Preprocessing for Propositional Model Counting

This paper is concerned with preprocessing techniques for propositional model counting. We have implemented a preprocessor which includes many elementary preprocessing techniques, including occurrence reduction, vivification, backbone identification, as well as equivalence, AND and XOR gate identification and replacement. We performed intensive experiments, using a huge number of benchmarks coming from a large number of families. Two approaches to model counting have been considered downstream: "direct" model counting using Cachet and compilation-based model counting, based on the C2D compiler. The experimental results we have obtained show that our preprocessor is both efficient and robust.

[1]  Lucas Bordeaux,et al.  Knowledge Compilation Properties of Tree-of-BDDs , 2007, AAAI.

[2]  Lakhdar Sais,et al.  Tractable Cover Compilations , 1997, IJCAI.

[3]  Pierre Marquis,et al.  Extending the Knowledge Compilation Map: Krom, Horn, Affine and Beyond , 2008, AAAI.

[4]  Alvaro del Val Tractable Databases: How to Make Propositional Unit Resolution Complete Through Compilation , 1994, KR.

[5]  Hantao Zhang,et al.  An Efficient Algorithm for Unit Propagation , 1996 .

[6]  Toniann Pitassi,et al.  Combining Component Caching and Clause Learning for Effective Model Counting , 2004, SAT.

[7]  Gilles Audemard,et al.  Predicting Learnt Clauses Quality in Modern SAT Solvers , 2009, IJCAI.

[8]  Dan Roth,et al.  On the Hardness of Approximate Reasoning , 1993, IJCAI.

[9]  Lakhdar Sais,et al.  Vivifying Propositional Clausal Formulae , 2008, ECAI.

[10]  Paolo Liberatore,et al.  Redundancy in logic I: CNF propositional formulae , 2002, Artif. Intell..

[11]  Gilles Audemard,et al.  Just-In-Time Compilation of Knowledge Bases , 2013, IJCAI.

[12]  Olivier Roussel,et al.  Redundancy in Random SAT Formulas , 2000, AAAI/IAAI.

[13]  Lakhdar Sais,et al.  Recovering and Exploiting Structural Knowledge from CNF Formulas , 2002, CP.

[14]  Henry A. Kautz,et al.  Performing Bayesian Inference by Weighted Model Counting , 2005, AAAI.

[15]  Bart Selman,et al.  A New Approach to Model Counting , 2005, SAT.

[16]  Armin Biere,et al.  Efficient CNF Simplification Based on Binary Implication Graphs , 2011, SAT.

[17]  Adnan Darwiche,et al.  On probabilistic inference by weighted model counting , 2008, Artif. Intell..

[18]  Ronen I. Brafman,et al.  Lifted MEU by Weighted Model Counting , 2012, AAAI.

[19]  Blai Bonet,et al.  Pruning Conformant Plans by Counting Models on Compiled d-DNNF Representations , 2005, ICAPS.

[20]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[21]  Adnan Darwiche,et al.  Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence SDD: A New Canonical Representation of Propositional Knowledge Bases , 2022 .

[22]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[23]  Jean-Marie Lagniez,et al.  Knowledge Compilation for Model Counting: Affine Decision Trees , 2013, IJCAI.

[24]  Adnan Darwiche,et al.  Decomposable negation normal form , 2001, JACM.

[25]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[26]  Fabio Somenzi,et al.  Alembic: An Efficient Algorithm for CNF Preprocessing , 2007, 2007 44th ACM/IEEE Design Automation Conference.

[27]  Mikolás Janota,et al.  On Unit-Refutation Complete Formulae with Existentially Quantified Variables , 2012, KR.

[28]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[29]  Dhiraj K. Pradhan,et al.  NiVER: Non Increasing Variable Elimination Resolution for Preprocessing SAT instances , 2004, SAT.

[30]  Armin Biere,et al.  Effective Preprocessing in SAT Through Variable and Clause Elimination , 2005, SAT.

[31]  Inês Lynce,et al.  Probing-based preprocessing techniques for propositional satisfiability , 2003, Proceedings. 15th IEEE International Conference on Tools with Artificial Intelligence.

[32]  Fahiem Bacchus,et al.  Effective Preprocessing with Hyper-Resolution and Equality Reduction , 2003, SAT.

[33]  Joao Marques-Silva,et al.  Knowledge Compilation with Empowerment , 2012, SOFSEM.

[34]  Meinolf Sellmann,et al.  Streamlined Constraint Reasoning , 2004, CP.

[35]  Armin Biere,et al.  Simulating Circuit-Level Simplifications on CNF , 2011, Journal of Automated Reasoning.

[36]  Armin Biere,et al.  Clause Elimination Procedures for CNF Formulas , 2010, LPAR.

[37]  Carmel Domshlak,et al.  Fast Probabilistic Planning through Weighted Model Counting , 2006, ICAPS.