Search Results (10)

Exact probabilistic inference in Bayesian Networks (BNs) becomes increasingly expensive as network size and structural complexity grow, limiting its applicability in time-sensitive decision-support systems. This study presents a hybrid inference framework that accelerates the deterministic component of Bayesian reasoning by integrating Boolean Satisfiability (SAT) techniques with Bayesian Networks. The proposed approach transforms deterministic conditional probability table (CPT) entries into conjunctive normal form (CNF), enabling SAT-based logical inference over deterministic constraints while preserving the original Bayesian model for probabilistic reasoning. The framework was evaluated on 25 benchmark Bayesian networks using five independent executions per dataset under identical experimental conditions. Performance was assessed through execution time, instrumented operation counts, and inference coverage, with results reported as mean values, standard deviations, and 95% confidence intervals. Experimental results demonstrate substantial reductions in deterministic inference time while maintaining high coverage of deterministic variable assignments across the evaluated benchmarks. Throughout this paper, the reported performance gains refer exclusively to empirical reductions in execution time and instrumented operation counts. They should not be interpreted as evidence of a reduction in the asymptotic computational complexity of exact Bayesian inference, which remains #P-complete in the general case. Rather, the proposed framework provides an efficient mechanism for accelerating deterministic logical inference within Bayesian Networks under the evaluated benchmark conditions. Full article

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

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

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

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

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

This paper reviews recent approaches on how to accelerate Boolean Satisfiability (SAT) search by exploiting symmetries in the problem space. SAT search algorithms traverse an exponentially large search space looking for an assignment that satisfies a set of constraints. The presence of symmetries in the search space induces equivalence classes on the set of truth assignments. The goal is to use symmetries to avoid traversing all assignments by constraining the search to visit a few representative assignments in each equivalence class. This can lead to a significant reduction in search runtime without affecting the completeness of the search. Full article