Calculus-based heuristics, like Newton's method or gradient descent, use principles of calculus to find solutions to complex problems. They involve calculating slopes or gradients to understand how a function changes. For instance, gradient descent moves towards the lowest point of a function, similar to finding the bottom of a valley - this point is often the best solution. These methods are powerful for optimizing problems, like in machine learning or economics, where finding the most efficient point is crucial.
The 3-SAT (3-Satisfiability) problem is a classic question in computer science and mathematical logic. It's a specific type of Boolean satisfiability problem. In 3-SAT, you're given a formula composed of several clauses, where each clause is a disjunction (an "OR" operation) of exactly three literals (variables or their negations). The challenge is to determine if there exists an assignment of truth values (true or false) to the variables that makes the entire formula true. This problem is known for being NP-complete, meaning it's easy to check a solution but potentially very hard to find one, especially as the number of variables increases. This characteristic makes 3-SAT important in theoretical computer science, particularly in studies related to computational complexity.