Record link: 
http://hdl.handle.net/20.500.12708/230570
https://doi.org/10.34727/2026/isbn.978-3-85448-093-8_75
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Title: 
Solution Space Partitioning for Extremal Set Theory
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Citation: 
Looney, J., McDonald, J., Klingler, A., Wu, G., Pulaj, J., & Wu, H. (2026). Solution Space Partitioning for Extremal Set Theory. In B. Dutertre & B. Könighofer (Eds.), Proceedings of the 26th Conference on Formal Methods in Computer-Aided Design – FMCAD 2026 (pp. 757–768). TU Wien Academic Press. https://doi.org/10.34727/2026/isbn.978-3-85448-093-8_75
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reposiTUm DOI: 
10.34727/2026/isbn.978-3-85448-093-8_75
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CatalogPlus: 
AC18000699
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Looney, Jesse 
McDonald, Jonah 
Klingler, Allison 
Wu, Gloria 
Pulaj, Jonad 
Wu, Haoze 
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Editors: 
Dutertre, Bruno 
Könighofer, Bettina 
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Organisational Unit: 
E000 - Technische Universität Wien 
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Series: 
Conference Series: Formal Methods in Computer-Aided Design 
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Published in: 
Proceedings of the 26th Conference on Formal Methods in Computer-Aided Design – FMCAD 2026 
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Date (published): 
Sep-2026
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Number of Pages: 
12
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Publisher: 
TU Wien Academic Press
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Peer reviewed: 
Yes
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Keywords: 
formal methods; computer-aided system design; hardware and system verification
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Abstract: 
We present a method for partitioning the solution space of statements in extremal set theory. Compared with domain-agnostic partitioning methods like look-ahead, we perform case analysis on the strategies by which a candidate solution can be constructed. We demonstrate that our approach can decompose problems in extremal set theory more effectively than look-ahead. Combining this new partitioning strategy with an exact proof-producing MILP solver, we are able to verify larger finite cases of Chvátal’s Conjecture—a long-standing open question in extremal combinatorics—compared to previous work.
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Is part of: 
10.34727/2026/isbn.978-3-85448-093-8
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Research Areas: 
Logic and Computation: 40%
Computer Engineering and Software-Intensive Systems: 40%
Computer Science Foundations: 20%
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Science Branch: 
1020 - Informatik: 100%
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License: 
CC BY 4.0 CC BY 4.0
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Version History
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2 20.500.12708/230570 Krassnig, David 2026-09-11 11:36:14.506 Correction of the interchanged "max solve time (s)" values for "symbreak (1s)" and "symbreak (3s)" in Table II (p. 765)
1 20.500.12708/230570.1 Ziemkendorf, Silvia 2026-09-03 11:21:15.0
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