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Miloslav Ciz 2022-04-13 21:22:00 +02:00
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p_vs_np.md
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@ -8,7 +8,7 @@ It is believed and sometimes relied on that P != NP (in which case P would be a
In the context of [computational complexity](computational_complexity.md) of algorithms we talk about different types of algorithm time complexities, i.e. different "speeds" of algorithms. This "speed" doesn't mean actual running time of the algorithm in real life but rather how quickly the running time grows depending on the amount of input data to it, i.e. we are interested only in the shape of the function that describes how the amount of input data affects the running time of the algorithm. The types of time complexity are named after mathematical functions that grow as quickly as this dependence, so we have a *constant* time complexity, *logarithmic* time complexity, *linear* time complexity etc.
Then we have classes of computational problems. The classes divide the problem based on how "fast" these problems can be solved.
Then we have classes of computational problems. The classes divide problems based on how "fast" they can be solved.
The class P stands for **polynomial** and is defined as all problems that can be solved by an algorithm run on a **deterministic [Turing machine](turing_machine.md)** (a theoretical computer) with a *polynomial* time complexity.