Jia Hui Liang

Clafer tools for product line engineering

Clafer is a lightweight yet expressive language for structural modeling: feature modeling and configuration, class and object modeling, and metamodeling. Clafer Tools is an integrated set of tools based on Clafer. In this paper, we describe some product-line variability modeling scenarios of Clafer Tools from the viewpoints of product-line owner, product-line engineer, and product engineer.

Learning Rate Based Branching Heuristic for SAT Solvers

In this paper, we propose a framework for viewing solver branching heuristics as optimization algorithms where the objective is to maximize the learning rate, defined as the propensity for variables to generate learnt clauses. By viewing online variable selection in SAT solvers as an optimization problem, we can leverage a wide variety of optimization algorithms, especially from machine learning, to design effective branching heuristics. In particular, we model the variable selection optimization problem as an online multi-armed bandit, a special-case of reinforcement learning, to learn branching variables such that the learning rate of the solver is maximized. We develop a branching heuristic that we call learning rate branching or LRB, based on a well-known multi-armed bandit algorithm called exponential recency weighted average and implement it as part of MiniSat and CryptoMiniSat. We upgrade the LRB technique with two additional novel ideas to improve the learning rate by accounting for reason side rate and exploiting locality. The resulting LRB branching heuristic is shown to be faster than the VSIDS and conflict history-based (CHB) branching heuristics on 1975 application and hard combinatorial instances from 2009 to 2014 SAT Competitions. We also show that CryptoMiniSat with LRB solves more instances than the one with VSIDS. These experiments show that LRB improves on state-of-the-art.

Understanding VSIDS Branching Heuristics in Conflict-Driven Clause-Learning SAT Solvers

Conflict-Driven Clause-Learning (CDCL) SAT solvers crucially depend on the Variable State Independent Decaying Sum (VSIDS) branching heuristic for their performance. Although VSIDS was proposed nearly fifteen years ago, and many other branching heuristics for SAT solving have since been proposed, VSIDS remains one of the most effective branching heuristics. Despite its widespread use and repeated attempts to understand it, this additive bumping and multiplicative decay branching heuristic has remained an enigma.

SAT-based analysis of large real-world feature models is easy

Modern conflict-driven clause-learning (CDCL) Boolean SAT solvers provide efficient automatic analysis of real-world feature models (FM) of systems ranging from cars to operating systems. It is well-known that solver-based analysis of real-world FMs scale very well even though SAT instances obtained from such FMs are large, and the corresponding analysis problems are known to be NP-complete. To better understand why SAT solvers are so effective, we systematically studied many syntactic and semantic characteristics of a representative set of large real-world FMs. We discovered that a key reason why large real-world FMs are easy-to-analyze is that the vast majority of the variables in these models are unrestricted, i.e., the models are satisfiable for both true and false assignments to such variables under the current partial assignment. Given this discovery and our understanding of CDCL SAT solvers, we show that solvers can easily find satisfying assignments for such models without too many backtracks relative to the model size, explaining why solvers scale so well. Further analysis showed that the presence of unrestricted variables in these real-world models can be attributed to their high-degree of variability. Additionally, we experimented with a series of well-known nonbacktracking simplifications that are particularly effective in solving FMs. The remaining variables/clauses after simplifications, called the core, are so few that they are easily solved even with backtracking, further strengthening our conclusions. We explain the connection between our findings and backdoors, an idea posited by theorists to explain the power of SAT solvers. This connection strengthens our hypothesis that SAT-based analysis of FMs is easy. In contrast to our findings, previous research characterizes the difficulty of analyzing randomly-generated FMs in terms of treewidth. Our experiments suggest that the difficulty of analyzing real-world FMs cannot be explained in terms of treewidth.

SMTIBEA: a hybrid multi-objective optimization algorithm for configuring large constrained software product lines

A key challenge to software product line engineering is to explore a huge space of various products and to find optimal or near-optimal solutions that satisfy all predefined constraints and balance multiple often competing objectives. To address this challenge, we propose a hybrid multi-objective optimization algorithm called SMTIBEA that combines the indicator-based evolutionary algorithm (IBEA) with the satisfiability modulo theories (SMT) solving. We evaluated the proposed algorithm on five large, constrained, real-world SPLs. Compared to the state-of-the-art, our approach significantly extends the expressiveness of constraints and simultaneously achieves a comparable performance. Furthermore, we investigate the performance influence of the SMT solving on two evolutionary operators of the IBEA.

SATGraf : Visualizing the Evolution of SAT Formula Structure in Solvers

In this paper, we present SATGraf, a tool for visualizing the evolution of the structure of a Boolean SAT formula in real time as it is being processed by a conflict-driven clause-learning (CDCL) solver. The tool is parametric, allowing the user to define the structure to be visualized. In particular, the tool can visualize the community structure of real-world Boolean satisfiability (SAT) instances and their evolution during solving. Such visualizations have been the inspiration for several hypotheses about the connection between community structure and the running time of CDCL SAT solvers, some which we have already empirically verified. SATGraf has enabled us in making the following empirical observations regarding CDCL solvers: First, we observe that the Variable State Independent Decaying Sum (VSIDS) branching heuristic consistently chooses variables with a high number of inter-community edges, i.e., high-centrality bridge variables. Second, we observe that the VSIDS branching heuristic and hence the CDCL search procedure is highly focused, i.e., VSIDS disproportionately picks variables from a few communities in the community-structure of input SAT formulas.

Adaptive Restart and CEGAR-Based Solver for Inverting Cryptographic Hash Functions

SAT solvers are increasingly being used for cryptanalysis of hash functions and symmetric encryption schemes. Inspired by this trend, we present MapleCrypt which is a SAT solver-based cryptanalysis tool for inverting hash functions. We reduce the hash function inversion problem for fixed targets into the satisfiability problem for Boolean logic, and use MapleCrypt to construct preimages for these targets. MapleCrypt has two key features, namely, a multi-armed bandit based adaptive restart (MABR) policy and a counterexample-guided abstraction refinement (CEGAR) technique. The MABR technique uses reinforcement learning to adaptively choose between different restart policies during the run of the solver. The CEGAR technique abstracts away certain steps of the input hash function, replacing them with the identity function, and verifies whether the solution constructed by MapleCrypt indeed hashes to the previously fixed targets. If it is determined that the solution produced is spurious, the abstraction is refined until a correct inversion to the input hash target is produced. We show that the resultant system is faster for inverting the SHA-1 hash function than state-of-the-art inversion tools.

An Empirical Study of Branching Heuristics Through the Lens of Global Learning Rate

In this paper, we analyze a suite of 7 well-known branching heuristics proposed by the SAT community and show that the better heuristics tend to generate more learnt clauses per decision, a metric we define as the global learning rate (GLR). Like our previous work on the LRB branching heuristic, we once again view these heuristics as techniques to solve the learning rate optimization problem. First, we show that there is a strong positive correlation between GLR and solver efficiency for a variety of branching heuristics. Second, we test our hypothesis further by developing a new branching heuristic that maximizes GLR greedily. We show empirically that this heuristic achieves very high GLR and interestingly very low literal block distance (LBD) over the learnt clauses. In our experiments this greedy branching heuristic enables the solver to solve instances faster than VSIDS, when the branching time is taken out of the equation. This experiment is a good proof of concept that a branching heuristic maximizing GLR will lead to good solver performance modulo the computational overhead. Third, we propose that machine learning algorithms are a good way to cheaply approximate the greedy GLR maximization heuristic as already witnessed by LRB. In addition, we design a new branching heuristic, called SGDB, that uses a stochastic gradient descent online learning method to dynamically order branching variables in order to maximize GLR. We show experimentally that SGDB performs on par with the VSIDS branching heuristic.

Synthesis and Exploration of Multi-level, Multi-perspective Architectures of Automotive Embedded Systems (SoSYM Abstract)

In industry, evaluating candidate architectures for automotive embedded systems is routinely done during the design process. Todays engineers, however, are limited in the number of candidates that they are able to evaluate in order to find the optimal architectures. This limitation results from the difficulty in defining the candidates as it is a mostly manual process. In this work, we propose a way to synthesize multilevel, multi-perspective candidate architectures and to explore them across the different layers and perspectives. Using a reference model similar to the EAST-ADL domain model but with a focus on early design, we explore the candidate architectures for two case studies: an automotive power window system and the central door locking system. Further, we provide a comprehensive set of questions, based on the different layers and perspectives, that engineers can ask to synthesize only the candidates relevant to their task at hand. Finally, using the modeling language Clafer, which is supported by automated backend reasoners, we show that it is possible to synthesize and explore optimal candidate architectures for two highly configurable automotive subsystems.

Synthesis and exploration of multi-level, multi-perspective architectures of automotive embedded systems

In industry, evaluating candidate architectures for automotive embedded systems is routinely done during the design process. Today’s engineers, however, are limited in the number of candidates that they are able to evaluate in order to find the optimal architectures. This limitation results from the difficulty in defining the candidates as it is a mostly manual process. In this work, we propose a way to synthesize multi-level, multi-perspective candidate architectures and to explore them across the different layers and perspectives. Using a reference model similar to the EAST-ADL domain model but with a focus on early design, we explore the candidate architectures for two case studies: an automotive power window system and the central door locking system. Further, we provide a comprehensive set of question templates, based on the different layers and perspectives, that engineers can ask to synthesize only the candidates relevant to their task at hand. Finally, using the modeling language Clafer, which is supported by automated backend reasoners, we show that it is possible to synthesize and explore optimal candidate architectures for two highly configurable automotive sub-systems.