A Simple and Flexible Way of Computing Small Unsatisfiable Cores in SAT Modulo Theories

Finding small unsatisfiable cores for SAT problems has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many interesting verification problems, which can be more naturally addressed in the framework of Satisfiability Modulo Theories, SMT. Surprisingly, the problem of finding unsatisfiable cores in SMT has received very little attention in the literature; in particular, we are not aware of any work aiming at producing small unsatisfiable cores in SMT. In this paper we present a novel approach to this problem. The main idea is to combine an SMT solver with an external propositional core extractor: the SMT solver produces the theory lemmas found during the search; the core extractor is then called on the boolean abstraction of the original SMT problem and of the theory lemmas. This results in an unsatisfiable core for the original SMT problem, once the remaining theory lemmas have been removed. The approach is conceptually interesting, since the SMT solver is used to dynamically lift the suitable amount of theory information to the boolean level, and it also has several advantages in practice. In fact, it is extremely simple to implement and to update, and it can be interfaced with every propositional core extractor in a plug-and-play manner, so that to benefit for free of all unsat-core reduction techniques which have been or will be made available. We have evaluated our approach by an extensive empirical test on SMT-LIB benchmarks, which confirms the validity and potential of this approach

Finding Unsatisfiable Subformulas with Stochastic Method

Abstract. Explaining the causes of infeasibility of Boolean formulas has many practical applications in various fields. A small unsatisfiable subformula provides a succinct explanation of infeasibility and is valuable for applications. In recent years the problem of finding unsatisfiable subformulas has been addressed frequently by research works, which are mostly based on the SAT solvers with DPLL backtrack-search algorithm. However little attention has been concentrated on extraction of unsatisfiable subformulas using stochastic methods. In this paper, we propose a resolution-based stochastic local search algorithm to derive unsatisfiable subformulas. This approach directly constructs the resolution sequences for proving unsatisfiability with a local search procedure, and then extracts small unsatisfiable subformulas from the refutation traces. We report and analyze the experimental results on benchmarks

The KB paradigm and its application to interactive configuration

The knowledge base paradigm aims to express domain knowledge in a rich formal language, and to use this domain knowledge as a knowledge base to solve various problems and tasks that arise in the domain by applying multiple forms of inference. As such, the paradigm applies a strict separation of concerns between information and problem solving. In this paper, we analyze the principles and feasibility of the knowledge base paradigm in the context of an important class of applications: interactive configuration problems. In interactive configuration problems, a configuration of interrelated objects under constraints is searched, where the system assists the user in reaching an intended configuration. It is widely recognized in industry that good software solutions for these problems are very difficult to develop. We investigate such problems from the perspective of the KB paradigm. We show that multiple functionalities in this domain can be achieved by applying different forms of logical inferences on a formal specification of the configuration domain. We report on a proof of concept of this approach in a real-life application with a banking company. To appear in Theory and Practice of Logic Programming (TPLP).Comment: To appear in Theory and Practice of Logic Programming (TPLP

Re-implementing and Extending a Hybrid SAT-IP Approach to Maximum Satisfiability

Real-world optimization problems, such as those found in logistics and bioinformatics, are often NP-hard. Maximum satisfiability (MaxSAT) provides a framework within which many such problems can be efficiently represented. MaxHS is a recent exact algorithm for MaxSAT. It is a hybrid approach that uses a SAT solver to compute unsatisfiable cores and an integer programming (IP) solver to compute minimum-cost hitting sets for the found cores. This thesis analyzes and extends the MaxHS algorithm. To enable this, the algorithm is re-implemented from scratch using the C++ programming language. The resulting MaxSAT solver LMHS recently gained top positions at an international evaluation of MaxSAT solvers. This work looks into various aspects of the MaxHS algorithm and its applications. The impact of different IP solvers on the MaxHS algorithm and the behavior induced by different strategies of postponing IP solver calls is examined. New methods of enhancing the computation of unsatisfiable cores in MaxHS are examined. Fast core extraction through parallelization by partitioning soft clauses is explored. A modification of the final conflict analysis procedure of a SAT solver is used to generate additional cores without additional SAT solver invocations. The use of additional constraint propagation procedures in the SAT solver used by MaxHS is investigated. As a case study, acyclicity constraint propagation is implemented and its effectiveness for bounded treewidth Bayesian network structure learning using MaxSAT is evaluated. The extension of MaxHS to the labeled MaxSAT framework, which allows for more efficient use of preprocessing techniques and group MaxSAT encodings in MaxHS, is discussed. The re-implementation of the MaxHS algorithm, LMHS, also enables incrementality in efficiently adding constraints to a MaxSAT instance during the solving process. As a case study, this incrementality is used in solving subproblems with MaxSAT within GOBNILP, a tool for finding optimal Bayesian network structures

A Survey of Constrained Combinatorial Testing

Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider applicability of CT in the presence of constrained problem domains, large and diverse efforts have been invested towards the techniques and applications of constrained combinatorial testing. In this paper, we provide a comprehensive survey of representations, influences, and techniques that pertain to constraints in CT, covering 129 papers published between 1987 and 2018. This survey not only categorises the various constraint handling techniques, but also reviews comparatively less well-studied, yet potentially important, constraint identification and maintenance techniques. Since real-world programs are usually constrained, this survey can be of interest to researchers and practitioners who are looking to use and study constrained combinatorial testing techniques

Automated pairwise testing approach based on classification tree modeling and negative selection algorithm

Generating the test cases for analysis is an important activity in software testing to increase the trust level of users. The traditional way to generate test cases is called exhaustive testing. It is infeasible and time consuming because it generates too many numbers of test cases. A combinatorial testing was used to solve the exhaustive testing problem. The popular technique in combinatorial testing is called pairwise testing that involves the interaction of two parameters. Although pairwise testing can cover the exhaustive testing problems, there are several issues that should be considered. First issue is related to modeling of the system under test (SUT) as a preprocess for test case generation as it has yet to be implemented in automated proposed approaches. The second issue is different approaches generate different number of test cases for different covering arrays. These issues showed that there is no one efficient way to find the optimal solution in pairwise testing that would consider the invalid combination or constraint. Therefore, a combination of Classification Tree Method and Negative Selection Algorithm (CTM-NSA) was developed in this research. The CTM approach was revised and enhanced to be used as the automated modeling and NSA approach was developed to optimize the pairwise testing by generate the low number of test cases. The findings showed that the CTM-NSA outperformed the other modeling method in terms of easing the tester and generating a low number of test cases in the small SUT size. Furthermore, it is comparable to the efficient approaches as compared to many of the test case generation approaches in large SUT size as it has good characteristic in detecting the self and non-self-sample. This characteristic occurs during the detection stage of NSA by covering the best combination of values for all parameters and considers the invalid combinations or constraints in order to achieve a hundred percent pairwise testing coverage. In addition, validation of the approach was performed using Statistical Wilcoxon Signed-Rank Test. Based on these findings, CTM-NSA had been shown to be able perform modeling in an automated way and achieve the minimum or a low number of test cases in small SUT size

Blazing Fast PSI from Improved OKVS and Subfield VOLE

We present new semi-honest and malicious secure PSI protocols that outperform all prior works by several times in both communication and running time. For example, our semi-honest protocol for $n=2^{20}$ can be performed in 0.37 seconds compared to the previous best of 2 seconds (Kolesnikov et al., CCS 2016). This can be further reduced to 0.16 seconds with 4 threads, a speedup of $12\times$. Similarly, our protocol sends $187n$ bits compared to $426n$ bits of the next most communication efficient protocol (Rindal et al., Eurocrypt 2021). Additionally, we apply our new techniques to the circuit PSI protocol of Rindal et al. and $6\times$ improvement in running time. These performance results are obtained by two types of improvements. The first is an optimization to the protocol of Rindal et al. to utilize sub-field vector oblivious linear evaluation. This optimization allows our construction to be the first to achieve a communication complexity of $\mathcal{O}(n\lambda + n\log n)$ where $\lambda$ is the statistical security parameter. In particular, the communication overhead of our protocol does not scale with the computational security parameter times $n$. Our second improvement is to the OKVS data structure which our protocol crucially relies on. In particular, our construction improves both the computation and communication efficiency as compared to prior work (Garimella et al., Crypto 2021). These improvements stem from algorithmic changes to the data structure along with new techniques for obtaining both asymptotic and tight concrete bounds on its failure probability. This in turn allows for a highly optimized parameter selection and thereby better performance

Systematic techniques for more effective fault localization and program repair

Debugging faulty code is a tedious process that is often quite expensive and can require much manual effort. Developers typically perform debugging in two key steps: (1) fault localization, i.e., identifying the location of faulty line(s) of code; and (2) program repair, i.e., modifying the code to remove the fault(s). Automating debugging to reduce its cost has been the focus of a number of research projects during the last decade, which have introduced a variety of techniques. However, existing techniques suffer from two basic limitations. One, they lack accuracy to handle real programs. Two, they focus on automating only one of the two key steps, thereby leaving the other key step to the developer. Our thesis is that an approach that integrates systematic search based on state-of-the-art constraint solvers with techniques to analyze artifacts that describe application specific properties and behaviors, provides the basis for developing more effective debugging techniques. We focus on faults in programs that operate on structurally complex inputs, such as heap-allocated data or relational databases. Our approach lays the foundation for a unified framework for localization and repair of faults in programs. We embody our thesis in a suite of integrated techniques based on propositional satisfiability solving, correctness specifications analysis, test-spectra analysis, and rule-learning algorithms from machine learning, implement them as a prototype tool-set, and evaluate them using several subject programs.Electrical and Computer Engineerin