MaxSAT Solvers Research Articles

To be precise: regression aware debugging

Bounded model checking based debugging solutions search for mutations of program expressions that produce the expected output for a currently failing test. However, the current localization tools are not regression aware : they do not use information from the passing tests in their localization formula. On the other hand, the current repair tools attempt to guarantee regression freedom : when provided with a set of passing tests, they guarantee that none of these tests can break due to the suggested repair patch, thereby constructing a large repair formula. In this paper, we propose regression awareness as a means to improve the quality of localization and to scale repair. To enable regression awareness, we summarize the proof of correctness of each passing test by computing Craig Interpolants over a symbolic encoding of the passing execution, and use these summaries as additional soft constraints while synthesizing altered executions corresponding to failing tests. Intuitively, these additional constraints act as roadblocks, thereby discouraging executions that may damage the proof of a passing test. We use a partial MAXSAT solver to relax the proofs in a systematic way, and use a ranking function that penalizes mutations that damage the existing proofs. We have implemented our algorithms into a tool, TINTIN, that enables regression aware localization and repair. For localizations, our strategy is effective in extracting a superior ranking of suspicious locations: on a set of 52 different versions across 12 different programs spanning three benchmark suites, TINTIN achieves a saving of developer effort by almost 45% (in terms of the locations that must be examined by a developer to reach the ground-truth repair) in the worst case and 27% in the average case over existing techniques. For automated repairs, on our set of benchmarks, TINTIN achieves a 2.3X speedup over existing techniques without sacrificing much on the ranking of the repair patches: the ground-truth repair appears as the topmost suggestion in more than 70% of our benchmarks.

MaxSAT by improved instance-specific algorithm configuration

Our objective is to boost the state-of-the-art performance in MaxSAT solving. To this end, we employ the instance-specific algorithm configurator ISAC, and improve it with the latest in portfolio technology. Experimental results on SAT show that this combination marks a significant step forward in our ability to tune algorithms instance-specifically. We then apply the new methodology to a number of MaxSAT problem domains and show that the resulting solvers consistently outperform the best existing solvers on the respective problem families. In fact, the solvers presented here were independently evaluated at the 2013 and 2014 MaxSAT Evaluations where they won several categories.

MiFuMax—a Literate MaxSAT Solver

The main motivation behind the MaxSAT solver MiFuMax is twofold. It provides a baseline implementation of core-based algorithms for both weighted and unweighted MaxSAT. Such baseline implementation may serve for evaluation of evolving solvers. MiFuMax is written in literate programming and as such is instructive for anyone interested in learning about the implementation of modern core-based MaxSAT solvers. Despite its educative background, the solver has placed 1st in the Unweighted Max-SAT-Industrial track of the 2013 MaxSAT Evaluation and it has been successfully applied in other research.

Ahmaxsat: Description and Evaluation of a Branch and Bound Max-SAT Solver

Branch and bound (BnB) solvers for Max-SAT count at each node of the search tree the number of disjoint inconsistent subsets to compute the lower bound. In the last ten years, important advances have been made regarding the lower bound computation. Unit propagation based methods have been introduced to detect inconsistent subsets and a resolution-like inference rules have been proposed which allow a more incremental lower bound computation. We present in this paper our solver Ahmaxsat, which uses these new methods and improves them in several ways. The main contributions of our solver over the state of the art are: a new unit propagation scheme which considers all the variable propagation sources; extended sets of patterns which increase the amount of learning performed by the solver; a heuristic which modifies the order of application of the max-resolution rule when transforming inconsistent subset; and a new inconsistent subset treatment method which improves the lower bound estimation. We describe these four main contributions and we give a general overview of \ahmaxsat, with additional implementation details. Finally, we present the result of the experimental study we have conducted. We first evaluate the impact of each contribution on \ahmaxsat performances before comparing our solver to the current best performing BnB solvers. The obtained results confirm the ones of the Max-SAT Evaluation 2014 where \ahmaxsat was ranked first in three of the nine categories.

Solving #SAT and MAXSAT by Dynamic Programming

We look at dynamic programming algorithms for propositional model counting, also called #SAT, and MaxSAT. Tools from graph structure theory, in particular treewidth, have been used to successfully identify tractable cases in many subfields of AI, including SAT, Constraint Satisfaction Problems (CSP), Bayesian reasoning, and planning. In this paper we attack #SAT and MaxSAT using similar, but more modern, graph structure tools. The tractable cases will include formulas whose class of incidence graphs have not only unbounded treewidth but also unbounded clique-width. We show that our algorithms extend all previous results for MaxSAT and #SAT achieved by dynamic programming along structural decompositions of the incidence graph of the input formula. We present some limited experimental results, comparing implementations of our algorithms to state-of-the-art #SAT and MaxSAT solvers, as a proof of concept that warrants further research.

Probabilistic satisfiability: algorithms with the presence and absence of a phase transition

We study algorithms for probabilistic satisfiability (PSAT), an NP-complete problem that is central to logic-probabilisti reasoning, focusing on the presence and absence of a phase transition phenomenon for each algorithm. Our study starts by defining a PSAT normal form, on which all algorithms are based. The proposed algorithms consist of several forms of reductions of PSAT to classical propositional satisfiability (SAT). The first algorithm is a canonical reduction of PSAT instances to SAT instances; three other algorithms are reductions to linear optimization with distinct column generation procedures, namely on auxiliary calls to SAT, weighted MAXSAT or SMT solvers. Theoretical and practical limitations of each algorithm are discussed. Several implementations were developed and compared by means of experiments using randomly generated input problems. Some of the implementations are shown to present a phase transition behavior. We show that variations of these algorithms may lead to the partial occlusion of the phase transition phenomenon and discuss the reasons for this change ofc practical behavior.

Crowdsourced Action-Model Acquisition for Planning

AI planning techniques often require a given set of action models provided as input. Creating action models is, however, a difficult task that costs much manual effort. The problem of action-model acquisition has drawn a lot of interest from researchers in the past. Despite the success of the previous systems, they are all based on the assumption that there are enough training examples for learning high-quality action models. In many real-world applications, e.g., military operation, collecting a large amount of training examples is often both difficult and costly. Instead of collecting training examples, we assume there are abundant annotators, i.e., the crowd, available to provide information learning action models. Specifically, we first build a set of soft constraints based on the labels (true or false) given by the crowd or annotators. We then builds a set of soft constraints based on the input plan traces. After that we put all the constraints together and solve them using a weighted MAX-SAT solver, and convert the solution of the solver to action models. We finally exhibit that our approach is effective in the experiment.

MaxSAT-based encodings for Group MaxSAT

Weighted Partial MaxSAT (WPMS) is a well-known optimization variant of Boolean Satisfiability (SAT) that finds a wide range of practical applications. WPMS divides the formula in two sets of clauses: The hard clauses that must be satisfied and the soft clauses that can be falsified with a penalty given by their associated weight. However, some applications may require each original constraint to be modeled as a set or group of clauses. Then, the cost or penalty of falsifying one or several clauses of the same group is exactly the same. The resulting formalism is referred to as Group MaxSAT. This paper overviews Group MaxSAT, and shows how several optimization problems can be modeled as Group MaxSAT. Several encodings from Group MaxSAT to standard MaxSAT are formalized and refined. A comprehensive empirical study compares the performance of several MaxSAT solvers with the proposed encodings. The results indicate that, depending on the underlying MaxSAT solver and problem domain, the solver may perform better with a given encoding than with the others.

Maximum Satisfiability Using Core-Guided MaxSAT Resolution

Core-guided approaches to solving MAXSAT have proved to be effective on industrial problems. These approaches solve a MAXSAT formula by building a sequence of SAT formulas, where in each formula a greater weight of soft clauses can be relaxed. The soft clauses are relaxed via the addition of blocking variables, and the total weight of soft clauses that can be relaxed is limited by placing constraints on the blocking variables. In this work we propose an alternative approach. Our approach also builds a sequence of new SAT formulas. However, these formulas are constructed using MAXSAT resolution, a sound rule of inference for MAXSAT. MAXSAT resolution can in the worst case cause a quadratic blowup in the formula, so we propose a new compressed version of MAXSAT resolution. Using compressed MAXSAT resolution our new core-guided solver improves the state-of-theart, solving significantly more problems than other state-ofthe-art solvers on the industrial benchmarks used in the 2013 MAXSAT Solver Evaluation.

Learning hierarchical task network domains from partially observed plan traces

Hierarchical Task Network (HTN) planning is an effective yet knowledge intensive problem-solving technique. It requires humans to encode knowledge in the form of methods and action models. Methods describe how to decompose tasks into subtasks and the preconditions under which those methods are applicable whereas action models describe how actions change the world. Encoding such knowledge is a difficult and time-consuming process, even for domain experts. In this paper, we propose a new learning algorithm, called HTNLearn, to help acquire HTN methods and action models. HTNLearn receives as input a collection of plan traces with partially annotated intermediate state information, and a set of annotated tasks that specify the conditions before and after the tasks' completion. In addition, plan traces are annotated with potentially empty partial decomposition trees that record the processes of decomposing tasks to subtasks. HTNLearn outputs are a collection of methods and action models. HTNLearn first encodes constraints about the methods and action models as a constraint satisfaction problem, and then solves the problem using a weighted MAX-SAT solver. HTNLearn can learn methods and action models simultaneously from partially observed plan traces (i.e., plan traces where the intermediate states are partially observable). We test HTNLearn in several HTN domains. The experimental results show that our algorithm HTNLearn is both effective and efficient.

Authorization query method for RBAC based on partial MAX-SAT solver

In order to ensure system security and reflect availability in authorization management,a method for querying authorization was proposed based on solvers for partial maximal satisfiability problem.Static authorization descriptions and dynamic mutually exclusive constraints were translated into hard clauses.The algorithm was adopted to update hard clauses and translate requested permissions into soft clauses.Soft clauses were effectively encoded,and the recursive algorithm was utilized to satisfy all hard clauses and as many soft clauses as possible.The experimental results show that the method can ensure system security,it follows the least privilege principle,and the query efficiency outperforms solvers for maximal satisfiability problem.

Greedy or Not? Best Improving versus First Improving Stochastic Local Search for MAXSAT

Stochastic local search (SLS) is the dominant paradigm for incomplete SAT and MAXSAT solvers. Early studies on small 3SAT instances found that the use of “best improving” moves did not improve search compared to using an arbitrary “first improving” move. Yet SLS algorithms continue to use best improving moves. We revisit this issue by studying very large random and industrial MAXSAT problems. Because locating best improving moves is more expensive than first improving moves, we designed an “approximate best” improving move algorithm and prove that it is as efficient as first improving move SLS. For industrial problems the first local optima found using best improving moves are statistically significantly better than local optima found using first improving moves. However, this advantage reverses as search continues and algorithms must explore equal moves on plateaus. This reversal appears to be associated with critical variables that are in many clauses and that also yield large improving moves.

SAT-based MaxSAT algorithms

Many industrial optimization problems can be translated to MaxSAT. Although the general problem is NP hard, like SAT, many practical problems may be solved using modern MaxSAT solvers. In this paper we present several algorithms specially designed to deal with industrial or real problems. All of them are based on the idea of solving MaxSAT through successive calls to a SAT solver. We show that this SAT-based technique is efficient in solving industrial problems. In fact, all state-of-the-art MaxSAT solvers that perform well in industrial instances are based on this technique. In particular, our solvers won the 2009 partial MaxSAT and the 2011 weighted partial MaxSAT industrial categories of the MaxSAT evaluation. We prove the correctness of all our algorithms. We also present a complete experimental study comparing the performance of our algorithms with latest MaxSAT solvers.

Incomplete inference for graph problems

Recently, a resolution-based transformation has been introduced for the usual Max-SAT encoding of several graph problems such as the Minimum Vertex Covering, Maximum Clique and Combinatorial Auctions which consists in iteratively applying specific inference rules to transform and simplify the original formula. Such transformation was shown suitable to improve the performance of local and systematic search procedures. In this paper, we present several refinements for such transformation. In particular, we introduce a more suitable transformation for the Minimum Vertex Covering problem, specially for its weighted version, and we extend its use for the Maximum Cut problem. Empirical results indicate that systematic Max-SAT solvers improve substantially their performance.

Planning as satisfiability with IPC simple preferences and action costs

Planning as Satisfiability SAT is currently the best approach for optimally wrt makespan solving classical planning problems and the extension of this framework to include preferences is nowadays considered the reference approach to compute “optimal” plans in SAT-based planning. It includes reasoning about soft goals and plans length as introduced in the 2006 and 2008 editions of the International Planning Competitions IPCs. Despite the fact that the planning as satisfiability with preferences framework has helped to enhance the applicability of the SAT-based approach in planning, the actual approach used within the framework somehow suffers from some main limitations: the metrics, i.e. linear optimization functions defined over goals and/or actions, which account for plan quality issues, are fully reduced to SAT formulas, further increasing the size of often already big formulas; moreover, the search for optimal solutions is performed by forcing a heuristic ordering.In this paper we address these issues by reducing the IPC planning problems with soft goals from IPC-5 and/or action costs from IPC-6 to optimization problems extending SAT and that can naturally handle the integer “weights” of the metrics, i.e. to Max-SAT and Pseudo-Boolean PB problems. Our idea is partially motivated by the approach followed by IPPLAN in the deterministic part of the IPC-5 and by the recent availability of efficient Max-SAT and PB solvers. First, we prove that our approach is correct; then, we implement these ideas in SATPLAN and run a wide experimental analysis on planning problems from IPC-5 and IPC-6, taking as references state-of-the-art planners on these competitions and the previous SAT-based approach. Our analysis shows that our approach is competitive and helps to further widen the set of benchmarks that a SAT-based framework can efficiently deal with. At the same time, as a side effect of this analysis, challenging Max-SAT and PB benchmarks have been identified, as well as the Max-SAT and PB solvers performing best on these planning problems.

QMaxSAT: A Partial Max-SAT Solver

We present a partial Max-SAT solver QMaxSAT which uses CNF encoding of Boolean cardinality constraints. The old version 0.1 was obtained by adapting a CDCL based SAT solver MiniSat to manage cardinality constraints. It was placed rst in the industrial subcategory and second in the crafted subcategory of partial Max-SAT category of the 2010 Max-SAT Evaluation. The new version 0.2 is obtained by modifying version 0.1 to decrease the number of clauses for the cardinality encoding. We compare the two versions by solving Max-SAT instances taken from the 2010 Max-SAT Evaluation.

Core-Guided Binary Search Algorithms for Maximum Satisfiability

Several MaxSAT algorithms based on iterative SAT solving have been proposed in recent years. These algorithms are in general the most efficient for real-world applications. Existing data indicates that, among MaxSAT algorithms based on iterative SAT solving, the most efficient ones are core-guided, i.e. algorithms which guide the search by iteratively computing unsatisfiable subformulas (or cores). For weighted MaxSAT, core-guided algorithms exhibit a number of important drawbacks, including a possibly exponential number of iterations and the use of a large number of auxiliary variables. This paper develops two new algorithms for (weighted) MaxSAT that address these two drawbacks. The first MaxSAT algorithm implements core-guided iterative SAT solving with binary search. The second algorithm extends the first one by exploiting disjoint cores. The empirical evaluation shows that core-guided binary search is competitive with current MaxSAT solvers.

Cross-Domain Action-Model Acquisition for Planning via Web Search

Applying learning techniques to acquire action models is an area of intense research interest. Most previous works in this area have assumed that there is a significant amount of training data available in a planning domain of interest, which we call target domain, where action models are to be learned. However, it is often difficult to acquire sufficient training data to ensure that the learned action models are of high quality. In this paper, we develop a novel approach to learning action models with limited training data in the target domain by transferring knowledge from related auxiliary or source domains. We assume that the action models in the source domains have already been created before, and seek to transfer as much of the the available information from the source domains as possible to help our learning task. We first exploit a Web searching method to bridge the target and source domains, such that transferrable knowledge from source domains is identified. We then encode the transferred knowledge together with the available data from the target domain as constraints in a maximum satisfiability problem, and solve these constraints using a weighted MAX-SAT solver. We finally transform the solutions thus obtained into high-quality target-domain action models. We empirically show that our transfer-learning based framework is effective in several domains, including the International Planning Competition (IPC) domains and some synthetic domains.

Max-SAT formalisms with hard and soft constraints

The study of Max-SAT formalisms and the development of fast Max-SAT solvers have become very active research topics in the last few years. This PhD dissertation focus on the design, implementation and evaluation of solving techniques for two Max-SAT formalisms that incorporate the notion of partiality. The first one, called Block-SAT, is a new formalism that deals with blocks of clauses instead of individual clauses. The second one is Partial Max-SAT, which has become a standard in the community. For each formalism, we compare our solvers with state-of-the-art solvers using an exhaustive test suite. The empirical results provide evidence that the proposed solving techniques are competitive and often produce important speed-ups.

Restoring CSP Satisfiability with MaxSAT

The extraction of a Minimal Unsatisfiable Core (MUC) in a Constraint Satisfaction Problem (CSP) aims to identify a subset of constraints that make a CSP instance unsatisfiable. Recent work has addressed the identification of a Minimal Set of Unsatisfiable Tuples (MUST) in order to restore the CSP satisfiability with respect to that MUC. A two-step algorithm has been proposed: first, a MUC is identified, and second, a MUST in the MUC is identified. This paper proposes an integrated algorithm for restoring satisfiability in a CSP, making use of a MaxSAT solver. The proposed approach encodes the CSP instance as a partial MaxSAT instance, in such a way that solving the MaxSAT instance corresponds to identifying the smallest set of tuples to be removed from the CSP instance to restore satisfiability. Experimental results illustrate the feasibility of the approach.