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NP stands for Nondeterministic Polynomial Time. It includes decision problems for which a solution can be verified in polynomial time by a deterministic Turing machine. Significance: The famous P vs NP question involves this class, asking whether problems that can be verified quickly can also be solved quickly.

EXPTIME (or EXP) is the class of problems solvable by a deterministic Turing machine in exponential time. Specifically, it refers to problems solvable in $O(2^{p(n)})$, where $p(n)$ is a polynomial. Significance: EXPTIME problems are typically considered infeasible for large inputs due to their high complexity.

NP-complete is a subset of NP. It includes the hardest problems in NP, in the sense that every problem in NP can be reduced to every NP-complete problem in polynomial time. Significance: If any NP-complete problem can be solved in polynomial time, then P = NP.

P stands for Polynomial Time. It is the complexity class that contains all decision problems that can be solved by a deterministic Turing machine in polynomial time. Significance: P is often considered as a class of 'efficiently solvable' or 'tractable' problems.