Proving unsatisfiability with hitting formulas

Yuval Filmus, Edward A. Hirsch, Artur Riazanov, Alexander Smal and Marc Vinyals
ITCS 2024

Tree-like Resolution proves the unsatisfiability of a CNF $\varphi$ by giving a decision tree for the falsified clause problem. The leaves of the free form a partition of $\{0,1\}^n$ into “monochromatic” subcubes, each of which is a strengthening of a negation of a term of $\varphi$.

We consider the HITTING proof system, in which a CNF is refuted by giving a partition of $\{0,1\}^n$ into monochromatic subcubes, and analyze its relation to other proof systems. We also consider a linear analog of HITTING which is a generalization of Tree-like Resolution over linear forms.

The work is part of a three paper series. The first part is about partitions of $\mathbb{F}_q^n$ into affine subspaces, and the second part is about partitions of $\{0,1\}^n$ into subcubes.


 author = {Filmus, Yuval and Hirsch, Edward A. and Riazanov, Artur and Smal, Alexander and Vinyals, Marc},
 title = {{Proving Unsatisfiability with Hitting Formulas}},
 booktitle = {15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
 pages = {48:1--48:20},
 series = {Leibniz International Proceedings in Informatics (LIPIcs)},
 ISBN = {978-3-95977-309-6},
 ISSN = {1868-8969},
 year = {2024},
 volume = {287},
 editor = {Guruswami, Venkatesan},
 publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
 address = {Dagstuhl, Germany},
 URL = {},
 URN = {urn:nbn:de:0030-drops-195762},
 doi = {10.4230/LIPIcs.ITCS.2024.48},
 annote = {Keywords: hitting formulas, polynomial identity testing, query complexity}
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