Proof Complexity of Propositional Model Counting

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 MIC E ′ that is polynomially equivalent to MICE. We then establish an exponential lower bound for the number of proof steps in MIC E ′ (and hence also in MICE) for a specific family of CNFs. We also explain a tight connection between MIC E ′ proofs and decision DNNFs.