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Partial Minimum Branching Program Size Problem Is ETH-Hard

Authors Ludmila Glinskih , Artur Riazanov

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Author Details

Ludmila Glinskih
  • Google, Mountain View, CA, USA
Artur Riazanov
  • EPFL, Lausanne, Switzerland

Funding

Artur Riazanov was supported by the Swiss State Secretariat for Education, Research and Innovation (SERI) under contract number MB22.00026. Ludmila Glinskih was supported by a Sloan Research Fellowship to Mark Bun. Most of this work was done while Ludmila was at Boston University, and in part while she was visiting the Simons Institute for the Theory of Computing.

Acknowledgements

The authors are grateful to Rahul Santhanam for suggesting working on connections between meta-complexity and branching programs, and to Mark Bun and anonymous reviewers for very helpful feedback on the preliminary versions of this paper.

Cite As Get BibTex

Ludmila Glinskih and Artur Riazanov. Partial Minimum Branching Program Size Problem Is ETH-Hard. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 54:1-54:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.54

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} [Ludmila Glinskih and Artur Riazanov, 2022], 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Circuit complexity
Keywords
  • MCSP
  • branching programs
  • meta-complexity
  • lower bounds

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