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Daniel Kleber

dblp:426/8318 · DBLP profile ↗
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1ranked-venue papers
0as first author
1since 2021 · last 2026
—ORCID · none

Domains — the database's venue-derived domains; a paper can count in several

Theory of computation · 1 · 1 since 2021

Expertise — from the expertise taxonomy: the topics of the expert's papers under the CCF categories. A weight counts papers with recency: 1 for a paper about the topic, 0.3 when the topic is its context, halved every five years.

Theoretical computer science
1 paper
Computational complexity · 100%

Topics — the 4 heaviest of 4, each with the papers that count most for it

TopicWeightPapersLastEvidence papers
Computational complexity
circuit complexity
1.012026
Optimal Depth-Three Circuits for Inner Product · CCC 2026
Computational complexity › circuit complexity
circuit lower bounds
1.012026
Optimal Depth-Three Circuits for Inner Product · CCC 2026
Computational complexity › algebraic complexity › arithmetic circuit complexity
depth-3 circuit
1.012026
Optimal Depth-Three Circuits for Inner Product · CCC 2026
Computational complexity
algebraic complexity
0.312026
Optimal Depth-Three Circuits for Inner Product · CCC 2026

Methods — techniques the papers use, named apart from their topics

computer search · 1.0automorphism group orbits · 1.0analytic combinatorics · 1.0
YearPublicationVenuePosition
2026 Optimal Depth-Three Circuits for Inner Product
abstract
We show that Inner Product in 2n variables, IP_n(x, y) = x₁y₁ ⊕ … ⊕ x_ny_n, can be computed by depth-3 bottom fan-in 2 circuits of size poly(n)⋅ (9/5)ⁿ, matching the lower bound of Göös, Guan, and Mosnoi (Inform. Comput.'24). Our construction is obtained via the following steps. 1) We provide a general template for constructing optimal depth-3 circuits with bottom fan-in k for an arbitrary function f. We do this in two steps. First, we partition f^{-1}(1) into orbits of its automorphism group. Second, for each orbit, we construct one k-CNF that (a) accepts the largest number of inputs from that orbit and (b) rejects all inputs rejected by f. 2) We instantiate the template for IP_n and k = 2. Guided by the intuition (which we call modularity principle) that optimal 2-CNFs can be constructed by taking the conjunction of variable-disjoint copies of smaller 2-CNFs, we use computer search to identify a small set of building block 2-CNFs over at most 4 variables. 3) We again use computer search to discover appropriate combinations (disjoint conjunctions) of building blocks to arrive at optimal 2-CNFs and analyze them using techniques from analytic combinatorics. We believe that the approach outlined in this paper can be applied to a wide range of functions to determine their depth-3 complexity.
Mohit Gurumukhani, Daniel Kleber, Ramamohan Paturi, Christopher D. Rosin, Navid Talebanfard
CCC2