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Sophus Valentin Willumsgaard

dblp:420/9480 · DBLP profile ↗
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1ranked-venue papers
0as first author
1since 2021 · last 2026
0009-0009-5161-4567ORCID · reported

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 · 75% Algorithms and data structures · 25%

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

TopicWeightPapersLastEvidence papers
Algorithms and data structures › symbolic computation › computational algebra
algebraic algorithms
1.012026
Ideals, Macaulay Bases, and PCPs · STOC 2026
Computational complexity › probabilistically checkable proofs
PCP composition
1.012026
Ideals, Macaulay Bases, and PCPs · STOC 2026
Computational complexity › probabilistically checkable proofs
PCP theorem
1.012026
Ideals, Macaulay Bases, and PCPs · STOC 2026
Computational complexity
probabilistically checkable proofs
1.012026
Ideals, Macaulay Bases, and PCPs · STOC 2026

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

composition steps · 1.0algebraic construction · 1.0
YearPublicationVenuePosition
2026 Ideals, Macaulay Bases, and PCPs
abstract
All known proofs of the PCP theorem rely on multiple ”composition” steps, where PCPs over large alphabets are turned into PCPs over much smaller alphabets at a (relatively) small price in the soundness error of the PCP. Algebraic proofs, starting with the work of Arora, Lund, Motwani, Sudan, and Szegedy use at least 2 such composition steps, whereas the ”Gap amplification” proof of Dinur uses Θ(logn) such composition steps. In this work, we present the first PCP construction using just one composition step. The key ingredient, missing in previous work and finally supplied in this paper, is a basic PCP (of Proximity) of size 2nε, for any ε > 0, that makes Oε(1) queries.
Prashanth Amireddy, Amik Raj Behera, Srikanth Srinivasan 0001, Madhu Sudan 0001, Sophus Valentin Willumsgaard
STOC5