Compositional Models for Complex Systems

Breiner, Spencer; Sriram, Ram D.; Subrahmanian, Eswaran

doi:10.1016/b978-0-12-817636-8.00013-2

Cited by 14 publications

(11 citation statements)

References 8 publications

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“…Graphs of models are representable in the broader hypergraph category, which enables of model analysis, composition, comparison, and utilization [15]. Representing a system as a category with component types and inter-component relations as morphisms, with Ologs (knowledge representation structures that capture non-mathematical, freely-defined relations among objects as morphisms) to specify design constructs, current-state situations, constraints, and requirements [51,52] Iterative co-design of electro-mechanical functions in a cyber-physical system architecture [53][54][55][56] hierarchical requirements engineering, gradually evolving a system architecture; formal and verifiable system design [57][58][59] Structural and functional composition of system models [60] Using operads-categorical structures that map multi-object compositions to a single object-for hierarchical decomposition, design synthesis, separation of syntax from semantics, and semantic reasoning about complex systems [61,62] Model-Driven Software Engineering…”

Section: Applications Of Category Theory In Systems Engineering Analysis and Designmentioning

confidence: 99%

Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle

2021

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We introduce the Concept→Model→Graph→View Cycle (CMGVC). The CMGVC facilitates coherent architecture analysis, reasoning, insight, and decision making based on conceptual models that are transformed into a generic, robust graph data structure (GDS). The GDS is then transformed into multiple views of the model, which inform stakeholders in various ways. This GDS-based approach decouples the view from the model and constitutes a powerful enhancement of model-based systems engineering (MBSE). The CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. We show that modeling languages are categories, drawing an analogy to programming languages. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a stakeholder-informing matrix that stimulates system architecture insight.

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Section: Applications Of Category Theory In Systems Engineering Analysis and Designmentioning

confidence: 99%

Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle

2021

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“… A requirement model is sound if joint validity entails external validity, corresponding to the dashed arrow above. With some work, one can show that these diagrams form the operations in an operad of entailments Ent ; see ([21], 6) for a similar construction. The intuition is quite clear There is a functor Context:Entfalse→boldRboldeboldl×, which extracts the relation across the bottom row of each entailment.…”

Section: Functorial Systems Analysismentioning

confidence: 99%

Operads for complex system design specification, analysis and synthesis

et al. 2021

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As the complexity and heterogeneity of a system grows, the challenge of specifying, documenting and synthesizing correct, machine-readable designs increases dramatically. Separation of the system into manageable parts is needed to support analysis at various levels of granularity so that the system is maintainable and adaptable over its life cycle. In this paper, we argue that operads provide an effective knowledge representation to address these challenges. Formal documentation of a syntactically correct design is built up during design synthesis, guided by semantic reasoning about design effectiveness. Throughout, the ability to decompose the system into parts and reconstitute the whole is maintained. We describe recent progress in effective modelling under this paradigm and directions for future work to systematically address scalability challenges for complex system design.

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“…In general, category theory is effective in describing hybrid systems [48], [51], [52] and more recently there has been successful work in modeling and analysis of CPS using category theory [11], [53], [54], [55]. An important motivation for developing a categorical modeling security framework is the theory of co-design, a way of dealing with abstraction and refinement in models, which has recently been applied categorically to robotics [56] and control system design [57].…”

Section: Related Workmentioning

confidence: 99%

Yoneda Hacking: The Algebra of Attacker Actions

Bakirtzis¹,

Genovese²,

Fleming³

2021

Preprint

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Our work focuses on modeling 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 are able to model attacker reconnaissance missions. In this context, the Yoneda lemma formally shows us that if two system representations, one being complete and the other being the attacker's incomplete view, agree at every possible test, then they behave the same. The implication is that attackers can still successfully exploit the system even with incomplete information. Second, we model the possible changes that can occur to the system via an exploit. An exploit either manipulates the interactions between system components, for example, providing the wrong values to a sensor, or changes the components themselves, for example, manipulating the firmware of a global positioning system (GPS). One additional benefit of using category theory is that mathematical operations can be represented as formal diagrams, which is useful for applying this analysis in a model-based design setting. We illustrate this modeling framework using a cyber-physical system model of an unmanned aerial vehicle (UAV). We demonstrate and model two types of attacks (1) a rewiring attack, which violates data integrity, and (2) a rewriting attack, which violates availability.

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Compositional Models for Complex Systems

Cited by 14 publications

References 8 publications

Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle

Category-Theoretic Formulation of the Model-Based Systems Architecting Cognitive-Computational Cycle

Operads for complex system design specification, analysis and synthesis

Yoneda Hacking: The Algebra of Attacker Actions

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