Transition Graph Research Articles

On the right track: decoding self-regulated learning in young students’ log data with the digital train track task

Assessing self-regulated learning (SRL)—the interplay between monitoring and control behavior—remains challenging, particularly in young learners. The unobtrusive assessment with log data to investigate SRL offers a promising method to deepen the understanding of the SRL process of young students. Despite the significant potential of log data to enhance the measurement of SRL, recent research encounters new challenges of operationalization, transparency, generalizability, validity, and reproducibility. This study introduces an innovative instrument, the digital train track task (TTT), for assessing SRL with log data in young learners, focusing on monitoring and controlling behavior. Log data of 85 primary school students (second to fifth grades, aged 7–13 years) performing one simple and one complex TTT were analyzed. As a novel method, finite state machines (FSM) were applied to extract SRL-related actions and states from the log data. To evaluate and explore the potential of the digital TTT, monitoring, and control behavior during simple and complex tasks were compared, employing frequency-based statistical analysis and transition graphs. Additionally, the log data were multimethodically linked with think-aloud data. The results revealed differences in monitoring and control behavior during the simple and the complex tasks regarding frequency, duration, and transitions between the SRL-related states. Extracted SRL-related states from log data and corresponding think-aloud data showed significant correlations. Adding to the growing body of log data research, this study offers an innovative task to validly assess the metacognitive self-regulation processes of young learners during problem-solving. The transparent, theory-based operationalization of SRL in this study, taking into account recent demands for SRL log data research, allows better reproducibility and transfer and adds to the generalizability of findings from SRL log data research.

New Dynamic Programming algorithm for the Multiobjective Minimum Spanning Tree problem

The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.

Revisiting block deordering in finite-domain state variable planning

Plan deordering removes unnecessary ordering constraints between actions in a plan, facilitating plan execution flexibility and several other tasks, such as plan reuse, modification, and decomposition. Block deordering is a variant of plan deordering that encapsulates coherent actions into blocks to eliminate further ordering constraints from a partial-order plan (POP) and is useful in many applications (e.g., generating macro-actions and improving the overall plan quality). The existing block deordering strategy is formulated in propositional encodings. Finite-domain state variable encodings (e.g., SAS+ representation), in contrast with propositional encodings, can capture the internal structure and the behavior of state variables of a planning instance through concise constructs such as causal graphs (CGs) and domain transition graphs (DTGs). This work redefines the semantics of block deordering terminologies and related plan deordering concepts in finite domain representation (FDR). Our proposed semantics also resolves some limitations of the existing block semantics and further enhance plan flexibility. In addition, this work exploits block deordering to eliminate redundant actions from a POP. A comparative analysis is also performed on block deordering with various deordering/reordering techniques using explanation-based order generalization (EOG) and MaxSAT. Our experiments on the benchmark problems from International Planning Competitions (IPC) show that our FDR formalism of block deordering significantly improves the plan execution flexibility while maintaining good coverage and execution time.

Modelling of Reliability Indicators of a Mining Plant

The evaluation and prediction of reliability and testability of mining machinery and equipment are crucial, as advancements in mining technology have increased the importance of ensuring the safety of both the technological process and human life. This study focuses on developing a reliability model to analyze the controllability of mining equipment. The model, which examines the reliability of a mine cargo-passenger hoist, utilizes statistical methods to assess failures and diagnostic controlled parameters. It is represented as a transition graph and is supported by a system of equations. This model enables the estimation of the reliability of equipment components and the equipment as a whole through a diagnostic system designed for monitoring and controlling mining equipment. A mathematical and logical model is proposed to calculate availability and downtime coefficients for different structures within the mining equipment system. This analysis considers the probability of failure-free operation of the lifting unit based on the structural scheme, with additional redundancy for elements with lower reliability. The availability factor of the equipment for monitoring and controlling the mine hoisting plant is studied for various placements of diagnostic systems. Additionally, a logistic concept is introduced for organizing preventive maintenance systems and reducing equipment recovery time by optimizing spare parts, integrating them into strategies aimed at enhancing the reliability of mine hoisting plants.

Developing information technology for evaluating and enhancing application-layer DDoS attack detection methods

The subject matter of this article is the methods to detect distributed denial-of-service (DDoS) attacks at the Hypertext Transfer Protocol (HTTP) level with the purpose of justifying the requirements for creating software capable of identifying malicious web server clients. The goal of this article is to develop an information technology to evaluate the efficiency of DDoS attack detection methods, which will quantify their operating time, memory consumption, and approximate classification accuracy. In addition, this paper proposes hypotheses and a potential approach to improve existing application-layer DDoS attack detection methods with the intention of increasing their accuracy and identification speed. The tasks of this study are as follows: to analyse modern methods for detecting application-layer DDoS attacks; to investigate their features and short­comings; to develop a software system to assess DDoS attack detection methods; to programmatically implement these methods and experimentally measure their performance indicators, specifically: classification ac­curacy, operating time, and memory usage; to compare the efficiency of the investigated methods; to formulate hypotheses and propose an approach to improve existing methods and/or develop new methods based on the results obtained. The methods employed are abstraction, analysis, systematic approach, and empirical research. In particular, the datasets generated by DDoS utilities were processed using the synthetic minority oversampling technique (SMOTE) to balance them. Furthermore, the studied DDoS attack detection methods were implemented, including fitting the required parameters and training artificial neural network models for evaluation. The following results were obtained. The average classification accuracy, operating time, and random-access memory (RAM) consumption during Internet traffic classification were determined for six DDoS attack detection methods under the same conditions. This study has demonstrated that the development of a novel method to detect DDoS attacks at the HTTP level with enhanced accuracy and classification speed is strongly required. The experimental results demonstrate that the time series-based method exhibited the shortest operating time (1.33 ms for 5000 vectors), whereas the deep neural network-based method exhibited the highest average classification accuracy (ranging from 99.07% to 99.97%) and the lowest memory consumption (39.09 KB for 5000 vectors). Conclusions. In this study, a software system was developed to assess the average accuracy of DDoS attack classification methods and measure the computational resources utilized. The scientific novelty of the obtained results lies in the formulation of two hypotheses and a potential approach to the creation of a novel method for detecting DDoS attacks at the HTTP level, which will have both high classification accuracy and a short operating time to surpass previously studied analogues in these respects. The first hypothesis is based on the additional usage of HTTP request attributes during Internet traffic classification. The second hypothesis is to analyse a graph of user transitions between website pages. The article also superficially describes a potential approach that involves the implementation of the described hypotheses as well as the proposed software architecture of an application-layer DDoS attack detection system for the Kubernetes platform and the Istio framework, which addresses the issue of collecting web request parameter values for websites that use the cryptographically secured HTTPS protocol.

Synthesis of Self-Checking Circuits for Train Route Traffic Control at Intermediate Stations with Control of Calculations Based on Weight-Based Sum Codes

When synthesizing systems for railway interlocking, it is recommended to use automated models to implement the logic of railway automation and remote control units. Finite-state machines (FSMs) can be implemented on any hardware component. When using relay technology, the functional safety of electrical interlocking is achieved by using uncontrolled (safety) relays with a high coefficient of asymmetry of failures in types 1 → 0 and 0 → 1. When using programmable components, the use of backup and diverse protection methods is required. This paper presents a flexible approach to synthesizing FSMs for railway automation and remote control units that offer both individual and route-based control. Unlike existing solutions, this proposal considers the pre-failure states of railway automation and remote control units during the finite-state machine synthesis stage. This enables the implementation of self-checking and self-diagnostic modules to manage automation units. By increasing the number of states for individual devices and considering the states of interconnected objects, the transition graphs can be expanded. This expansion allows for the synthesis of the transition graph of the control subsystem and other systems. The authors used a field-programmable gate array (FPGA) to implement a finite-state machine. In this case, the proposal is to encode the states of a finite-state machine using weight-based sum codes in the residue class ring based on a given modulus. The best coverage of errors occurring at the outputs of the logic converter in the structure of the FSM can be ensured by selecting the weighting coefficients and the value of the module. This paper presents an example of synthesizing an FPGA-based FSM using state encoding through modular weight-based sum codes. The operation of the synthesized device was modeled. It was found to operate according to the same algorithm as the real devices. When synthesizing self-checking and self-controlled train control devices, it is recommended to consider the solutions proposed in this paper.

Constructing neural networks with pre-specified dynamics

A main goal in neuroscience is to understand the computations carried out by neural populations that give animals their cognitive skills. Neural network models allow to formulate explicit hypotheses regarding the algorithms instantiated in the dynamics of a neural population, its firing statistics, and the underlying connectivity. Neural networks can be defined by a small set of parameters, carefully chosen to procure specific capabilities, or by a large set of free parameters, fitted with optimization algorithms that minimize a given loss function. In this work we alternatively propose a method to make a detailed adjustment of the network dynamics and firing statistic to better answer questions that link dynamics, structure, and function. Our algorithm—termed generalised Firing-to-Parameter (gFTP)—provides a way to construct binary recurrent neural networks whose dynamics strictly follows a user pre-specified transition graph that details the transitions between population firing states triggered by stimulus presentations. Our main contribution is a procedure that detects when a transition graph is not realisable in terms of a neural network, and makes the necessary modifications in order to obtain a new transition graph that is realisable and preserves all the information encoded in the transitions of the original graph. With a realisable transition graph, gFTP assigns values to the network firing states associated with each node in the graph, and finds the synaptic weight matrices by solving a set of linear separation problems. We test gFTP performance by constructing networks with random dynamics, continuous attractor-like dynamics that encode position in 2-dimensional space, and discrete attractor dynamics. We then show how gFTP can be employed as a tool to explore the link between structure, function, and the algorithms instantiated in the network dynamics.

GenTrajRec: A Graph-Enhanced Trajectory Recovery Model Based on Signaling Data

Signaling data are records of the interactions of users’ mobile phones with their nearest cellular stations, which could provide long-term and continuous-time location data of large-scale citizens, and therefore have great potential in intelligent transportation, smart cities, and urban sensing. However, utilizing the raw signaling data often suffers from two problems: (1) Low positioning accuracy. Since the signaling data only describes the interaction between the user and the mobile base station, they can only restore users’ approximate geographical location. (2) Poor data quality. Due to the limitations of mobile signals, user signaling may be missing and drifting. To address the above issues, we propose a graph-enhanced trajectory recovery network, GenTrajRec, to recover precise trajectories from signaling data. GenTrajRec encodes signaling data through spatiotemporal encoders and enhances the traveling semantics by constructing a signaling transition graph. In fusing the spatiotemporal information as well as the deep traveling semantics, GenTrajRec can well tackle the challenge of poor data quality, and recover precise trajectory from raw signaling data. Extensive experiments have been conducted on two real-world datasets from Mobile Signaling and Geolife, and the results confirm the effectiveness of our approach, and the positioning accuracy can be improved from 315 m per point to 82 m per point for signaling data using our network.

Dependency-aware action planning for smart home.

How can a smart home system control a connected device to be in a desired state? Recent developments in the Internet of Things (IoT) technology enable people to control various devices with the smart home system rather than physical contact. Furthermore, smart home systems cooperate with voice assistants such as Bixby or Alexa allowing users to control their devices through voice. In this process, a user's query clarifies the target state of the device rather than the actions to perform. Thus, the smart home system needs to plan a sequence of actions to fulfill the user's needs. However, it is challenging to perform action planning because it needs to handle a large-scale state transition graph of a real-world device, and the complex dependence relationships between capabilities. In this work, we propose SmartAid (Smart Home Action Planning in awareness of Dependency), an action planning method for smart home systems. To represent the state transition graph, SmartAid learns models that represent the prerequisite conditions and operations of actions. Then, SmartAid generates an action plan considering the dependencies between capabilities and actions. Extensive experiments demonstrate that SmartAid successfully represents a real-world device based on a state transition log and generates an accurate action sequence for a given query.

QUEUING SYSTEM WITH BULK SERVICE AS A MODEL OF SCTP PROTOCOL FUNCTIONING

The article presents the results of developing a model for the Stream Control Transmission Protocol functioning as a queuing system with bulk service. It constructs a graph of states and transitions for deriving linear and differential equation systems regarding the state probabilities. We obtain explicit solutions to analyse the basic SCTP functioning. Keywords: computer network, protocol, probabilistic model, queuing system, bulk service.

Частная полумарковская модель как инструмент снижения сложности задачи оценивания устойчивости функционирования элементов информационной инфраструктуры, подверженной воздействию угроз

Decision-making on information infrastructure (II) security for its sustainable functioning in the face of threats requires a tool to assess the sustainability of its individual elements. The application of the semi-Markov model to assess the stability of the functioning of elements of II exposed to threats in a direct setting is associated with the increasing complexity of the description of the object of delineation (parametric space) in step progression from the number of the considered impacts, which reduces its practical significance. However, no studies have been found in the scientific literature to reduce the complexity of the semi-Markov model. The article presents an approach to reducing the complexity of modeling by adopting correct assumptions when forming the initial data. Given the conditions under which it is possible to take a series. It was a cost to limit the applicability of the model by significantly reducing the complexity of the modelling. The problem statement and the modified transition graph are given. The novelty of the problem statement is to take into account the limitations on the available resources for the restoration of functionality of the element. To explain the physical essence of the modeling process, a thought experiment with a model is introduced. To solve the problem, the following methods were used: a) expert methods for extraction of initial data; b) mathematical models of private semi-Markov processes; c) methods of transformation of Laplace; r) methods of planning of experiment. Illustrative examples and graphs accompany the task sequence demonstration. As a result of the experiment, the regularities of the studied process, the existence of which was proved formally. As a result of the experiment, the regularities of the studied process were revealed, the existence of which was officially proved. The results of the study broaden knowledge about the application of methods of Markov processes to assess the stability of the functioning of AI elements in relation to the conditions of the impact of threats.

ОЦІНЮВАННЯ ВПЛИВУ ЗАСОБІВ ПІДКЛЮЧЕННЯ РЕЗЕРВУ НА ПОКАЗНИКИ НАДІЙНОСТІ СИСТЕМИ ПЕРЕДАВАННЯ ДАНИХ

Structural redundancy is included in modern data transmission systems to ensure the specified reliability indicators. Structural redundancy gives the system fault tolerance and significantly increases its reliability. To manage the redundant resource, it is necessary to have additional tools that will connect the redundant equipment to the main configuration of the data transmission system. The redundant equipment is a separate technical means and, from the point of view of reliability, it is connected in series with other modules of the data transmission system. Thus, the inclusion of redundant connection facilities in the data transmission system reduces its reliability. In addition, even with perfect reliability, redundant connections may fail or malfunction and, under certain conditions, cause the transmission system to fail. To determine the impact of reserve connection facilities on the reliability of the transmission system, the article applies an original technology for building models of discrete-continuous stochastic systems. ASNA software was used as a software tool for modeling the reliable behavior of the data transmission system. This software provides automated construction of the model in the form of a graph of states and transitions based on a structural automaton model. Based on the graph of states and transitions, an analytical model is automatically generated in the form of a system of linear differential Kolmogorov-Chapman equations. Using the developed model, the article quantitatively analyzes the impact of redundant connection means (switches) on the reliability indicators of the data transmission system. In the study, the proposed models, unlike the existing ones, take into account both reliability indicators (probability of failure) and functionality indicators (probability of switching, speed) of the reserve connection means. On the basis of the developed model, the limit values of reliability and functionality of the redundant connection means (switches) were determined, at which they will minimize the reliability of the fault-tolerant data transmission system. Based on the analysis of the obtained results, practical recommendations for the selection of reliability indicators of the backup connection means, their speed and probability of switching are formed.

Group-aware graph neural networks for sequential recommendation

Sequential recommendations play a crucial role in recommender systems. Existing methods commonly focus on extracting sequential patterns within individual item sequences to make personalized recommendations. However, this paper argues that such a closure strategy has limitations. Firstly, the inherent uncertainty and sparsity within these sequences pose considerable challenges in accurately capturing sequential patterns. Secondly, ignoring group behaviors beyond the sequence hinders the modeling of user similarities, which are essential for recommendations. To address these limitations, this paper proposes a novel collaborative sequential recommendation approach, called Group-aware Graph Neural Networks (GaGNN). GaGNN seeks to incorporate group behaviors within sequential recommendations, thereby enhancing the modeling of user preferences through the assimilation of collective wisdom. GaGNN constructs two transition graphs, each offering a distinct behavioral perspective. The group transition graph is designed to capture the collaborative effects and learn collaborative information, whereas the individual transition graph aims to articulate individual behaviors, thereby extracting sequential information. Additionally, a multi-source information fusion module is designed to bridge semantic gaps between the two types of information and yield a holistic understanding of user preferences. Through rigorous experimental comparisons and ablation studies, the superiority of GaGNN and the beneficial integration of collaborative information are emphatically validated.

Human learning of hierarchical graphs.

Humans are exposed to sequences of events in the environment, and the interevent transition probabilities in these sequences can be modeled as a graph or network. Many real-world networks are organized hierarchically and while much is known about how humans learn basic transition graph topology, whether and to what degree humans can learn hierarchical structures in such graphs remains unknown. We probe the mental estimates of transition probabilities via the surprisal effect phenomenon: humans react more slowly to less expected transitions. Using mean-field predictions and numerical simulations, we show that surprisal effects are stronger for finer-level than coarser-level hierarchical transitions, and that surprisal effects at coarser levels are difficult to detect for limited learning times or in small samples. Using a serial response experiment with human participants (n=100), we replicate our predictions by detecting a surprisal effect at the finer level of the hierarchy but not at the coarser level of the hierarchy. We then evaluate the presence of a trade-off in learning, whereby humans who learned the finer level of the hierarchy better also tended to learn the coarser level worse, and vice versa. This study elucidates the processes by which humans learn sequential events in hierarchical contexts. More broadly, our work charts a road map for future investigation of the neural underpinnings and behavioral manifestations of graph learning.

Potential-based reward shaping using state–space segmentation for efficiency in reinforcement learning

Reinforcement Learning (RL) algorithms encounter slow learning in environments with sparse explicit reward structures due to the limited feedback available on the agent’s behavior. This problem is exacerbated particularly in complex tasks with large state and action spaces. To address this inefficiency, in this paper, we propose a novel approach based on potential-based reward-shaping using state–space segmentation to decompose the task and to provide more frequent feedback to the agent. Our approach involves extracting state–space segments by formulating the problem as a minimum cut problem on a transition graph, constructed using the agent’s experiences during interactions with the environment via the Extended Segmented Q-Cut algorithm. Subsequently, these segments are leveraged in the agent’s learning process through potential-based reward shaping. Our experimentation on benchmark problem domains with sparse rewards demonstrated that our proposed method effectively accelerates the agent’s learning without compromising computation time while upholding the policy invariance principle.

Transition Propagation Graph Neural Networks for Temporal Networks.

Researchers of temporal networks (e.g., social networks and transaction networks) have been interested in mining dynamic patterns of nodes from their diverse interactions. Inspired by recently powerful graph mining methods like skip-gram models and graph neural networks (GNNs), existing approaches focus on generating temporal node embeddings sequentially with nodes' sequential interactions. However, the sequential modeling of previous approaches cannot handles the transition structure between nodes' neighbors with limited memorization capacity. In detail, an effective method for the transition structures is required to both model nodes' personalized patterns adaptively and capture node dynamics accordingly. In this article, we propose a method, namely t ransition p ropagation g raph n eural n etworks (TIP-GNN), to tackle the challenges of encoding nodes' transition structures. The proposed TIP-GNN focuses on the bilevel graph structure in temporal networks: besides the explicit interaction graph, a node's sequential interactions can also be constructed as a transition graph. Based on the bilevel graph, TIP-GNN further encodes transition structures by multistep transition propagation and distills information from neighborhoods by a bilevel graph convolution. Experimental results over various temporal networks reveal the efficiency of our TIP-GNN, with at most 7.2% improvements of accuracy on temporal link prediction. Extensive ablation studies further verify the effectiveness and limitations of the transition propagation module. Our code is available at https://github.com/doujiang-zheng/TIP-GNN.

Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Neural Gaussian Similarity Modeling for Differential Graph Structure Learning

Graph Structure Learning (GSL) has demonstrated considerable potential in the analysis of graph-unknown non-Euclidean data across a wide range of domains. However, constructing an end-to-end graph structure learning model poses a challenge due to the impediment of gradient flow caused by the nearest neighbor sampling strategy. In this paper, we construct a differential graph structure learning model by replacing the non-differentiable nearest neighbor sampling with a differentiable sampling using the reparameterization trick. Under this framework, we argue that the act of sampling nearest neighbors may not invariably be essential, particularly in instances where node features exhibit a significant degree of similarity. To alleviate this issue, the bell-shaped Gaussian Similarity (GauSim) modeling is proposed to sample non-nearest neighbors. To adaptively model the similarity, we further propose Neural Gaussian Similarity (NeuralGauSim) with learnable parameters featuring flexible sampling behaviors. In addition, we develop a scalable method by transferring the large-scale graph to the transition graph to significantly reduce the complexity. Experimental results demonstrate the effectiveness of the proposed methods.

Temporal Graph Contrastive Learning for Sequential Recommendation

Sequential recommendation is a crucial task in understanding users' evolving interests and predicting their future behaviors. While existing approaches on sequence or graph modeling to learn interaction sequences of users have shown promising performance, how to effectively exploit temporal information and deal with the uncertainty noise in evolving user behaviors is still quite challenging. To this end, in this paper, we propose a Temporal Graph Contrastive Learning method for Sequential Recommendation (TGCL4SR) which leverages not only local interaction sequences but also global temporal graphs to comprehend item correlations and analyze user behaviors from a temporal perspective. Specifically, we first devise a Temporal Item Transition Graph (TITG) to fully leverage global interactions to understand item correlations, and augment this graph by dual transformations based on neighbor sampling and time disturbance. Accordingly, we design a Temporal item Transition graph Convolutional network (TiTConv) to capture temporal item transition patterns in TITG. Then, a novel Temporal Graph Contrastive Learning (TGCL) mechanism is designed to enhance the uniformity of representations between augmented graphs from identical sequences. For local interaction sequences, we design a temporal sequence encoder to incorporate time interval embeddings into the architecture of Transformer. At the training stage, we take maximum mean discrepancy and TGCL losses as auxiliary objectives. Extensive experiments on several real-world datasets show the effectiveness of TGCL4SR against state-of-the-art baselines of sequential recommendation.

Compact Circuits for Efficient Möbius Transform

The Möbius transform is a linear circuit used to compute the evaluations of a Boolean function over all points on its input domain. The operation is very useful in finding the solution of a system of polynomial equations over GF(2) for obvious reasons. However the operation, although linear, needs exponential number of logic operations (around n · 2n−1 bit xors) for an n-variable Boolean function. As such, the only known hardware circuit to efficiently compute the Möbius Transform requires silicon area that is exponential in n. For Boolean functions whose algebraic degree is bound by some parameter d, recursive definitions of the Möbius Transform exist that requires only O(nd+1) space in software. However converting the mathematical definition of this space-efficient algorithm into a hardware architecture is a non-trivial task, primarily because the recursion calls notionally lead to a depth-first search in a transition graph that requires context switches at each recursion call for which straightforward mapping to hardware is difficult. In this paper we look to overcome these very challenges in an engineering sense. We propose a space efficient sequential hardware circuit for the Möbius Transform that requires only polynomial circuit area (i.e. O(nd+1)) provided the algebraic degree of the Boolean function is limited to d. We show how this circuit can be used as a component to efficiently solve polynomial equations of degree at most d by using fast exhaustive search. We propose three different circuit architectures for this, each of which uses the Möbius Transform circuit as a core component. We show that asymptotically, all the solutions of a system of m polynomials in n unknowns and algebraic degree d over GF(2) can be found using a circuit of silicon area proportional to m · nd+1 and circuit depth proportional to 2 · log2(n − d).In the second part of the paper we introduce a fourth hardware solver that additionally aims to achieve energy efficiency. The main idea is to reduce the solution space to a small enough value by parallel application of Möbius Transform circuits over the first few equations of the system. This is done so that one can check individually whether the vectors of this reduced solution space satisfy each of the remaining equations of the system using lower power consumption. The new circuit has area also bound by m · nd+1 and has circuit depth proportional to d · log2 n. We also show that further optimizations with respect to energy consumption may be obtained by using depth-bound Möbius circuits that exponentially decrease run time at the cost of additional logic area and depth.