Partial Minimum Branching Program Size Problem is ETH-hard

Ludmila Glinskih; Artur Riazanov

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arXiv · 2407.04632

Partial Minimum Branching Program Size Problem is ETH-hard

Ludmila Glinskih·Artur Riazanov

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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.

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Ludmila Glinskih, Artur Riazanov. 2024-07-05. Partial Minimum Branching Program Size Problem is ETH-hard. https://arxiv.org/abs/2407.04632

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