Partial Minimum Branching Program Size Problem is ETH-hard
Abstract
We show that assuming the Exponential Time Hypothesis, the Partial Minimum Branching Program Size Problem (MBPSP*) requires superpolynomial time. This result also applies to the partial minimization problems for many interesting subclasses of branching programs, such as read-k branching programs and OBDDs. Combining these results with the recent unconditional lower bounds for MCSP [Glinskih, Riazanov'22], we obtain an unconditional superpolynomial lower bound on the size of Read-Once Nondeterministic Branching Programs (1-NBP) computing the total versions of the minimum BP, read-k-BP, and OBDD size problems. Additionally we show that it is NP-hard to check whether a given BP computing a partial Boolean function can be compressed to a BP of a given size.
Cite
@article{arxiv.2407.04632,
title = {Partial Minimum Branching Program Size Problem is ETH-hard},
author = {Ludmila Glinskih and Artur Riazanov},
journal= {arXiv preprint arXiv:2407.04632},
year = {2024}
}