2026-07-23T16:50:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:27081 2026-07-23T11:36:20Z ddc:004 open_access

Faux Determinism Ben-David, Shalev Ebtehaj, M. H. Decision Trees Search Problems Query Complexity Pseudodeterminism TFNP Refutation In the context of search problems, a pseudodeterministic algorithm is one which uses randomness but appears to be deterministic in its external behavior: it outputs the same answer when it is run on any one input multiple times. We introduce the relaxed notion of computationally-secure pseudodeterminism, which we call faux determinism. A faux-deterministic algorithm must appear to be deterministic to any external adversary with bounded resources. In other words, an algorithm is faux-deterministic if the task of "finding an input on which it fails to deterministically solve the search problem" is computationally intractable. In the black-box setting, we show that every verifiable search problem which has a randomized algorithm also has a faux-deterministic algorithm; this is not true of pseudodeterministic algorithms, which do not always exist. We highlight two reasons why this faux derandomization result is interesting: first, due to the computational indistinguishability, faux-deterministic algorithms may be used in place of pseudodeterministic ones in cryptographic settings. Second, from a conceptual point of view, our result helps explain why pseudodeterministic lower bounds are often hard to prove: such lower bounds must be inherently nonconstructive, since within FZPP∩FNP, there is no efficient black-box algorithm for finding a hard input for a given faux-deterministic algorithm. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Shalev Ben-David and M. H. Ebtehaj 2026 Is Part Of LIPIcs, Volume 383, 41st Computational Complexity Conference (CCC 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CCC.2026.39 urn:nbn:de:0030-drops-270812 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2026.39 eng https://creativecommons.org/licenses/by/4.0/legalcode