Securing dynamic networks against adversarial actions is challenging because of the need to anticipate and counter strategic disruptions by adversarial entities within complex network structures. Traditional game-theoretic models, while insightful, often fail to model the unpredictability and constraints of real-world threat assessment scenarios. We refinesabotage gamesto reflect the realistic limitations of the saboteur and the network operator. By transforming sabotage games into reachability problems, our approach allows applying existing computational solutions to model realistic restrictions on attackers and defenders within the game. Modifying sabotage games into dynamic network security problems successfully captures the nuanced interplay of strategy and uncertainty in dynamic network security. Theoretically, we extend sabotage games to model network security contexts and thoroughly explore if the additional restrictions raise their computational complexity, often the bottleneck of game theory in practical contexts. Practically, this research sets the stage for actionable insights for developing robust defense mechanisms by understanding what risks to mitigate in dynamic networks under threat.

Compositional knowledge representations in reinforcement learning (RL) facilitate modular, interpretable, and safe task specifications. However, generating compositional models requires the characterization of minimal assumptions for the robustness of the compositionality feature, especially in the case of functional decompositions. Using a categorical point of view, we develop a knowledge representation framework for a compositional theory of RL. Our approach relies on the theoretical study of the category $\mathsf{MDP}$, whose objects are Markov decision processes (MDPs) acting as models of tasks. The categorical semantics models the compositionality of tasks through the application of pushout operations akin to combining puzzle pieces. As a practical application of these pushout operations, we introduce zig-zag diagrams that rely on the compositional guarantees engendered by the category $\mathsf{MDP}$. We further prove that properties of the category $\mathsf{MDP}$ unify concepts, such as enforcing safety requirements and exploiting symmetries, generalizing previous abstraction theories for RL.

In reinforcement learning, conducting task composition by forming cohesive, executable sequences from multiple tasks remains challenging. However, the ability to (de)compose tasks is a linchpin in developing robotic systems capable of learning complex behaviors. Yet, compositional reinforcement learning is beset with difficulties, including the high dimensionality of the problem space, scarcity of rewards, and absence of system robustness after task composition. To surmount these challenges, we view task composition through the prism of category theory—a mathematical discipline exploring structures and their compositional relationships. The categorical properties of Markov decision processes untangle complex tasks into manageable sub-tasks, allowing for strategical reduction of dimensionality, facilitating more tractable reward structures, and bolstering system robustness. Experimental results support the categorical theory of reinforcement learning by enabling skill reduction, reuse, and recycling when learning complex robotic arm tasks.

Abstract Cyber-physical systems are complex systems that require the integration of diverse software, firmware, and hardware to be practical and useful. This increased complexity is impacting the management of models necessary for designing cyber-physical systems that are able to take into account a number of “-ilities”, such that they are safe and secure and ultimately resilient to disruption of service. We propose an ontological metamodel for system design that augments an already existing industry metamodel to capture the relationships between various model elements (requirements, interfaces, physical, and functional) and safety, security, and resilient considerations. Employing this metamodel leads to more cohesive and structured modeling efforts with an overall increase in scalability, usability, and unification of already existing models. In turn, this leads to a mission-oriented perspective in designing security defenses and resilience mechanisms to combat undesirable behaviors. We illustrate this metamodel in an open-source GraphQL implementation, which can interface with a number of modeling languages. We support our proposed metamodel with a detailed demonstration using an oil and gas pipeline model.

Our work focuses on modeling the security of systems from their component-level designs. Towards this goal, we develop a categorical formalism to model attacker actions. Equipping the categorical formalism with algebras produces two interesting results for security modeling. First, using the Yoneda lemma, we can model attacker reconnaissance missions. In this context, the Yoneda lemma shows us that if two system representations, one being complete and the other being the attacker’s incomplete view, agree at every possible test, they behave the same. The implication is that attackers can still successfully exploit the system even with incomplete information. Second, we model the potential changes to the system via an exploit. An exploit either manipulate the interactions between system components, such as providing the wrong values to a sensor, or changes the components themselves, such as controlling a global positioning system (GPS). One additional benefit of using category theory is that mathematical operations can be represented as formal diagrams, helpful in applying this analysis in a model-based design setting. We illustrate this modeling framework using an unmanned aerial vehicle (UAV) cyber-physical system model. We demonstrate and model two types of attacks (1) a rewiring attack, which violates data integrity, and (2) a rewriting attack, which violates availability.

Cyber-physical systems require the construction and management of various models to assure their correct, safe, and secure operation. These various models are necessary because of the coupled physical and computational dynamics present in cyber-physical systems. However, to date the different model views of cyber-physical systems are largely related informally, which raises issues with the degree of formal consistency between those various models of requirements, system behavior, and system architecture. We present a category-theoretic framework to make different types of composition explicit in the modeling and analysis of cyber-physical systems, which could assist in verifying the system as a whole. This compositional framework for cyber-physical systems gives rise to unified system models, where system behavior is hierarchically decomposed and related to a system architecture using the systems-as-algebras paradigm. As part of this paradigm, we show that an algebra of (safety) contracts generalizes over the state of the art, providing more uniform mathematical tools for constraining the behavior over a richer set of composite cyber-physical system models, which has the potential of minimizing or eliminating hazardous behavior.

Today, there is a plethora of software security tools employing visualizations that enable the creation of useful and effective interactive security analyst dashboards. Such dashboards can assist the analyst to understand the data at hand and, consequently, to conceive more targeted preemption and mitigation security strategies. Despite the recent advances, model-based security analysis is lacking tools that employ effective dashboards-to manage potential attack vectors, system components, and requirements. This problem is further exacerbated because model-based security analysis produces significantly larger result spaces than security analysis applied to realized systems-where platform specific information, software versions, and system element dependencies are known. Therefore, there is a need to manage the analysis complexity in model-based security through better visualization techniques. Towards that goal, we propose an interactive security analysis dashboard that provides different views largely centered around the system, its requirements, and its associated attack vector space. This tool makes it possible to start analysis earlier in the system lifecycle. We apply this tool in a significant area of engineering design-the design of cyber-physical systems-where security violations can lead to safety hazards.