2026-08-04T15:25:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:17570 2024-03-12T12:01:05Z ddc:004 open_access

Downward Self-Reducibility in TFNP Harsha, Prahladh Mitropolsky, Daniel Rosen, Alon downward self-reducibility TFNP TFUP factoring PLS CLS A problem is downward self-reducible if it can be solved efficiently given an oracle that returns solutions for strictly smaller instances. In the decisional landscape, downward self-reducibility is well studied and it is known that all downward self-reducible problems are in PSPACE. In this paper, we initiate the study of downward self-reducible search problems which are guaranteed to have a solution - that is, the downward self-reducible problems in TFNP. We show that most natural PLS-complete problems are downward self-reducible and any downward self-reducible problem in TFNP is contained in PLS. Furthermore, if the downward self-reducible problem is in TFUP (i.e. it has a unique solution), then it is actually contained in UEOPL, a subclass of CLS. This implies that if integer factoring is downward self-reducible then it is in fact in UEOPL, suggesting that no efficient factoring algorithm exists using the factorization of smaller numbers. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Prahladh Harsha and Daniel Mitropolsky and Alon Rosen 2023 Is Part Of LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2023.67 urn:nbn:de:0030-drops-175700 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.67 eng https://creativecommons.org/licenses/by/4.0/legalcode