Boolean Satisfiability Research Articles

Data-Aware Declarative Process Mining with SAT

Process Mining is a family of techniques for analyzing business process execution data recorded in event logs. Process models can be obtained as output of automated process discovery techniques or can be used as input of techniques for conformance checking or model enhancement. In Declarative Process Mining, process models are represented as sets of temporal constraints (instead of procedural descriptions where all control-flow details are explicitly modeled). An open research direction in Declarative Process Mining is whether multi-perspective specifications can be supported, i.e., specifications that not only describe the process behavior from the control-flow point of view, but also from other perspectives like data or time. In this article, we address this question by considering SAT (Propositional Satisfiability Problem) as a solving technology for a number of classical problems in Declarative Process Mining, namely, log generation, conformance checking, and temporal query checking. To do so, we first express each problem as a suitable FO (First-Order) theory whose bounded models represent solutions to the problem, and then find a bounded model of such theory by compilation into SAT.

A Resolution Proof System for Dependency Stochastic Boolean Satisfiability

A Resolution Proof System for Dependency Stochastic Boolean Satisfiability

Certified SAT solving with GPU accelerated inprocessing

Since 2013, the leading SAT solvers in SAT competitions all use inprocessing, which, unlike preprocessing, interleaves search with simplifications. However, inprocessing is typically a performance bottleneck, in particular for hard or large formulas. In this work, we introduce the first attempt to parallelize inprocessing on GPU architectures. As one of the main challenges in GPU programming is memory locality, we present new compact data structures and devise a data-parallel garbage collector. It runs in parallel on the GPU to reduce memory consumption and improve memory locality. Our new parallel variable elimination algorithm is roughly twice as fast as previous work. Moreover, we augment the variable elimination with the first parallel algorithm for functional dependency extraction in an attempt to find more logical gates to eliminate that cannot be found with syntactic approaches. We present a novel algorithm to generate clausal proofs in parallel to validate all simplifications running on the GPU besides the CDCL search, giving high credibility to our solver and its use in critical applications such as model checkers. In experiments, our new solver ParaFROST solves numerous benchmarks faster on the GPU than its sequential counterparts. With functional dependency extraction, inprocessing in ParaFROST was more effective in reducing the solving time. Last but not least, all proofs generated by ParaFROST were successfully verified.

A Comprehensive Test Pattern Generation Approach Exploiting the SAT Attack for Logic Locking

The need for reducing manufacturing defect escape in today's safety-critical applications requires increased fault coverage. However, generating a test set using commercial automatic test pattern generation (ATPG) tools that lead to zero-defect escape is still an open problem. It is challenging to detect all stuck-at faults to reach 100% fault coverage. In parallel, the hardware security community has been actively involved in developing solutions for logic locking to prevent IP piracy. In logic locking, locks are inserted in different locations of the netlist to modify the original functionality. Unless the correct key is programmed into the IC, the circuit functions incorrectly. Unfortunately, the Boolean satisfiability (SAT) based attack, introduced in [1], can determine the secret key efficiently, and break different logic locking schemes. In this paper, we propose a novel test pattern generation approach using the powerful SAT attack on logic locking. A stuck-at fault is modeled as a locked gate with a secret key, where it can effectively deduce the satisfiable assignment with reduced backtracks under key initialization of the SAT attack. The input pattern that determines the key is a test for the stuck-at fault. We propose two different approaches for test pattern generation. First, a single stuck-at fault is targeted, and a corresponding locked circuit with one key bit is created. This approach generates one test pattern per fault. Second, we consider a group of faults and convert the circuit to its locked version with multiple key bits. The inputs obtained from the SAT attack tool are the test set for detecting this group of faults. Our approach can find test patterns for all hard-to-detect faults that were previously undetected in commercial ATPG tools. The proposed test pattern generation approach can efficiently detect redundant faults as well. We demonstrate the effectiveness of the approach on ITC'99 benchmarks. The results show that we can detect all the hard-to-detect faults and identify redundant faults and a 100% stuck fault coverage is achieved. In addition, we show that test generation time saving becomes significant for Approach 2 as multiple faults help reduce or remove conflicts.

An incremental SAT-based approach for solving the real-time taxi-sharing service problem

This paper deals with a combinatorial optimization problem that models real-time taxi-sharing services. Because finding an optimal solution to this problem is NP -hard, most previous studies have developed the corresponding optimization algorithms based on well-known metaheuristics for its simplified problem. In this study, we focus on assigning an appropriate taxi and re-planning its route for each newly arisen demand so that the service can minimize the sum of the planned travel time for transporting all passengers who are allocated to this taxi. We propose a novel algorithm based on incremental Boolean satisfiability solving, to optimize the taxi allocation for demands occurring in real time. In our experiment, we generate instances by simulating urban traffic based on a road network. The experimental result shows that our new approach is overall faster than its equivalent integer programming-based solving method.

BLOOP: Boolean Satisfiability-based Optimized Loop Pipelining

Modulo scheduling is the premier technique for throughput maximization of loops in high-level synthesis by interleaving consecutive loop iterations. The number of clock cycles between data insertions is called the initiation interval (II). For throughput maximization, this value should be as low as possible; therefore, its minimization is the main optimization goal. Despite its long historical existence, modulo scheduling always remained a relevant research topic over the years with many exact and heuristic algorithms available in the literature. Nevertheless, we are able to leverage the scalability of modern Boolean Satisfiability (SAT) solvers to outperform state-of-the-art ILP-based algorithms for latency-optimal modulo scheduling for both integer and rational IIs. Our algorithm is able to compute valid modulo schedules for the whole CHStone and MachSuite benchmark suites, with 99% of the solutions being proven to be throughput optimal for a timeout of only 10 minutes per candidate II. For various time limits, not a single tested scheduler from the state of the art is able to compute more verified optimal solutions or even a single schedule with a higher throughput than our proposed approach. Using an HLS toolflow, we show that our algorithm can be effectively used to generate Pareto-optimal FPGA implementations regarding throughput and resource usage.

SAT-boosted Tabu Search for Coloring Massive Graphs

Graph coloring is the problem of coloring the vertices of a graph with as few colors as possible, avoiding monochromatic edges. It is one of the most fundamental NP-hard computational problems. For decades researchers have developed exact and heuristic methods for graph coloring. While methods based on propositional satisfiability (SAT) feature prominently among these exact methods, the encoding size is prohibitive for large graphs. For such graphs, heuristic methods have been proposed, with tabu search among the most successful ones. In this article, we enhance tabu search for graph coloring within the SAT-based local improvement (SLIM) framework. Our hybrid algorithm incrementally improves a candidate solution by repeatedly selecting small subgraphs and coloring them optimally with a SAT solver. This approach scales to dense graphs with several hundred thousand vertices and over 1.5 billion edges. Our experimental evaluation shows that our hybrid algorithm beats state-of-the-art methods on large dense graphs.

Fractional Encoding of At-Most-K Constraints on SAT

The satisfiability problem (SAT) in propositional logic determines if there is an assignment of values that makes a given propositional formula true. Recently, fast SAT solvers have been developed, and SAT encoding research has gained attention. This enables various real-world problems to be transformed into SAT and solved, realizing a solution to the original problems. We propose a new encoding method, Fractional Encoding, which focuses on the At-Most-K constraints—a bottleneck of computational complexity—and reduces the scale of logical expressions by dividing target variables. Furthermore, we confirm that Fractional Encoding outperforms existing methods in terms of the number of generated clauses and required auxiliary variables. Hence, it enables the efficient solving of real-world problems like planning and hardware verification.

Local Search For Satisfiability Modulo Integer Arithmetic Theories

Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first-order theories. In this article, we focus on Satisfiablity Modulo Integer Arithmetic, which is referred to as SMT(IA), including both linear and non-linear integer arithmetic theories. Dominant approaches to SMT rely on calling a CDCL-based SAT solver, either in a lazy or eager flavour. Local search, a competitive approach to solving combinatorial problems including SAT, however, has not been well studied for SMT. We develop the first local-search algorithm for SMT(IA) by directly operating on variables, breaking through the traditional framework. We propose a local-search framework by considering the distinctions between Boolean and integer variables. Moreover, we design a novel operator and scoring functions tailored for integer arithmetic, as well as a two-level operation selection heuristic. Putting these together, we develop a local search SMT(IA) solver called LocalSMT. Experiments are carried out to evaluate LocalSMT on benchmark sets from SMT-LIB. The results show that LocalSMT is competitive and complementary with state-of-the-art SMT solvers, and performs particularly well on those formulae with only integer variables. A simple sequential portfolio with Z3 improves the state-of-the-art on satisfiable benchmark sets from SMT-LIB.

A survey on varieties generated by small semigroups and a companion website

This paper presents new findings on varieties generated by small semigroups and groups, and offers a survey of existing results. A companion website is provided which hosts a computational system integrating automated reasoning tools, finite model builders, SAT solvers, and GAP. This platform is a living guide to the literature. In addition, the first complete and justified list of identity bases for all varieties generated by a semigroup of order up to 4 is provided as supplementary material. The paper concludes with an extensive list of open problems.

Using Machine Learning Classifiers in SAT Branching [Extended Abstract

The Boolean Satisfiability Problem (SAT) can be framed as a binary classification task. Recently, numerous machine and deep learning techniques have been successfully deployed to predict whether a CNF has a solution. However, these approaches do not provide a variables assignment when the instance is satisfiable and have not been used as part of SAT solvers. In this work, we investigate the possibility of using a machine-learning SAT/UNSAT classifier to assign a truth value to a variable. A heuristic solver can be created by iteratively assigning one variable to the value that leads to higher predicted satisfiability. We test our approach with and without probing features and compare it to a heuristic assignment based on the variable's purity. We consider as objective the maximisation of the number of literals fixed before making the CNF unsatisfiable. The preliminary results show that this iterative procedure can consistently fix variables without compromising the formula's satisfiability, finding a complete assignment in almost all test instances.

SAT Feature Analysis for Machine Learning Classification Tasks

The extraction of meaningful features from CNF instances is crucial to applying machine learning to SAT solving, enabling algorithm selection and configuration for solver portfolios and satisfiability classification. While many approaches have been proposed for feature extraction, their relevance to these tasks is unclear. Their applicability and comparison of the information extracted and the computational effort needed are complicated by the lack of working or updated implementations, negatively affecting reproducibility. In this paper, we analyse the performance of five sets of features presented in the literature on SAT/UNSAT and problem category classification over a dataset of 3000 instances across ten problem classes distributed equally between SAT and UNSAT. To increase reproducibility and encourage research in this area, we released a Python library containing an updated and clear implementation of structural, graph-based, statistical and probing features presented in the literature for SAT CNF instances; and we define a clear pipeline to compare feature sets in a given learning task robustly. We analysed which of the computed features are relevant for the specific task and the tradeoff they provide between accuracy and computational effort. The results of the analysis provide insights into which features mostly affect an instance's satisfiability and which can be used to identify the problem's type. These insights can be used to develop more effective solver portfolios and satisfiability classification algorithms.

Understand Restart of SAT Solver Using Search Similarity Index (Student Abstract)

SAT solvers are widely used to solve many industrial problems because of their high performance, which is achieved by various heuristic methods. Understanding why these methods are effective is essential to improving them. One approach to this is analyzing them using qualitative measurements. In our previous study, we proposed search similarity index (SSI), a metric to quantify the similarity between searches. SSI significantly improved the performance of the parallel SAT solver. Here, we apply SSI to analyze the effect of restart, a key SAT solver technique. Experiments using SSI reveal the correlation between the difficulty of instances and the search change effect by restart, and the reason behind the effectiveness of the state-of-the-art restart method is also explained.

Investigating the reviewer assignment problem: A systematic literature review

The assignment of appropriate reviewers to academic articles, known as the reviewer assignment problem (RAP), has become a crucial issue in academia. While there has been much research on RAP, there has not yet been a systematic literature review (SLR) examining the various approaches, techniques, algorithms and discoveries related to this topic. To conduct the SLR, we identified and evaluated relevant articles from four databases using defined inclusion and exclusion criteria. We analysed the selected articles and extracted information, and assessed their quality. Our review identified 67 articles on RAP published in conferences and journals up to mid-2022. As one of the main challenges in RAP is acquiring open data, we have studied the data sources used by researchers and found that most studies use real data from conferences, bibliographic databases and online academic search engines. RAP is divided into two main phases: (1) finding/recommending expert reviewers and (2) assigning reviewers to submitted manuscripts. In Phase 1, we have identified that decision support systems, recommendation systems, and machine learning-oriented approaches are more commonly used due to better results. In Phase 2, heuristics and metaheuristics are the approaches that present better results and are consequently more commonly used by researchers. Based on the analysed studies, we have identified potential areas for future research that could lead to improved results. Specifically, we suggest exploring the application of deep neural networks for calculating the degree of correspondence and using the Boolean satisfiability problem to optimise the attribution process.

Strategyproofness and Proportionality in Party-Approval Multiwinner Elections

In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each party can be assigned multiple seats. Two central requirements in this setting are proportional representation and strategyproofness. Intuitively, proportional representation requires that every sufficiently large group of voters with similar preferences is represented in the committee. Strategyproofness demands that no voter can benefit by misreporting her true preferences. We show that these two axioms are incompatible for anonymous party-approval multiwinner voting rules, thus proving a far-reaching impossibility theorem. The proof of this result is obtained by formulating the problem in propositional logic and then letting a SAT solver show that the formula is unsatisfiable. Additionally, we demonstrate how to circumvent this impossibility by considering a weakening of strategyproofness which requires that only voters who do not approve any elected party cannot manipulate. While most common voting rules fail even this weak notion of strategyproofness, we characterize Chamberlin-Courant approval voting within the class of Thiele rules based on this strategyproofness notion.

Lifting (D)QBF Preprocessing and Solving Techniques to (D)SSAT

Dependency stochastic Boolean satisfiability (DSSAT) generalizes stochastic Boolean satisfiability (SSAT) in existential variables being Henkinized allowing their dependencies on randomized variables to be explicitly specified. It allows NEXPTIME problems of reasoning under uncertainty and partial information to be compactly encoded. To date, no decision procedure has been implemented for solving DSSAT formulas. This work provides the first such tool by converting DSSAT into SSAT with dependency elimination, similar to converting dependency quantified Boolean formula (DQBF) to quantified Boolean formula (QBF). Moreover, we extend (D)QBF preprocessing techniques and implement the first standalone (D)SSAT preprocessor. Experimental results show that solving DSSAT via dependency elimination is highly applicable and that existing SSAT solvers may benefit from preprocessing.

SharpSSAT: A Witness-Generating Stochastic Boolean Satisfiability Solver

Stochastic Boolean satisfiability (SSAT) is a formalism allowing decision-making for optimization under quantitative constraints. Although SSAT solvers are under active development, existing solvers do not provide Skolem-function witnesses, which are crucial for practical applications. In this work, we develop a new witness-generating SSAT solver, SharpSSAT, which integrates techniques, including component caching, clause learning, and pure literal detection. It can generate a set of Skolem functions witnessing the attained satisfying probability of a given SSAT formula. We also equip the solver ClauSSat with witness generation capability for comparison. Experimental results show that SharpSSAT outperforms current state-of-the-art solvers and can effectively generate compact Skolem-function witnesses. The new witness-generating solver may broaden the applicability of SSAT to practical applications.

The Multi-Agent Transportation Problem

We introduce the multi-agent transportation (MAT) problem, where agents have to transport containers from their starting positions to their designated goal positions. Movement takes place in a common environment where collisions between agents and between containers must be avoided. In contrast to other frameworks such as multi-agent pathfinding (MAPF) or multi-agent pickup and delivery (MAPD), the agents are allowed to separate from the containers at any time, which can reduce the makespan and also allows for plans in scenarios that are unsolvable otherwise. We present a complexity analysis establishing the problem's NP-completeness and show how the problem can be reduced to a sequence of SAT problems when optimizing for makespan. A MAT solver is empirically evaluated with regard to varying input characteristics and movement constraints and compared to a MAPD solver that utilizes conflict-based search (CBS).

Boolean satisfiability verification by quantum annealing

Boolean satisfiability verification by quantum annealing

NAPOLY: A Non-deterministic Automata Processor OverLaY

Deterministic and Non-deterministic Finite Automata (DFA and NFA) comprise the core of many big data applications. Recent efforts to develop Domain-Specific Architectures (DSAs) for DFA/NFA have taken divergent approaches, but achieving consistent throughput for arbitrarily-large pattern sets, state activation rates, and pattern match rates remains a challenge. In this article, we present NAPOLY (Non-Deterministic Automata Processor OverLaY), an FPGA overlay and associated compiler. A common limitation of prior efforts is a limit on NFA size for achieving the advertised throughput. NAPOLY is optimized for fast re-programming to permit practical time-division multiplexing of the hardware and permit high asymptotic throughput for NFAs of unlimited size, unlimited state activation rate, and high pattern reporting rate. NAPOLY also allows for offline generation of configurations having tradeoffs between state capacity and transition capacity. In this article, we (1) evaluate NAPOLY using benchmarks packaged in the ANMLZoo benchmark suite, (2) evaluate the use of an SAT solver for allocating physical resources, and (3) compare NAPOLY’s performance against existing solutions. NAPOLY performs most favorably on larger benchmarks, benchmarks with higher state activation frequency, and benchmarks with higher reporting frequency. NAPOLY outperforms the fastest of the CPU and GPU implementations in 10 out of 12 benchmarks.