Editing Monte Carlo algorithm (section)

==Complexity classes==
The [[complexity class]] [[Bounded-error probabilistic polynomial|BPP]] describes [[decision problem]]s that can be solved by polynomial-time Monte Carlo algorithms with a bounded probability of two-sided errors, and the complexity class [[RP (complexity)|RP]] describes problems that can be solved by a Monte Carlo algorithm with a bounded probability of one-sided error: if the correct answer is '''false''', the algorithm always says so, but it may answer '''false''' incorrectly for some instances where the correct answer is '''true'''.<ref name=":0">{{Cite book |last1=Kudelić |first1=Robert |last2=Ivković |first2=Nikola |last3=Šmaguc |first3=Tamara |chapter=A Brief Overview of Randomized Algorithms |series=Lecture Notes in Networks and Systems |date=2023 |volume=720 |editor-last=Choudrie |editor-first=Jyoti |editor2-last=Mahalle |editor2-first=Parikshit N. |editor3-last=Perumal |editor3-first=Thinagaran |editor4-last=Joshi |editor4-first=Amit |title=IOT with Smart Systems |chapter-url=https://link.springer.com/chapter/10.1007/978-981-99-3761-5_57 |language=en |location=Singapore |publisher=Springer Nature |pages=651–667 |doi=10.1007/978-981-99-3761-5_57 |isbn=978-981-99-3761-5}}</ref> In contrast, the complexity class [[ZPP (complexity)|ZPP]] describes problems solvable by polynomial expected time Las Vegas algorithms. {{nowrap|ZPP ⊆ RP ⊆ BPP}}, but it is not known whether any of these complexity classes is distinct from each other; that is, Monte Carlo algorithms may have more computational power than Las Vegas algorithms, but this has not been proven.<ref name=":0" /> Another complexity class, [[PP (complexity)|PP]], describes decision problems with a polynomial-time Monte Carlo algorithm that is more accurate than flipping a coin but where the error probability cannot necessarily be bounded away from {{frac|1|2}}.<ref name=":0" />