Search Results (16)

This paper introduces a lightweight cryptographic hash algorithm, LWH-128, developed using a sponge-based construction and specifically adapted for operation under constrained computational and energy conditions typical of embedded systems and Internet of Things devices. The algorithm employs a two-layer processing structure based on simple logical operations (XOR, cyclic shifts, and S-boxes) and incorporates a preliminary diffusion transformation function G, along with the Davis–Meyer compression scheme, to enhance irreversibility and improve cryptographic robustness. A comparative analysis of hardware implementation demonstrates that LWH-128 exhibits balanced characteristics in terms of circuit complexity, memory usage, and processing speed, making it competitive with existing lightweight hash algorithms. As part of the cryptanalytic evaluation, a Boolean SATisfiability (SAT) Problem-based model of the compression function is constructed in the form of a conjunctive normal form of Boolean variables. Experimental results using the Parkissat SAT solver show an exponential increase in computational time as the number of unknown input bits increased. These findings support the conclusion that the LWH-128 algorithm exhibits strong resistance to preimage attacks based on SAT-solving techniques. Full article

We propose SAT-GATv2, a graph neural network (GNN)-based model designed to solve the Boolean satisfiability problem (SAT) through graph-based deep learning techniques. SAT-GATv2 transforms SAT formulas into graph structures, leveraging message-passing neural networks (MPNNs) to propagate local information and dynamic attention mechanisms (GATv2) to accurately capture inter-node dependencies and enhance node feature representations. Unlike traditional heuristic-driven SAT solvers, SAT-GATv2 adopts a data-driven approach, learning structural patterns directly from graph representations and providing a complementary framework to existing methods. Experimental results demonstrate that SAT-GATv2 achieves an accuracy improvement of 1.75–5.51% over NeuroSAT on challenging random 3-SAT(n) instances, highlighting its effectiveness in handling difficult problem distributions, and outperforms other GNN-based models on SR(n) datasets, showcasing its scalability and adaptability. Ablation studies validate the critical roles of MPNNs and GATv2 in improving prediction accuracy and scalability. While SAT-GATv2 does not yet surpass CDCL-based solvers in overall performance, it addresses their limitations in scalability and adaptability to complex instances, offering an efficient graph-based alternative for tackling larger and more complex SAT problems. This study establishes a foundation for integrating deep learning with combinatorial optimization, emphasizing its potential for applications in artificial intelligence and operations research. Full article

This paper aims to outline the effectiveness of modern universal gate quantum computers when utilizing different configurations to solve the B-SAT (Boolean satisfiability) problem. The quantum computing experiments were performed using Grover’s search algorithm to find a valid solution. The experiments were performed under different variations to demonstrate their effects on the results. Changing the number of shots, qubit mapping, and using a different quantum processor were all among the experimental variables. The study also branched into a dedicated experiment highlighting a peculiar behavior that IBM quantum processors exhibit when running circuits with a certain number of shots. Full article

Inferring a functional specification from an existing digital design is a challenge that is suitable with reverse-engineering methods. One of the most widely used functional specification formats is a finite state machine (FSM). This article studies the possibility of blind passive specification mining for a digital device, where the device is treated as a “black box”. The presented approach treats an input and output signal waveform as the transition graph of an incomplete deterministic FSM and learns the FSM through FSM minimization. It employs a Boolean satisfiability problem (SAT) solver to find a minimal FSM that complies with observed object behavior. The known approach to identifying state machines in discrete event systems is adapted to operate with variables in the form of coloring and transition tables. The developed implementation produces a synthesizable specification in hardware description language (HDL) and a state diagram in unified modeling language (UML). The proposed approach for inferring an FSM from a waveform trace can serve as a supplementary tool during reverse engineering to provide developers with meaningful insight regarding the analyzed device. The presented case study defines metrics of successful FSM inference and applies them to a synthetic FSM and a real-world example FSM to demonstrate the applicability of the approach. Full article

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 ${\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 3}$ are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model ${ \mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}$ with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model ${\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}$ exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z₂ lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}\right)$ is the computational complexity by brute force search of the AMC model ${\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}\right)$, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 4}\right)$ is the computational complexity by brute force search of the K-SAT problem for K = 3 ${ \mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}=3}\right)$. Namely, ${\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}\ge 4}\right)={\mathrm{C}}_{\mathrm{L}}\left({\mathrm{M}}_{\mathrm{SGI}}^{3\mathrm{D}}\right)\ge {\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{AMC}}^{3\mathrm{D}}\right)={\mathrm{C}}^{\mathrm{U}}\left({\mathrm{M}}_{\mathrm{SAT}}^{\mathrm{K}=3}\right)$. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3. Full article

The (weighted) partial maximum satisfiability ((W)PMS) problem is an important generalization of the classic problem of propositional (Boolean) satisfiability with a wide range of real-world applications. In this paper, we propose an initialization and a diversification strategy to improve local search for the (W)PMS problem. Our initialization strategy is based on a novel definition of variables’ structural entropy, and it aims to generate a solution that is close to a high-quality feasible one. Then, our diversification strategy picks a variable in two possible ways, depending on a parameter: continuing to pick variables with the best benefits or focusing on a clause with the greatest penalty and then selecting variables probabilistically. Based on these strategies, we developed a local search solver dubbed $\mathit{ImSATLike}$, as well as a hybrid solver $\mathit{ImSATLike-TT}$, and experimental results on (weighted) partial MaxSAT instances in recent MaxSAT Evaluations show that they outperform or have nearly the same performances as state-of-the-art local search and hybrid competitors, respectively, in general. Furthermore, we carried out experiments to confirm the individual impacts of each proposed strategy. Full article

It has been proven that extended resolution (ER) has more powerful reasoning than general resolution for the pigeonhole principle in Cook’s paper. This fact indicates the possibility that a solver based on extended resolution can exceed Boolean satisfiability problem solvers (SAT solvers for short) based on general resolution. However, few studies have provided practical evidence of this assumption. This paper explores how extended resolution can improve SAT solvers by using the pigeonhole principle, which was the first problem solved by ER in polynomial steps. In fact, although Cook’s paper introduced how to add auxiliary variables, there is no evidence that these variables are really useful for practical solvers. We try to answer the question: If the SAT solver can add appropriate auxiliary variables as proposed in Cook’s paper, can the solver enhance its performance by utilizing these variables? Experimental results show that if the solver properly prioritizes the extended variables in the search, the solver can end the search in a shorter time. Full article

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms $T$ of the Boolean function from $T$ of ancilla qubits to $\approx {\log }_{2}T+1$. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost. Full article

In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube $K_n$ with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in $K_n$ is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined. Full article

In this paper, we introduce the notion of resolvable networks. A resolvable network is a digraph of subnetworks, where subnetworks may overlap, and the inner structure of subnetworks are not interesting from the viewpoint of the network. There are two special subnetworks, Source and Sink, with the following properties: there is no incoming edge to Source, and there is no outgoing edge from Sink. Any resolvable network can be represented by a satisfiability problem in Boolean logic (shortly, SAT problem), and any SAT problem can be represented by a resolvable network. Because of that, the resolution operation is valid also for resolvable networks. We can use resolution to find out or refine the inner structure of subnetworks. We give also a pessimistic and an optimistic interpretation of subnetworks. In the pessimistic case, we assume that inside a subnetwork, all communication possibilities are represented as part of the resolvable network. In the optimistic case, we assume that each subnetwork is strongly connected. We show that any SAT problem can be visualized using the pessimistic interpretation. We show that transitivity is very limited in the pessimistic interpretation, and in this case, transitivity corresponds to resolution of clauses. In the optimistic interpretation of subnetworks, we have transitivity without any further condition, but not all SAT problems can be represented in this case; however, any such network can be represented as a SAT problem. The newly introduced graphical concept allows to use terminology and tools from directed graphs in the field of SAT and also to give graphical representations of various concepts of satisfiability problems. A resolvable network is also a suitable data structure to study, for example, wireless sensor networks. The visualization power of resolvable networks is demonstrated on some pigeon hole SAT problems. Another important application field could be modeling the communication network of an information bank. Here, a subnetwork represents a dataset of a user which is secured by a proxy. Any communication should be done through the proxy, and this constraint can be checked using our model. Full article

Model-Based Diagnosis (MBD) is a well-known approach to diagnosis in medical domains. In this approach, the behavior of a system is modeled and used to identify faulty components, i.e., once a symptom of abnormal behavior is observed, an inference algorithm is run on the system model and returns possible explanations. Such explanations are referred to as diagnoses. A diagnosis is an assumption about which set of components are faulty and have caused the abnormal behavior. In this work, we focus on the case where multiple observations are available to the diagnoser, collected at different times, such that some of these observations exhibit symptoms of abnormal behavior. MBD with multiple observations is challenging because some components may fail intermittently, i.e., behave abnormally in one observation and behave normally in another, while other components may fail all the time (non-intermittently). Inspired by recent success in solving classical diagnosis problems using Boolean satisfiability (SAT) solvers, we describe two SAT-based approaches to solve this MBD with multiple observations problem. The first approach compiles the problem to a single SAT formula, and the second approach solves each observation independently and then merges them together. We compare these two approaches experimentally on a standard diagnosis benchmark and analyze their pros and cons. Full article

In January 2016, a new standard for symmetric block encryption was established in the Russian Federation. The standard contains two encryption algorithms: Magma and Kuznyechik. In this paper we propose to consider the possibility of applying the algebraic analysis method to these ciphers. To do this, we use the simplified algorithms Magma ⊕ and S-KN2. To solve sets of nonlinear Boolean equations, we choose two different approaches: a reduction and solving of the Boolean satisfiability problem (by using the CryptoMiniSat solver) and an extended linearization method (XL). In our research, we suggest using a security assessment approach that identifies the resistance of block ciphers to algebraic cryptanalysis. The algebraic analysis of an eight-round Magma (68 key bits were fixed) with the CryptoMiniSat solver demanded four known text pairs and took 3029.56 s to complete (the search took 416.31 s). The algebraic analysis of a five-round Magma cipher with weakened S-boxes required seven known text pairs and took 1135.61 s (the search took 3.36 s). The algebraic analysis of a five-round Magma cipher with disabled S-blocks (equivalent value substitution) led to getting only one solution for five known text pairs in 501.18 s (the search took 4.92 s). The complexity of the XL algebraic analysis of a four-round S-KN2 cipher with three text pairs was 236.33 s (took 1.191 Gb RAM). Full article

Boolean propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains. Membrane computing is a branch of natural computing which has been proven to solve NP problems in polynomial time with a parallel compute mode. This paper proposes a new algorithm for SAT problem which combines the traditional membrane computing algorithm of SAT problem with a classic simplification rule, the splitting rule, which can divide a clause set into two axisymmetric subsets, deal with them respectively and simultaneously, and obtain the solution of the original clause set with the symmetry of their solutions. The new algorithm is shown to be able to reduce the space complexity by distributing clauses with the splitting rule repeatedly, and also reduce both time and space complexity by executing one-literal rule and pure-literal rule as many times as possible. Full article

The Boolean satisfiability (SAT) problem is the key problem in computer theory and application. A novel algorithm is introduced to implement a SLS hardware solver called probSAT+. The algorithm has no complex heuristic, and it only depends on the concepts of preprocessing technology, probability distribution and centralized search. Through constraining the initial assignments of the variables, the number of flipped variables was reduced while the solver finding a solution. Moreover, the algorithm no longer adopts some non-continuous if-then-else decisions, but depends on a single continuous function f(x,v). The flipping probability is not obtained by complex calculations, instead being selected by looking up tables, which effectively improves the performance of the solver. As far as we know, the probability distribution selection strategy descripted by hardware description language is firstly adopted by hardware SAT solver, which can be easily transplanted to any programmable logic device. The experimental results show that the probSAT+ solver is generally lower than the advanced software solver in the number of flips (up to 9.8 $\times {10}^6$ ), and the speedup is approximately 2.6 times with single thread, which shows that the probSAT+ has better results with fewer variables flipping times when a solution can be found. In addition, the success ratio of the solver in finding a solution of the problem in a suitable time is 100%. Full article

In a Software Product Line (SPL), the central notion of implementability provides the requisite connection between specifications and their implementations, leading to the definition of products. While it appears to be a simple extension of the traceability relation between components and features, it involves several subtle issues that were overlooked in the existing literature. In this paper, we have introduced a precise and formal definition of implementability over a fairly expressive traceability relation. The consequent definition of products in the given SPL naturally entails a set of useful analysis problems that are either refinements of known problems or are completely novel. We also propose a new approach to solve these analysis problems by encoding them as Quantified Boolean Formulae (QBF) and solving them through Quantified Satisfiability (QSAT) solvers. QBF can represent more complex analysis operations, which cannot be represented by using propositional formulae. The methodology scales much better than the SAT-based solutions hinted in the literature and were demonstrated through a tool called SPLAnE (SPL Analysis Engine) on a large set of SPL models. Full article