In computational complexity theory,

**BPP**, which stands for

**bounded-error probabilistic polynomial time** is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded away from 1/3 for all instances.

**BPP** is one of the largest

*practical* classes of problems, meaning most problems of interest in

**BPP** have efficient probabilistic algorithms that can be run quickly on real modern machines.

**BPP** also contains

**P**, the class of problems solvable in polynomial time with a deterministic machine, since a deterministic machine is a special case of a probabilistic machine.

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In computational complexity theory, **BPP**, which stands for **bounded-error probabilistic polynomial time** is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded away from 1/3 for all instances. **BPP** is one of the largest *practical* classes of problems, meaning most problems of interest in **BPP** have efficient probabilistic algorithms that can be run quickly on real modern machines. **BPP** also contains **P**, the class of problems solvable in polynomial time with a deterministic machine, since a deterministic machine is a special case of a probabilistic machine.

Informally, a problem is in **BPP** if there is an algorithm for it that has the following properties:

- It is allowed to flip coins and make random decisions
- It is guaranteed to run in polynomial time
- On any given run of the algorithm, it has a probability of at most 1/3 of giving the wrong answer, whether the answer is YES or NO.

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