Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2506.12420

Deterministic Lifting Theorems for One-Way Number-on-Forehead Communication

Guangxu Yang·Jiapeng Zhang
View original source ↗Read source document ↗Export metadata ↓

Abstract

Lifting theorems are one of the most powerful tools for proving communication lower bounds, with numerous downstream applications in proof complexity, monotone circuit lower bounds, data structures, and combinatorial optimization. However, to the best of our knowledge, prior lifting theorems have primarily focused on the two-party communication. In this paper, we propose a new lifting theorem that establishes connections between two-party communication and the Number-on-Forehead (NOF) communication model. Specifically, we present a deterministic lifting theorem that translates one-way two-party communication lower bounds into one-way NOF lower bounds. Our lifting theorem yields two applications. First, we obtain an optimal explicit separation between randomized and deterministic one-way NOF communication, even in the multi-player setting. This improves the prior square-root vs. constant separation for three players established by Kelley and Lyu (arXiv 2025). Second, we achieve optimal separations between one-round and two-round deterministic NOF communication, improving upon the previous separation of $\Omega(\frac{n^{1/(k-1)}}{k^k})$ vs. $O(\log n)$ for $k$ players, as shown by Viola and Wigderson (FOCS 2007). Beyond the lifting theorems, we also apply our techniques to the disjointness problem. In particular, we provide a new proof that the deterministic one-way three-party NOF communication complexity of set disjointness is $\Omega(n)$, further demonstrating the broader applicability of our methods.

Explore related subjects

cs.CC

Keep this discovery

BibTeXRIS

Guangxu Yang, Jiapeng Zhang. 2025-06-14. Deterministic Lifting Theorems for One-Way Number-on-Forehead Communication. https://arxiv.org/abs/2506.12420

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC↗
arXiv2026

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC↗