Maximum satisfiability problem

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The Maximum Satisfiability Problem (MAX-SAT) is an optimization extension of the classical Boolean satisfiability problem (SAT), where the goal is to find a variable assignment that satisfies the maximum possible number of clauses in a logical formula, even when full satisfaction is impossible. Unlike standard SAT, which asks whether a complete solution exists, MAX-SAT seeks the best achievable solution under constraints, making it applicable to real-world problems that are inherently over-constrained. In robotics and AI, MAX-SAT and its variants are used for task planning, constraint satisfaction in hybrid systems, resource allocation, and combinatorial optimization problems where competing requirements must be balanced. It also appears in verification workflows for autonomous systems and control logic. MAX-SAT solvers are increasingly being explored on quantum hardware through algorithms like QAOA, as well as accelerated on high-performance computing platforms for large-scale parallel execution. Its importance lies in providing a principled, rigorous framework for decision-making under conflicting constraints, a ubiquitous challenge across intelligent and autonomous systems.