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Paper:

TR24-030 | 22nd February 2024 12:09

Proof Complexity of Propositional Model Counting

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TR24-030
Authors: Olaf Beyersdorff, Tim Hoffmann, Luc Nicolas Spachmann
Publication: 22nd February 2024 12:46
Downloads: 84
Keywords: 


Abstract:

Recently, the proof system MICE for the model counting problem #SAT was introduced by Fichte, Hecher and Roland (SAT’22). As demonstrated by Fichte et al., the system MICE can be used for proof logging for state-of-the-art #SAT solvers.
We perform a proof-complexity study of MICE. For this we first simplify the rules of MICE and obtain a calculus MICE? that is polynomially equivalent to MICE. We then establish an exponential lower bound for the number of proof steps in MICE? (and hence also in MICE) for a specific family of CNFs. We also explain a tight connection between MICE proofs and decision DNNFs.



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