Theory and Applications of Satisfiability Testing

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos New York University, NY, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany 3569 Fahiem Bacchus Toby Walsh (Eds.) Theory andApplications of Satisfiability Testing 8th International Conference, SAT 2005 St Andrews, UK, June 19-23, 2005 Proceedings 13 Volume Editors Fahiem Bacchus University of Toronto, Department of Computer Science 6 King’s College Road, Toronto, Ontario, M5S 3H5, Canada E-mail: fbacchus@cs.toronto.edu Toby Walsh National ICT Australia and University of New South Wales School of Computer Science and Engineering Sydney 2502, Australia E-mail: tw@cse.unsw.edu.au Library of Congress Control Number: 2005927321 CR Subject Classification (1998): F.4.1, I.2.3, I.2.8, I.2, F.2.2, G.1.6 ISSN ISBN-10 ISBN-13 0302-9743 3-540-26276-8 Springer Berlin Heidelberg New York 978-3-540-26276-3 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Printed on acid-free paper SPIN: 11499107 06/3142 543210 Preface The 8th International Conference on Theory and Applications of Satisfiability Testing (SAT 2005) provided an international forum for the most recent research on the satisfiablity problem (SAT). SAT is the classic problem of determining whether or not a propositional formula has a satisfying truth assignment. It was the first problem shown by Cook to be NP-complete. Despite its seemingly specialized nature, satisfiability testing has proved to extremely useful in a wide range of different disciplines, both from a practical as well as from a theoretical point of view. For example, work on SAT continues to provide insight into various fundamental problems in computation, and SAT solving technology has advanced to the point where it has become the most effective way of solving a number of practical problems. The SAT series of conferences are multidisciplinary conferences intended to bring together researchers from various disciplines who are interested in SAT. Topics of interest include, but are not limited to: proof systems and proof complexity; search algorithms and heuristics; analysis of algorithms; theories beyond the propositional; hard instances and random formulae; problem encodings; industrial applications; solvers and other tools. This volume contains the papers accepted for presentation at SAT 2005. The conference attracted a record number of 73 submissions. Of these, 26 papers were accepted for presentation in the technical programme. In addition, 16 papers were accepted as shorter papers and were presented as posters during the technical programme. The accepted papers and poster papers cover the full range of topics listed in the call for papers. We would like to thank a number of people and organizations: Ian Miguel, the Local Chair who helped us organize the conference remotely; our generous sponsors who helped us to keep costs down, especially for students; Daniel Le Berre and Laurent Simon for once again organizing the SAT Solver Competition; and Massimo Narizzano and Armando Tacchella for the QBF Solver Evaluation. We would also like to thank the members of the Programme Committee and the additional referees who contributed in the paper-reviewing process. St Andrews June 2005 Fahiem Bacchus, Toby Walsh Organization Conference Organization Conference Chairs: Fahiem Bacchus (University of Toronto, Canada) Toby Walsh (National ICT Australia and University of NSW, Australia) Local Chair: Ian Miguel (University of St Andrews, UK) Programme Committee Dimitris Achlioptas Fadi Aloul Clark Barrett Constantinos Bartzis Paul Beame Armin Biere Ronen Brafman Alessandro Cimatti Adnan Darwiche Alvaro del Val Enrico Giunchiglia Eugene Goldberg Ziyad Hanna Edward Hirsch Henry Kautz Eleftherios Kirousis Hans Kleine Büning Daniel Le Berre Chu-Min Li Fangzhen Lin Sharad Malik João Marques-Silva Ilkka Niemela Toniann Pitassi Steve Prestwich Jussi Rintanen Lakhdar Sais Karem Sakallah Laurent Simon Stefan Szeider Mirek Truszczynski Allen Van Gelder Hans van Maaren Lintao Zhang Sponsors Cadence Design Systems Intel Corporation Intelligence Information Systems Institute, Cornell Microsoft Research CoLogNet Network of Excellence Additional Referees Zaher S. Andraus Pierre Bonami Uwe Bubeck Yin Chen Sylvie Coste-Marquis Nadia Creignou Stefan Dantchev Sylvain Darras Gilles Dequen Laure Devendeville Niklas Een Malay K. Ganai VIII Organization Aarti Gupta Jean-Luc Guerin Keijo Heljanko Jinbo Huang Dmitry Itsyson Matti Järvisalo Tommi Junttila Bernard Jurkowiak Zurab Khasidashvili Arist Kojevnikov Ioannis Koutis Alexander Kulikov Oliver Kullman Theodor Lettmann Lengning Liu Ines Lynce Yogesh Mahajan Marco Maratea Victor Marek Bertrand Mazure Maher N. Mneimneh Alexander Nadel Massimo Narizzano Sergey Nikolenko Nishant Ninha Thomas Schiex Armando Tacchella Muralidhar Talupur Daijue Tang Yinlei Yu Table of Contents Preface Solving Over-Constrained Problems with SAT Technology Josep Argelich, Felip Manyà . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 A Symbolic Search Based Approach for Quantified Boolean Formulas Gilles Audemard, Lakhdar Saı̈s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Substitutional Definition of Satisfiability in Classical Propositional Logic Anton Belov, Zbigniew Stachniak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 A Clause-Based Heuristic for SAT Solvers Nachum Dershowitz, Ziyad Hanna, Alexander Nadel . . . . . . . . . . . . . . . 46 Effective Preprocessing in SAT Through Variable and Clause Elimination Niklas Eén, Armin Biere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 Resolution and Pebbling Games Nicola Galesi, Neil Thapen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Local and Global Complete Solution Learning Methods for QBF Ian P. Gent, Andrew G.D. Rowley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Equivalence Checking of Circuits with Parameterized Specifications Eugene Goldberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Observed Lower Bounds for Random 3-SAT Phase Transition Density Using Linear Programming Marijn Heule, Hans van Maaren . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 Simulating Cutting Plane Proofs with Restricted Degree of Falsity by Resolution Edward A. Hirsch, Sergey I. Nikolenko . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 Resolution Tunnels for Improved SAT Solver Performance Michal Kouril, John Franco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Diversification and Determinism in Local Search for Satisfiability Chu Min Li, Wen Qi Huang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 X Table of contents On Finding All Minimally Unsatisfiable Subformulas Mark H. Liffiton, Karem A. Sakallah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Optimizations for Compiling Declarative Models into Boolean Formulas Darko Marinov, Sarfraz Khurshid, Suhabe Bugrara, Lintao Zhang, Martin Rinard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Random Walk with Continuously Smoothed Variable Weights Steven Prestwich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 Derandomization of PPSZ for Unique-k-SAT Daniel Rolf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 Heuristics for Fast Exact Model Counting Tian Sang, Paul Beame, Henry Kautz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226 A Scalable Method for Solving Satisfiability of Integer Linear Arithmetic Logic Hossein M. Sheini, Karem A. Sakallah . . . . . . . . . . . . . . . . . . . . . . . . . . . 241 DPvis - A Tool to Visualize the Structure of SAT Instances Carsten Sinz, Edda-Maria Dieringer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 Constraint Metrics for Local Search Finnegan Southey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Input Distance and Lower Bounds for Propositional Resolution Proof Length Allen Van Gelder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282 Sums of Squares, Satisfiability and Maximum Satisfiability Hans van Maaren, Linda van Norden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Faster Exact Solving of SAT Formulae with a Low Number of Occurrences per Variable Magnus Wahlström . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 A New Approach to Model Counting Wei Wei, Bart Selman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324 Benchmarking SAT Solvers for Bounded Model Checking Emmanuel Zarpas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 Model-Equivalent Reductions Xishun Zhao, Hans Kleine Büning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Table of Contents XI Improved Exact Solvers for Weighted Max-SAT Teresa Alsinet, Felip Manyà, Jordi Planes . . . . . . . . . . . . . . . . . . . . . . . . 371 Quantifier Trees for QBFs Marco Benedetti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378 Quantifier Rewriting and Equivalence Models for Quantified Horn Formulas Uwe Bubeck, Hans Kleine Büning, Xishun Zhao . . . . . . . . . . . . . . . . . . . 386 A Branching Heuristics for Quantified Renamable Horn Formulas Sylvie Coste-Marquis, Daniel Le Berre, Florian Letombe . . . . . . . . . . . . 393 An Improved Upper Bound for SAT Evgeny Dantsin, Alexander Wolpert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 Bounded Model Checking with QBF Nachum Dershowitz, Ziyad Hanna, Jacob Katz . . . . . . . . . . . . . . . . . . . . 408 Variable Ordering for Efficient SAT Search by Analyzing Constraint-Variable Dependencies Vijay Durairaj, Priyank Kalla . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Cost-Effective Hyper-Resolution for Preprocessing CNF Formulas Roman Gershman, Ofer Strichman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Automated Generation of Simplification Rules for SAT and MAXSAT Alexander S. Kulikov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 Speedup Techniques Utilized in Modern SAT Solvers Matthew D.T. Lewis, Tobias Schubert, Bernd W. Becker . . . . . . . . . . . . 437 FPGA Logic Synthesis Using Quantified Boolean Satisfiability Andrew Ling, Deshanand P. Singh, Stephen D. Brown . . . . . . . . . . . . . . 444 On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization Vasco Manquinho, João Marques-Silva . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451 A New Set of Algebraic Benchmark Problems for SAT Solvers Andreas Meier, Volker Sorge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 A Branch-and-Bound Algorithm for Extracting Smallest Minimal Unsatisfiable Formulas Maher Mneimneh, Inês Lynce, Zaher Andraus, João Marques-Silva, Karem Sakallah . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 XII Table of contents Threshold Behaviour of WalkSAT and Focused Metropolis Search on Random 3-Satisfiability Sakari Seitz, Mikko Alava, Pekka Orponen . . . . . . . . . . . . . . . . . . . . . . . . 475 On Subsumption Removal and On-the-Fly CNF Simplification Lintao Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491