Vasco M. Manquinho

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.

Prime implicant computation using satisfiability algorithms

The computation of prime implicants has several and significant applications in different areas, including automated reasoning, non-monotonic reasoning, electronic design automation, among others. The authors describe a new model and algorithm for computing minimum-size prime implicants of propositional formulas. The proposed approach is based on creating an integer linear program (ILP) formulation for computing the minimum-size prime implicant, which simplifies existing formulations. In addition, they introduce two new algorithms for solving ILPs, both of which are built on top of an algorithm for propositional satisfiability (SAT). Given the organization of the proposed SAT algorithm, the resulting ILP procedures implement powerful search pruning techniques, including a non-chronological backtracking search strategy, clause recording procedures and identification of necessary assignments. Experimental results, obtained on several benchmark examples, indicate that the proposed model and algorithms are significantly more efficient than other existing solutions.

Open-WBO: A Modular MaxSAT Solver,

This paper presents open-wbo, a new MaxSAT solver. open-wbo has two main features. First, it is an open-source solver that can be easily modified and extended. Most MaxSAT solvers are not available in open-source, making it hard to extend and improve current MaxSAT algorithms. Second, open-wbo may use any MiniSAT-like solver as the underlying SAT solver. As many other MaxSAT solvers, open-wbo relies on successive calls to a SAT solver. Even though new techniques are proposed for SAT solvers every year, for many MaxSAT solvers it is hard to change the underlying SAT solver. With open-wbo, advances in SAT technology will result in a free improvement in the performance of the solver. In addition, the paper uses open-wbo to evaluate the impact of using different SAT solvers in the performance of MaxSAT algorithms.

Incremental Cardinality Constraints for MaxSAT

Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality constraints. Many of these algorithms are non-incremental in nature, i.e. at each iteration the formula is rebuilt and no knowledge is reused from one iteration to another. In this paper, we exploit the knowledge acquired across iterations using novel schemes to use cardinality constraints in an incremental fashion. We integrate these schemes with several MaxSAT algorithms. Our experimental results show a significant performance boost for these algorithms as compared to their non-incremental counterparts. These results suggest that incremental cardinality constraints could be beneficial for other constraint solving domains.

Towards more effective unsatisfiability-based maximum satisfiability algorithms

The MaxSAT problem and some of its well-known variants find an increasing number of practical applications in a wide range of areas. Examples include different optimization problems in system design and verification. However, most MaxSAT problem instances from these practical applications are too hard for existing branch and bound algorithms. One recent alternative to branch and bound MaxSAT algorithms is based on unsatisfiable subformula identification. A number of different unsatisfiability-based MaxSAT algorithms have been developed, which are effective at solving different classes of problem instances. All MaxSAT algorithms based on unsatisfiable subformula identification require using additional Boolean variables, either to allow relaxing some of the clauses or to encode cardinality constraints used by these algorithms. As a result, these algorithms may require using a significant number of additional Boolean variables, that can exceed the original number of variables for some problem instances. This paper proposes techniques for effectively reducing the number of auxiliary variables that must be used in unsatisfiability-based MaxSAT algorithms. Experimental results indicate that the techniques for reducing the number of auxiliary variables are effective, and contribute to more efficient MaxSAT algorithms.

Search pruning techniques in SAT-based branch-and-bound algorithms for the binate covering problem

Covering problems are widely used as a modeling tool in electronic design automation. Recent years have seen dramatic improvements in algorithms for the unate/binate covering problem (UCP/BCP). Despite these improvements, BCP is a well-known computationally hard problem with many existing real-world instances that currently are hard or even impossible to solve. In this paper we apply search pruning techniques from the Boolean satisfiability domain to branch-and-bound algorithms for BCP. Furthermore, we generalize these techniques, in particular the ability to infer and record new constraints from conflicts and the ability to backtrack nonchronologically, to situations where the branch-and-bound BCP algorithm backtracks due to bounding conditions. Experimental results, obtained on representative real-world instances of the UCP/BCP, indicate that the proposed techniques are effective and can provide significant performance gains for specific classes of instances.

An overview of parallel SAT solving

Boolean satisfiability (SAT) solvers are currently very effective in practice. However, there are still many challenging problems for SAT solvers. Nowadays, extra computational power is no longer coming from higher processor frequencies. At the same time, multicore architectures are becoming predominant. Exploiting this new architecture is essential for the evolution of SAT solvers. Due to the increasing interest in parallel SAT solving, it is important to give an overview of what has been done so far. This paper presents an overview of parallel SAT solving and it is expected to be a valuable document for researchers in this field. This overview covers the main topics of parallel SAT solving, namely, different approaches and a variety of clause sharing strategies. Additionally, an evaluation of multicore SAT solvers is presented, showing the evolution of multicore SAT solvers over the last years.

Effective lower bounding techniques for pseudo-Boolean optimization [EDA applications]

Linear pseudo-Boolean optimization (PBO) is a widely used modeling framework in electronic design automation (EDA). Due to significant advances in Boolean satisfiability (SAT), new algorithms for PBO have emerged, which are effective on highly constrained instances. However, these algorithms fail to handle effectively the information provided by the cost function of PBO. This paper addresses the integration of lower bound estimation methods with SAT-related techniques in PBO solvers. Moreover, the paper shows that the utilization of lower bound estimates can dramatically improve the overall performance of PBO solvers for most existing benchmarks from EDA.

Improving Search Space Splitting for Parallel SAT Solving

The last two decades progresses have led Propositional Satisfiability (SAT) to be a competitive practical approach to solve a wide range of industrial and academic problems. Thanks to these advances, the size and difficulty of the SAT instances have grown significantly. The demand for more computational power led to the creation of new computer architectures and paradigms composed by multiple machines connected by a network to act as one machine, like clusters and grids. However, extra computing power is not coming anymore from higher processor frequencies, but rather from a growing number of computing cores and processors. It becomes clear that exploiting this new architecture is essential for the evolution of SAT solvers. Search space splitting is probably the most commonly used strategy to explore the parallelism provided by the search space. However, it is not clear how to find the relevant set of variables to divide the search space. This paper extends a method based on the VSIDS heuristic to find the initial set of partition variables. A drawback of search space splitting is load balancing. To overcome this problem, we propose the use of a hybrid approach between search space splitting and portfolio. Preliminary results show that both these techniques improve the performance of the solver and reveal that combining search space splitting and portfolio approaches can lead to better results.

Improving unsatisfiability-based algorithms for boolean optimization

Recently, several unsatisfiability-based algorithms have been proposed for Maximum Satisfiability (MaxSAT) and other Boolean Optimization problems. These algorithms are based on being able to iteratively identify and relax unsatisfiable sub-formulas with the use of fast Boolean satisfiability solvers. It has been shown that this approach is very effective for several classes of instances, but it can perform poorly on others for which classical Boolean optimization algorithms find it easy to solve. This paper proposes the use of Pseudo-Boolean Optimization (PBO) solvers as a preprocessor for unsatisfiability-based algorithms in order to increase its robustness. Moreover, the use of constraint branching, a well-known technique from Integer Linear Programming, is also proposed into the unsatisfiability-based framework. Experimental results show that the integration of these features in an unsatisfiability-based algorithm results in an improved and more effective solver for Boolean optimization problems.