2026-07-20T05:59:11Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:8076 2024-03-06T10:40:52Z ddc:004 open_access

Satisfiable Tseitin Formulas Are Hard for Nondeterministic Read-Once Branching Programs Glinskih, Ludmila Itsykson, Dmitry Tseitin formula read-once branching program expander We consider satisfiable Tseitin formulas TS_{G,c} based on d-regular expanders G with the absolute value of the second largest eigenvalue less than d/3. We prove that any nondeterministic read-once branching program (1-NBP) representing TS_{G,c} has size 2^{\Omega(n)}, where n is the number of vertices in G. It extends the recent result by Itsykson at el. [STACS 2017] from OBDD to 1-NBP. On the other hand it is easy to see that TS_{G,c} can be represented as a read-2 branching program (2-BP) of size O(n), as the negation of a nondeterministic read-once branching program (1-coNBP) of size O(n) and as a CNF formula of size O(n). Thus TS_{G,c} gives the best possible separations (up to a constant in the exponent) between 1-NBP and 2-BP, 1-NBP and 1-coNBP and between 1-NBP and CNF. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Ludmila Glinskih and Dmitry Itsykson 2017 Is Part Of LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.MFCS.2017.26 urn:nbn:de:0030-drops-80767 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.26 eng https://creativecommons.org/licenses/by/3.0/legalcode