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- W3152142605 abstract "The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a pseudodeterministic approximation algorithm for this problem: a probabilistic polynomial-time algorithm that outputs a canonical approximation with high probability. Recently, it was shown that such an algorithm would imply that every approximation algorithm can be made pseudodeterministic (Dixon, Pavan, Vinodchandran; ITCS 2021). The main conceptual contribution of this work is to establish that the existence of a pseudodeterministic algorithm for APEP is fundamentally connected to the relationship between probabilistic promise classes and the corresponding standard complexity classes. In particular, we show the following equivalence: every promise problem in PromiseBPP has a solution in BPP if and only if APEP has a pseudodeterministic algorithm. Based on this intuition, we show that pseudodeterministic algorithms for APEP can shed light on a few central topics in complexity theory such as circuit lowerbounds, probabilistic hierarchy theorems, and multi-pseudodeterminism." @default.
- W3152142605 created "2021-04-13" @default.
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- W3152142605 date "2021-03-15" @default.
- W3152142605 modified "2023-09-27" @default.
- W3152142605 title "Promise Problems Meet Pseudodeterminism" @default.
- W3152142605 doi "https://doi.org/10.48550/arxiv.2103.08589" @default.
- W3152142605 hasPublicationYear "2021" @default.
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