Definition A language L is in BPP if and only if there exists a probabilistic Turing machine M, such that M runs for polynomial time on all inputs For all x in L, M outputs 1 with probability greater than or equal to 2/3 For all x not in L, M outputs 1 with probability less than or equal to 1/3 Unlike the complexity class ZPP, the machine M is required to run for polynomial time on all inputs, regardless of the outcome of the random coin flips.
Definition A language: L is in BPP if and only if there exists a probabilistic Turing machine M, such that M runs for polynomial time on all inputs Fo,r all x in L, M outputs 1 with probability greater than? or equal to 2/3 Fo.r all x not in L, M outputs 1 with probability less than or equal to 1/.3 Unlike the complexity class ZPP, the machine M is required to run for polynomial time on all inputs, regardless of the outcome of the random coin flips.