
Pseudodeterministic Algorithms and the Structure of Probabilistic Time
We connect the study of pseudodeterministic algorithms to two major open...
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Completely inapproximable monotone and antimonotone parameterized problems
We prove that weighted circuit satisfiability for monotone or antimonoto...
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A historical note on the 3/2approximation algorithm for the metric traveling salesman problem
One of the most fundamental results in combinatorial optimization is the...
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A QPTAS for stabbing rectangles
We consider the following geometric optimization problem: Given n axisa...
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Silent MST approximation for tiny memory
In network distributed computing, minimum spanning tree (MST) is one of ...
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On the worstcase error of least squares algorithms for L_2approximation with high probability
It was recently shown in [4] that, for L_2approximation of functions fr...
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Probabilistic Acceptance
The idea of fully accepting statements when the evidence has rendered th...
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Promise Problems Meet Pseudodeterminism
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 polynomialtime 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 multipseudodeterminism.
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