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Certified Knowledge Compilation with Application to Verified Model Counting

Authors Randal E. Bryant , Wojciech Nawrocki , Jeremy Avigad , Marijn J. H. Heule



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Author Details

Randal E. Bryant
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Wojciech Nawrocki
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA
Jeremy Avigad
  • Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA, USA
Marijn J. H. Heule
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA

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Randal E. Bryant, Wojciech Nawrocki, Jeremy Avigad, and Marijn J. H. Heule. Certified Knowledge Compilation with Application to Verified Model Counting. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 6:1-6:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.SAT.2023.6

Abstract

Computing many useful properties of Boolean formulas, such as their weighted or unweighted model count, is intractable on general representations. It can become tractable when formulas are expressed in a special form, such as the decision-decomposable, negation normal form (dec-DNNF) . Knowledge compilation is the process of converting a formula into such a form. Unfortunately existing knowledge compilers provide no guarantee that their output correctly represents the original formula, and therefore they cannot validate a model count, or any other computed value. We present Partitioned-Operation Graphs (POGs), a form that can encode all of the representations used by existing knowledge compilers. We have designed CPOG, a framework that can express proofs of equivalence between a POG and a Boolean formula in conjunctive normal form (CNF). We have developed a program that generates POG representations from dec-DNNF graphs produced by the state-of-the-art knowledge compiler D4, as well as checkable CPOG proofs certifying that the output POGs are equivalent to the input CNF formulas. Our toolchain for generating and verifying POGs scales to all but the largest graphs produced by D4 for formulas from a recent model counting competition. Additionally, we have developed a formally verified CPOG checker and model counter for POGs in the Lean 4 proof assistant. In doing so, we proved the soundness of our proof framework. These programs comprise the first formally verified toolchain for weighted and unweighted model counting.

Subject Classification

ACM Subject Classification
  • Theory of computation → Automated reasoning
Keywords
  • Propositional model counting
  • Proof checking

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