Finding More Property Violations in Model Checking via the Restart Policy

Model checking is an efficient formal verification technique that has been applied to a wide spectrum of applications in software engineering. Popular model checking algorithms include Bounded Model Checking (BMC) and Incremental Construction of Inductive Clauses for Indubitable Correctness/Property Directed Reachability(IC3/PDR). The recently proposed Complementary Approximate Reachability (CAR) model checking algorithm has a performance close to BMC in bug-finding, while its depth-first strategy sometimes leads the algorithm to a trap, which will waste lots of computation. In this paper, we enhance the recently proposed Complementary Approximate Reachability (CAR) model checking algorithm by integrating the restart policy, which yields a restartable CAR model (abbreviated as r-CAR). The restart policy can help avoid the trap problem caused by the depth-first strategy and has played an important role in modern SAT-solving algorithms to search for a satisfactory solution. As the bug-finding in model checking is reducible to a similar search problem, the restart policy can be useful to enhance the bug-finding capability. We made an extensive experiment to evaluate the new algorithm. Our results show that out of the 749 industrial instances, r-CAR is able to find 13 instances that the state-of-the-art BMC technique cannot find and can solve more than 11 instances than the original CAR. The new algorithm successfully contributes to the current model-checking portfolio in practice.

On the Temperature of SAT Formulas

The remarkable advances in SAT solving achieved in the last years have allowed to use this technology in many real-world applications of Artificial Intelligence, such as planning, formal verification, and scheduling, among others. Interestingly, these industrial SAT problems are commonly believed to be easier than classical random SAT formulas, but estimating their actual hardness is still a very challenging question, which in some cases even requires to solve them. In this context, realistic pseudo-industrial random SAT generators have emerged with the aim of reproducing the main features shared by the majority of these application problems. The study of these models may help to better understand the success of those SAT solving techniques and possibly improve them. In this work, we present a model to estimate the temperature of real-world SAT instances. This temperature represents the degree of distortion into the expected structure of the formula, from highly structured benchmarks (more similar to real-world SAT instances) to the complete absence of structure (observed in the classical random SAT model). Our solution is based on the Popularity-Similarity (PS) random model for SAT, which has been recently presented to reproduce two crucial features of application SAT benchmarks: scale-free and community structures. The PS model is able to control the hardness of the generated formula by introducing some randomizations in the expected structure. Our solution is a first step towards a hardness oracle based on the temperature of SAT formulas, which may be able to estimate the cost of solving real-world SAT instances without solving them.

Treewidth-Aware Cycle Breaking for Algebraic Answer Set Counting

Probabilistic reasoning, parameter learning, and most probable explanation inference for answer set programming have recently received growing attention. They are only some of the problems that can be formulated as Algebraic Answer Set Counting (AASC) problems. The latter are however hard to solve, and efficient evaluation techniques are needed. Inspired by Vlasser et al.'s Tp-compilation (JAR, 2016), we introduce Tp-unfolding, which employs forward reasoning to break the cycles in the positive dependency graph of a program by unfolding them. Tp-unfolding is defined for any normal answer set program and unfolds programs with respect to unfolding sequences, which are akin to elimination orders in SAT-solving. Using "good" unfolding sequences, we can ensure that the increase of the treewidth of the unfolded program is small. Treewidth is a measure adhering to a program's tree-likeness, which gives performance guarantees for AASC. We give sufficient conditions for the existence of good unfolding sequences based on the novel notion of component-boosted backdoor size, which measures the cyclicity of the positive dependencies in a program. The experimental evaluation of a prototype implementation, the AASC solver aspmc, shows promising results.

DynASP2.5: Dynamic Programming on Tree Decompositions in Action

Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, feedback vertex set, or vertex cover. In theory, instances, for which the considered parameter is small, can be solved fast (problem evaluation), i.e., the runtime is bounded exponential in the parameter. While such favorable theoretical guarantees exists, it is often unclear whether one can successfully implement these algorithms under practical considerations. In other words, can we design and construct implementations of parameterized algorithms such that they perform similar or even better than well-established problem solvers on instances where the parameter is small. Indeed, we can build an implementation that performs well under the theoretical assumptions. However, it could also well be that an existing solver implicitly takes advantage of a structure, which is often claimed for solvers that build on Sat-solving. In this paper, we consider finding one solution to instances of answer set programming (ASP), which is a logic-based declarative modeling and solving framework. Solutions for ASP instances are so-called answer sets. Interestingly, the problem of deciding whether an instance has an answer set is already located on the second level of the polynomial hierarchy. An ASP solver that employs treewidth as parameter and runs dynamic programming on tree decompositions is DynASP2. Empirical experiments show that this solver is fast on instances of small treewidth and can outperform modern ASP when one counts answer sets. It remains open, whether one can improve the solver such that it also finds one answer set fast and shows competitive behavior to modern ASP solvers on instances of low treewidth. Unfortunately, theoretical models of modern ASP solvers already indicate that these solvers can solve instances of low treewidth fast, since they are based on Sat-solving algorithms. In this paper, we improve DynASP2 and construct the solver DynASP2.5, which uses a different approach. The new solver shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution. We present empirical experiments where one can see that our new implementation solves ASP instances, which encode the Steiner tree problem on graphs with low treewidth, fast. Our implementation is based on a novel approach that we call multi-pass dynamic programming (MDPSINC). In the paper, we describe the underlying concepts of our implementation (DynASP2.5) and we argue why the techniques still yield correct algorithms.

Parallel Hybridization for SAT: An Efficient Combination of Search Space Splitting and Portfolio

International audience Search space splitting and portfolio are the two main approaches used in parallel SAT solving. Each of them has its strengths but also, its weaknesses. Decomposition in search space splitting can help improve speedup on satisfiable instances while competition in portfolio increases robustness. Many parallel hybrid approaches have been proposed in the literature but most of them still cope with load balancing issues that are the cause of a non-negligible overhead. In this paper, we describe a new parallel hybridization scheme based on both search space splitting and portfolio that does not require the use of load balancing mechanisms (such as dynamic work stealing). Les deux principales approches utilisées dans la résolution parallèle du problème de satisfiabilité propositionnelle sont DPR (Diviser Pour Régner) et portfolio. Chacune d’elles comporte des forces et des faiblesses. La décomposition dans DPR permet d’améliorer le speedup sur les instancessatisfiables tandis que la compétition dans les portfolios accroit la robustesse. Plusieurs approches hybrides pour la résolution parallèle de SAT ont été présentées dans la littérature mais la plupart d’entre elles souffrent encore des problèmes dus aux mécanismes de rééquilibrage dynamique decharges qui sont à l’origine d’un surcoût non négligeable. Nous décrivons dans ce papier un nouveau schéma d’hybridation parallèle basé sur les deux approches DPR et portfolio ne nécessitant pas la mise en œuvre des mécanismes de rééquilibrage de charges (tels que le vol de tâche).

Chapter 3. Complete Algorithms

Complete SAT algorithms form an important part of the SAT literature. From a theoretical perspective, complete algorithms can be used as tools for studying the complexities of different proof systems. From a practical point of view, these algorithms form the basis for tackling SAT problems arising from real-world applications. The practicality of modern, complete SAT solvers undoubtedly contributes to the growing interest in the class of complete SAT algorithms. We review these algorithms in this chapter, including Davis-Putnum resolution, Stalmarck’s algorithm, symbolic SAT solving, the DPLL algorithm, and modern clause-learning SAT solvers. We also discuss the issue of certifying the answers of modern complete SAT solvers.

Chapter 9. Preprocessing in SAT Solving

Preprocessing has become a key component of the Boolean satisfiability (SAT) solving workflow. In practice, preprocessing is situated between the encoding phase and the solving phase, with the aim of decreasing the total solving time by applying efficient simplification techniques on SAT instances to speed up the search subsequently performed by a SAT solver. In this chapter, we overview key preprocessing techniques proposed in the literature. While the main focus is on techniques applicable to formulas in conjunctive normal form (CNF), we also selectively cover main ideas for preprocessing structural and higher-level SAT instance representations.

Chapter 12. Automated Configuration and Selection of SAT Solvers

This chapter provides an introduction to the automated configuration and selection of SAT algorithms and gives an overview of the most prominent approaches. Since the early 2000s, these so-called meta-algorithmic approaches have played a major role in advancing the state of the art in SAT solving, giving rise to new ways of using and evaluating SAT solvers. At the same time, SAT has proven to be particularly fertile ground for research and development in the area of automated configuration and selection, and methods developed there have meanwhile achieved impact far beyond SAT, across a broad range of computationally challenging problems. Conceptually more complex approaches that go beyond “pure” algorithm configuration and selection are also discussed, along with some open challenges related to meta-algorithmic approaches, such as automated algorithm configuration and selection, to the tools based on these approaches, and to their effective application.