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Some problems are so complex that they can’t be solved in all the time we can possibly have (R, or “finite time”), and are simply undecidable. For instance: Turing’s Halting Problem.
There are special subclasses of problems that are of great interest to us, specifically: exponentially complex problems that we can solve in P time with a nondeterministic lucky guess. These problems are in a classification called “NP”. We can further divide this complexity class into decision problems that we can quickly verify (NP-Complete) and more complicated problems that are in Exp, but that other problems in NP can be reduced to in P time (NP-Hard).
There are special subclasses of problems that are of great interest to us, specifically: exponentially complex problems that we can solve in P time with a nondeterministic lucky guess. These problems are in a classification called “NP”. We can further divide this complexity class into decision problems that we can quickly verify (NP-Complete) and more complicated problems that are in Exp, but that other problems in NP can be reduced to in P time (NP-Hard).
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