Joao Marques-Silva

Theory and Applications of Satisfiability Testing (SAT 2007)

SAT: Past and Future.- Encodings of Problems in Effectively Propositional Logic.- Efficient Circuit to CNF Conversion.- Mapping CSP into Many-Valued SAT.- Circuit Based Encoding of CNF Formula.- Breaking Symmetries in SAT Matrix Models.- Partial Max-SAT Solvers with Clause Learning.- MiniMaxSat: A New Weighted Max-SAT Solver.- Solving Multi-objective Pseudo-Boolean Problems.- Improved Lower Bounds for Tree-Like Resolution over Linear Inequalities.- Horn Upper Bounds and Renaming.- Matched Formulas and Backdoor Sets.- Short XORs for Model Counting: From Theory to Practice.- Variable Dependency in Local Search: Prevention Is Better Than Cure.- Combining Adaptive Noise and Look-Ahead in Local Search for SAT.- From Idempotent Generalized Boolean Assignments to Multi-bit Search.- Satisfiability with Exponential Families.- Formalizing Dangerous SAT Encodings.- Algorithms for Variable-Weighted 2-SAT and Dual Problems.- On the Boolean Connectivity Problem for Horn Relations.- A First Step Towards a Unified Proof Checker for QBF.- Dynamically Partitioning for Solving QBF.- Backdoor Sets of Quantified Boolean Formulas.- Bounded Universal Expansion for Preprocessing QBF.- Effective Incorporation of Double Look-Ahead Procedures.- Applying Logic Synthesis for Speeding Up SAT.- Towards a Better Understanding of the Functionality of a Conflict-Driven SAT Solver.- A Lightweight Component Caching Scheme for Satisfiability Solvers.- Minimum 2CNF Resolution Refutations in Polynomial Time.- Polynomial Time SAT Decision for Complementation-Invariant Clause-Sets, and Sign-non-Singular Matrices.- Verifying Propositional Unsatisfiability: Pitfalls to Avoid.- A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories.- SAT Solving for Termination Analysis with Polynomial Interpretations.- Fault Localization and Correction with QBF.- Sensor Deployment for Failure Diagnosis in Networked Aerial Robots: A Satisfiability-Based Approach.- Inversion Attacks on Secure Hash Functions Using sat Solvers.

SMT-Based Bounded Model Checking for Embedded ANSI-C Software

Propositional bounded model checking has been applied successfully to verify embedded software, but remains limited by increasing propositional formula sizes and the loss of high-level information during the translation preventing potential optimizations to reduce the state space to be explored. These limitations can be overcome by encoding high-level information in theories richer than propositional logic and using SMT solvers for the generated verification conditions. Here, we propose the application of different background theories and SMT solvers to the verification of embedded software written in ANSI-C in order to improve scalability and precision in a completely automatic way. We have modified and extended the encodings from previous SMT-based bounded model checkers to provide more accurate support for variables of finite bit width, bit-vector operations, arrays, structures, unions, and pointers. We have integrated the CVC3, Boolector, and Z3 solvers with the CBMC front-end and evaluated them using both standard software model checking benchmarks and typical embedded software applications from telecommunications, control systems, and medical devices. The experiments show that our ESBMC model checker can analyze larger problems than existing tools and substantially reduce the verification time.

The Impact of Branching Heuristics in Propositional Satisfiability Algorithms

This paper studies the practical impact of the branching heuristics used in Propositional Satisfiability (SAT) algorithms, when applied to solving real-world instances of SAT. In addition, different SAT algorithms are experimentally evaluated. The main conclusion of this study is that even though branching heuristics are crucial for solving SAT, other aspects of the organization of SAT algorithms are also essential. Moreover, we provide empirical evidence that for practical instances of SAT, the search pruning techniques included in the most competitive SAT algorithms may be of more fundamental significance than branching heuristics.

Algorithms for Weighted Boolean Optimization

The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT) problems are natural optimization extensions of Boolean Satisfiability (SAT). In the recent past, different algorithms have been proposed for PBO and for MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT, and vice-versa. This papers proposes Weighted Boolean Optimization (WBO), a new unified framework that aggregates and extends PBO and MaxSAT. In addition, the paper proposes a new unsatisfiability-based algorithm for WBO, based on recent unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new algorithm can also be used to solve weighted MaxSAT and PBO, handling pseudo-Boolean constraints either natively or by translation to clausal form. Experimental results illustrate that unsatisfiability-based algorithms for MaxSAT can be orders of magnitude more efficient than existing dedicated algorithms. Finally, the paper illustrates how other algorithms for either PBO or MaxSAT can be extended to WBO.

Algorithms for maximum satisfiability using unsatisfiable cores

Many decision and optimization problems in electronic design automation (EDA) can be solved with Boolean satisfiability (SAT). Moreover, well-known extensions of SAT also find application in EDA, including pseudo-Boolean optimization, quantified Boolean formulas, multi-valued SAT and, more recently, Maximum Satisfiability (MaxSAT). Algorithms for MaxSAT are still fairly inefficient in industrial settings, in part because the most effective SAT techniques cannot be easily extended to MaxSAT. This paper proposes a novel algorithm for MaxSAT that improves existing state of the art solvers by orders of magnitude on industrial benchmarks. The new algorithm exploits modern SAT solvers, being based on the identification of unsatisfiable subformulas. Moreover, the new algorithm provides additional insights between unsatisfiable subformulas and the maximum satisfiability problem.

Iterative and core-guided MaxSAT solving: A survey and assessment

Maximum Satisfiability (MaxSAT) is an optimization version of SAT, and many real world applications can be naturally encoded as such. Solving MaxSAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in developing efficient algorithms and several families of algorithms have been proposed. This paper overviews recent approaches to handle MaxSAT and presents a survey of MaxSAT algorithms based on iteratively calling a SAT solver which are particularly effective to solve problems arising in industrial settings. First, classic algorithms based on iteratively calling a SAT solver and updating a bound are overviewed. Such algorithms are referred to as iterative MaxSAT algorithms. Then, more sophisticated algorithms that additionally take advantage of unsatisfiable cores are described, which are referred to as core-guided MaxSAT algorithms. Core-guided MaxSAT algorithms use the information provided by unsatisfiable cores to relax clauses on demand and to create simpler constraints. Finally, a comprehensive empirical study on non-random benchmarks is conducted, including not only the surveyed algorithms, but also other state-of-the-art MaxSAT solvers. The results indicate that (i) core-guided MaxSAT algorithms in general abort in less instances than classic solvers based on iteratively calling a SAT solver and that (ii) core-guided MaxSAT algorithms are fairly competitive compared to other approaches.

Boolean satisfiability in electronic design automation

Boolean Satisfiability (SAT) is often used as the underlying model for a significant and increasing number of applications in Electronic Design Automation (EDA) as well as in many other fields of Computer Science and Engineering. In recent years, new and efficient algorithms for SAT have been developed, allowing much larger problem instances to be solved. SAT “packages” are currently expected to have an impact on EDA applications similar to that of BDD packages since their introduction more than a decade ago. This tutorial paper is aimed at introducing the EDA professional to the Boolean satisfiability problem. Specifically, we highlight the use of SAT models to formulate a number of EDA problems in such diverse areas as test pattern generation, circuit delay computation, logic optimization, combinational equivalence checking, bounded model checking and functional test vector generation, among others. In addition, we provide an overview of the algorithmic techniques commonly used for solving SAT, including those that have seen widespread use in specific EDA applications. We categorize these algorithmic techniques, indicating which have been shown to be best suited for which tasks.

Combinational equivalence checking using satisfiability and recursive learning

The problem of checking the equivalence of combinational circuits is of key significance in the verification of digital circuits. Previously, several approaches have been proposed for solving this problem. Still, the hardness of the problem and the ever-growing complexity of logic circuits motivates studying and developing alternative solutions. In this paper we study the application of Boolean satisfiability (SAT) algorithms for solving the combinational equivalence checking (CEC) problem. Although existing SAT algorithms are in general ineffective for solving CEC, in this paper we show how to improve SAT algorithms by extending and applying recursive learning techniques to the analysis of instances of SAT. This in turn provides a new alternative and competitive approach for solving CEC. Preliminary experimental results indicate that the proposed improved SAT algorithm can be useful for a large variety of instances of CEC, in particular when compared with pure BDD-based approaches.

Towards robust CNF encodings of cardinality constraints

Motivated by the performance improvements made to SAT solvers in recent years, a number of different encodings of constraints into SAT have been proposed. Concrete examples are the different SAT encodings for ≤ 1 (x1, . . . , xn) constraints. The most widely used encoding is known as the pairwise encoding, which is quadratic in the number of variables in the constraint. Alternative encodings are in general linear, and require using additional auxiliary variables. In most settings, the pairwise encoding performs acceptably well, but can require unacceptably large Boolean formulas. In contrast, linear encodings yield much smaller Boolean formulas, but in practice SAT solvers often perform unpredictably. This lack of predictability is mostly due to the large number of auxiliary variables that need to be added to the resulting Boolean formula. This paper studies one specific encoding for ≤ 1 (x1, . . . , xn) constraints, and shows how a state-of-the-art SAT solver can be adapted to overcome the problem of adding additional auxiliary variables. Moreover, the paper shows that a SAT solver may essentially ignore the existence of auxiliary variables. Experimental results indicate that the modified SAT solver becomes significantly more robust on SAT encodings involving ≤ 1 (x1, . . . , xn) constraints.

Towards efficient MUS extraction

Minimally Unsatisfiable Subformulas (MUS) find a wide range of practical applications, including product configuration, knowledge-based validation, and hardware and software design and verification. MUSes also find application in recent Maximum Satisfiability algorithms and in CNF formula redundancy removal. Besides direct applications in Propositional Logic, algorithms for MUS extraction have been applied to more expressive logics. This paper proposes two algorithms for computation of MUSes of propositional formulas in Conjunctive Normal Form (CNF). The first algorithm is optimal in its class, meaning that it requires the smallest number of calls to a SAT solver. The second algorithm extends earlier work, but implements a number of new techniques. Among these, this paper analyzes in detail the technique of recursive model rotation, which provides significant performance gains in practice. Experimental results, obtained on representative practical benchmarks, indicate that the new algorithms achieve significant performance gains with respect to state of the art MUS extraction algorithms.