Quadratic-equation satisfiability over asks whether a finite system of polynomial equations of degree at most two over the finite field has a common solution.
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NP-completeness is a concept from computational complexity theory that classifies certain decision problems based on their solvability and the difficulty of solving them. Let's break down the relevant terms: 1. **P (Polynomial Time)**: This class consists of decision problems (problems with a yes/no answer) that can be solved by a deterministic Turing machine in polynomial time. In simpler terms, these are problems for which an efficient (i.e., fast) algorithm exists.