Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between Boolean networks. To tackle this challenge, we introduce BoolSkeleton, a novel Boolean network skeletonization method that improves the consistency and reliability of design-specific evaluations. BoolSkeleton comprises two key steps: preprocessing and reduction. In preprocessing, the Boolean network is transformed into a defined Boolean dependency graph, where nodes are assigned the functionality-related status. Next, the homogeneous and heterogeneous patterns are defined for the node-level pattern reduction step. Heterogeneous patterns are preserved to maintain critical functionality-related dependencies, while homogeneous patterns can be reduced. Parameter K of the pattern further constrains the fanin size of these patterns, enabling fine-tuned control over the granularity of graph reduction. To validate BoolSkeleton's effectiveness, we conducted four analysis/downstream tasks around the Boolean network: compression analysis, classification, critical path analysis, and timing prediction, demonstrating its robustness across diverse scenarios. Furthermore, it improves above 55% in the average accuracy compared to the original Boolean network for the timing prediction task. These experiments underscore the potential of BoolSkeleton to enhance design consistency in logic synthesis.

In this paper we investigate formal verification of extracted rules for Neural Networks under a complexity theoretic point of view. A rule is a global property or a pattern concerning a large portion of the input space of a network. These rules are algorithmically extracted from networks in an effort to better understand their inner way of working. Here, three problems will be in the focus: Does a given set of rules apply to a given network? Is a given set of rules consistent or do the rules contradict themselves? Is a given set of rules exhaustive in the sense that for every input the output is determined? Finding algorithms that extract such rules out of networks has been investigated over the last 30 years, however, to the author's current knowledge, no attempt in verification was made until now. A lot of attempts of extracting rules use heuristics involving randomness and over-approximation, so it might be beneficial to know whether knowledge obtained in that way can actually be trusted. We investigate the above questions for neural networks with ReLU-activation as well as for Boolean networks, each for several types of rules. We demonstrate how these problems can be reduced to each other and show that most of them are co-NP-complete.

--This paper introduces OpenLS-DGF, an adaptive logic synthesis dataset generation framework, to enhance machine learning (ML) applications within the logic synthesis process. Previous dataset generation flows were tailored for specific tasks or lacked integrated machine learning capabilities. While OpenLS-DGF supports various machine learning tasks by encapsulating the three fundamental steps of logic synthesis: Boolean representation, logic optimization, and technology mapping. It preserves the original information in both V erilog and machine-learning-friendly GraphML formats. The verilog files offer semi-customizable capabilities, enabling researchers to insert additional steps and incrementally refine the generated dataset. Furthermore, OpenLS-DGF includes an adaptive circuit engine that facilitates the final dataset management and downstream tasks. The generated OpenLS-D-v1 dataset comprises 46 combinational designs from established benchmarks, totaling over 966,000 Boolean circuits. OpenLS-D-v1 supports integrating new data features, making it more versatile for new challenges. This paper demonstrates the versatility of OpenLS-D-v1 through four distinct downstream tasks: circuit classification, circuit ranking, quality of results (QoR) prediction, and probability prediction. Each task is chosen to represent essential steps of logic synthesis, and the experimental results show the generated dataset from OpenLS-DGF achieves prominent diversity and applicability. OGIC synthesis is a key phase in the electronic design automation (EDA) flow of digital circuits, translating high-level specifications into a gate-level netlist. Recently, there has been a trend towards adopting ML approaches for the EDA [1] domain. V arious machine learning methodologies have been proposed, demonstrating improvements in different aspects of the logic synthesis process, including logic optimization [2], [3], [4], [5], [6], technology mapping [7], [8], [9], and formal verification [10], [11]. These machine learning-based techniques have shown their promise in improving the efficiency and quality of logic synthesis steps.

The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a hardware-friendly alternative that could enable more efficient implementation. However, their ability to match the performance of traditional networks has remained uncertain. This paper explores strategies to enhance deep Boolean networks with the aim of surpassing their traditional counterparts. We propose novel methods, including logical skip connections and spatiality preserving sampling, and validate them on vision tasks using widely adopted datasets, demonstrating significant improvement over existing approaches. Our analysis shows how deep Boolean networks can maintain high performance while minimizing computational costs through 1-bit logic operations. These findings suggest that Boolean networks are a promising direction for efficient, high-performance deep learning models, with significant potential for advancing hardware-accelerated AI applications.

Learning from interpretation transition (LFIT) is a framework for learning rules from observed state transitions. LFIT has been implemented in purely symbolic algorithms, but they are unable to deal with noise or generalize to unobserved transitions. Rule extraction based neural network methods suffer from overfitting, while more general implementation that categorize rules suffer from combinatorial explosion. In this paper, we introduce a technique to leverage variable permutation invariance inherent in symbolic domains. Our technique ensures that the permutation and the naming of the variables would not affect the results. We demonstrate the effectiveness and the scalability of this method with various experiments.

Answer Set Programming (ASP) is a declarative problem solving paradigm that can be used to encode a combinatorial problem as a logic program whose stable models correspond to the solutions of the considered problem. ASP has been widely applied to various domains in AI and beyond. The question "What can be said about stable models of a logic program from its static information?" has been investigated and proved useful in many circumstances. In this work, we dive into this direction more deeply by making the connection between a logic program and a Boolean network, which is a prominent modeling framework with applications to various areas. The proposed connection can bring the existing results in the rich history on static analysis of Boolean networks to explore and prove more theoretical results on ASP, making it become a unified and powerful tool to further study the static analysis of ASP. In particular, the newly obtained insights have the potential to benefit many problems in the field of ASP.

Dialectical frameworks are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. Their generality allow them to cover a number of different approaches with varying forms of representing the argumentation structure. Boolean regulatory networks are used to model the dynamics of complex biological processes, taking into account the interactions of biological compounds, such as proteins or genes. These models have proven highly useful for comprehending such biological processes, allowing to reproduce known behaviour and testing new hypotheses and predictions in silico, for example in the context of new medical treatments. While both these approaches stem from entirely different communities, it turns out that there are striking similarities in their appearence. In this paper, we study the relation between these two formalisms revealing their communalities as well as their differences, and introducing a correspondence that allows to establish novel results for the individual formalisms.

Effective exploration abilities are fundamental for robot swarms, especially when small, inexpensive robots are employed (e.g., micro- or nano-robots). Random walks are often the only viable choice if robots are too constrained regarding sensors and computation to implement state-of-the-art solutions. However, identifying the best random walk parameterisation may not be trivial. Additionally, variability among robots in terms of motion abilities-a very common condition when precise calibration is not possible-introduces the need for flexible solutions. This study explores how random walks that present chaotic or edge-of-chaos dynamics can be generated. We also evaluate their effectiveness for a simple exploration task performed by a swarm of simulated Kilobots. First, we show how Random Boolean Networks can be used as controllers for the Kilobots, achieving a significant performance improvement compared to the best parameterisation of a L\'evy-modulated Correlated Random Walk. Second, we demonstrate how chaotic dynamics are beneficial to maximise exploration effectiveness. Finally, we demonstrate how the exploration behavior produced by Boolean Networks can be optimized through an Evolutionary Robotics approach while maintaining the chaotic dynamics of the networks.

In this paper, I describe a digital social communication protocol (Gridt) based on Kauffman's NK boolean networks. The main assertion is that a communication network with this topology supports infinitely scalable self-organization of collective action without requiring hierarchy or central control. The paper presents the functionality of this protocol and substantiates the following propositions about its function and implications: (1) Communication via NK boolean networks facilitates coordination on collective action games for any variable number of users, and justifies the assumption that the game's payoff structure is common knowledge; (2) Use of this protocol increases its users' transfer empowerment, a form of intrinsic motivation that motivates coordinated action independent of the task or outcome; (3) Communication via this network can be considered 'cheap talk' and benefits the strategy of players with aligned interests, but not of players with conflicting interests; (4) Absence of significant barriers for its realization warrants a timely and continuing discussion on the ethics and implications of this technology; (5) Full realization of the technology's potential calls for a free-to-use service with maximal transparency of design and associated economic incentives.

Cellular reprogramming can be used for both the prevention and cure of different diseases. However, the efficiency of discovering reprogramming strategies with classical wet-lab experiments is hindered by lengthy time commitments and high costs. In this study, we develop a novel computational framework based on deep reinforcement learning that facilitates the identification of reprogramming strategies. For this aim, we formulate a control problem in the context of cellular reprogramming for the frameworks of BNs and PBNs under the asynchronous update mode. Furthermore, we introduce the notion of a pseudo-attractor and a procedure for identification of pseudo-attractor state during training. Finally, we devise a computational framework for solving the control problem, which we test on a number of different models.