An Ising Model inspired Extension of the Product-based MP Framework for SAT

ABSTRACT. Message Passing (MP) has been presented in a unified and consistent notational frame in \cite{gableske}. The paper explained the product-based MP framework (PMPF) and various MP heuristics (BP, SP, and several interpolations). The paper concluded, that an increased flexibility of MP heuristics (in the form of tuneable parameters) leads to a tuneable MP algorithm that can be helpful to solve a wide variety of different CNFs. Based on this work, the paper at hand makes three contributions. First, we extend the PMPF regarding flexibility based on theoretical insights from the Ising Model \cite{ising}. As an immediate result, this extended PMPF (ePMPF) provides new possibilities for parameter tuning. Second, the ePMPF will also allow us to uncover various theoretical connections between well-known variable and value ordering heuristics for SAT (Zero-first, One-first, occurrence-based heuristics). We show, that these heuristics can be understood as special cases of Message Passing. Third, we show that the ePMPF provides numerous possibilities to tightly integrate Message Passing with various aspects of the CDCL search paradigm.