Exploring Probabilistic Turing Machines and the Relationship between BPP, PH, and NP

Dec 05, 2025

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This paper discusses the implications of alternating quantifiers and probabilistic Turing machines (TMs) on the classifications of decision problems within computational complexity, specifically focusing on the relationship between BPP and NP, and the proof of cases when an instance of certain languages is a "yes" or "no" based on defined probability distributions. The work aims to provide insights into random divide amplification mechanisms and examines instances leading to specific decision outcomes in relation to known complexity classes.

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Exploring Probabilistic Turing Machines and the Relationship between BPP, PH, and NP

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