We continue the study of pseudo-deterministic algorithms initiated by Gat and Goldwasser
[GG11]. A pseudo-deterministic algorithm is a probabilistic algorithm which produces a fixed
output with high probability. We explore pseudo-determinism in the settings of learning and ap-
proximation. Our goal is to simulate known randomized algorithms in these settings ... more >>>

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 ... more >>>

A randomized algorithm for a search problem is *pseudodeterministic* if it produces a fixed canonical solution to the search problem with high probability. In their seminal work on the topic, Gat and Goldwasser posed as their main open problem whether prime numbers can be pseudodeterministically constructed in polynomial time.

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We exhibit an $n$-bit partial function with randomized communication complexity $O(\log n)$ but such that any completion of this function into a total one requires randomized communication complexity $n^{\Omega(1)}$. In particular, this shows an exponential separation between randomized and pseudodeterministic communication protocols. Previously, Gavinsky (2025) showed an analogous separation in ... more >>>