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arXiv · 2603.09975

d-DNNF Modulo Theories: A General Framework for Polytime SMT Queries

Gabriele Masina·Emanuele Civini·Massimo Michelutti·Giuseppe Spallitta·Roberto Sebastiani
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Abstract

In Knowledge Compilation (KC) a propositional knowledge base is compiled off-line into some target form, typically into deterministic decomposable negation normal form (d-DNNF) or one of its subcases, which is then used on-line to answer a large number of queries in polytime, such as clausal entailment, model counting, and others. The general idea is to push as much of the computational effort into the off-line compilation phase, which is amortized over all on-line polytime queries. In this paper, we present for the first time a novel and general technique to leverage d-DNNF compilation and querying to SMT level. Intuitively, before d-DNNF compilation, the input SMT formula is combined with a list of pre-computed ad-hoc theory lemmas, so that the queries at SMT level reduce to those at propositional level. This approach has several features: (i) it works for every theory, or theory combination thereof; (ii) it works for all forms of d-DNNF; (iii) it is easy to implement on top of any d-DNNF compiler and any theory-lemma enumerator, which are used as black boxes; (iv) most importantly, these compiled SMT d-DNNFs can be queried in polytime by means of a standard propositional d-DNNF reasoner. As proof of concept, we have implemented a tool on top of state-of-the-art d-DNNF packages and of the MathSAT SMT solver. Some preliminary empirical evaluation supports the effectiveness of the approach.

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Gabriele Masina, Emanuele Civini, Massimo Michelutti, Giuseppe Spallitta, Roberto Sebastiani. 2026-03-10. d-DNNF Modulo Theories: A General Framework for Polytime SMT Queries. https://arxiv.org/abs/2603.09975

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