Top-Down Knowledge Compilation for Counting Modulo Theories
This work addresses the understudied area of knowledge compilation for #SMT, which is incremental as it adapts existing top-down techniques from propositional model counting to the modulo theory context.
The paper tackles the problem of counting solutions modulo theories (#SMT) by proposing a top-down knowledge compilation method based on DPLL(T) search traces, aiming to efficiently compile formulas into deterministic decomposable negation normal form (d-DNNF) for this setting.
Propositional model counting (#SAT) can be solved efficiently when the input formula is in deterministic decomposable negation normal form (d-DNNF). Translating an arbitrary formula into a representation that allows inference tasks, such as counting, to be performed efficiently, is called knowledge compilation. Top-down knowledge compilation is a state-of-the-art technique for solving #SAT problems that leverages the traces of exhaustive DPLL search to obtain d-DNNF representations. While knowledge compilation is well studied for propositional approaches, knowledge compilation for the (quantifier free) counting modulo theory setting (#SMT) has been studied to a much lesser degree. In this paper, we discuss compilation strategies for #SMT. We specifically advocate for a top-down compiler based on the traces of exhaustive DPLL(T) search.