Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Max-k-SAT | Statement: [Max-3-SAT, isSpecialCaseOf, Max-k-SAT]

Target entity: Max-k-SAT
Context triple: [Max-3-SAT, isSpecialCaseOf, Max-k-SAT]

• A. Max-SAT
  Max-SAT is the optimization variant of the Boolean satisfiability problem in which the goal is to find an assignment that satisfies the maximum possible number of clauses, making it a central problem in approximation algorithms and complexity theory.
• B. Max-3-SAT
  Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
• C. k-SAT
  k-SAT is a canonical NP-complete decision problem in Boolean logic where one asks whether there exists a truth assignment satisfying a formula expressed as a conjunction of clauses, each containing at most k literals.
• D. Max-CSP
  Max-CSP is a general optimization framework in theoretical computer science where the goal is to assign values to variables to satisfy as many given constraints as possible.
• E. 3-SAT
  3-SAT is a classic Boolean satisfiability problem where each clause has exactly three literals and which serves as a fundamental NP-complete benchmark in computational complexity theory.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Max-k-SAT
Target entity description: Max-k-SAT is the optimization version of the k-SAT problem, where the goal is to find a truth assignment that satisfies the maximum possible number of clauses in a Boolean formula with at most k literals per clause.

• A. Max-SAT chosen
  Max-SAT is the optimization variant of the Boolean satisfiability problem in which the goal is to find an assignment that satisfies the maximum possible number of clauses, making it a central problem in approximation algorithms and complexity theory.
• B. Max-3-SAT
  Max-3-SAT is an optimization variant of the Boolean satisfiability problem where the goal is to maximize the number of satisfied clauses, each containing exactly three literals, and it serves as a central problem in the study of approximation algorithms and hardness of approximation.
• C. k-SAT
  k-SAT is a canonical NP-complete decision problem in Boolean logic where one asks whether there exists a truth assignment satisfying a formula expressed as a conjunction of clauses, each containing at most k literals.
• D. Max-CSP
  Max-CSP is a general optimization framework in theoretical computer science where the goal is to assign values to variables to satisfy as many given constraints as possible.
• E. 3-SAT
  3-SAT is a classic Boolean satisfiability problem where each clause has exactly three literals and which serves as a fundamental NP-complete benchmark in computational complexity theory.
• F. None of above.