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

TL;DR

This paper introduces a novel framework that leverages d-DNNF knowledge compilation for efficient SMT query answering across various theories, combining propositional and SMT reasoning.

Contribution

It presents a general, theory-agnostic technique to perform polynomial-time SMT queries using d-DNNF compilation and pre-computed lemmas, compatible with existing tools.

Findings

The approach works for all theories and their combinations.

It can be implemented on top of existing d-DNNF and SMT tools.

Preliminary experiments show promising effectiveness.

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.