main clause applies.
3
Apply the established rules to the specific case of the Verde algorithm.
Because Verde efficiently resolves left-branching ambiguities, it must utilize a dynamic memoization matrix. Because it handles context-sensitive grammars, it is not restricted to context-free grammars.
Connecting the factual statements about Verde to the conditional rules yields deductions about its properties.
4
Chain the deductions to reach final conclusions.
Since Verde utilizes a matrix AND is not context-free, it triggers the rule from Step 2. Therefore, Verde cannot operate strictly in linear time.
Formal logic dictates that satisfying the sufficient conditions of a valid rule guarantees the necessary condition.

Key Concept

Formal Logic: Conditional Chaining and Contrapositives
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Topics

Must Be True / Most Strongly Supported

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