Workshop on applied category theory:

Breiner, Spencer; Pollard, Blake S.; Subrahmanian, Eswaran

doi:10.6028/nist.sp.1249

Cited by 7 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The envisioned platform's robustness would allow for domain-agnostic cherry-picking and assembling of constructs and transforms. A roadmap for bridging the gap between theory and practice, including particular applications for systems engineering, was published by the US National Institute of Standards and Technology (NIST) [47]. Stateof-the-art applications of Category Theory in systems analysis, engineering, and design are summarized in Table 2.…”

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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…Software tools are increasingly focused on scaling up computation, e.g. [95][96][97][98], as opposed to software to augment human calculation, as in [77,99,100], and managing complex domains with commercial-grade tools [27,[61][62][63]. Recent work to optimize quantum circuits [75,76] leverages such developments.…”

Section: (Iii) Synthesis With Applied Operads and Categoriesmentioning

confidence: 99%

“…Relative to computational efforts to apply operads or monoidal categories, e.g. [95,96,98], this sketch places greater emphasis on specification and exploitation: specification of a domain is possible without exposing the meta-model, algorithms searching within each model are treated as black boxes that produce valid designs. Separate specification greatly facilitates set up by experts in the domain, but not the meta-model.…”

Section: Towards Practical Automated Analysis and Synthesismentioning

confidence: 99%

Operads for complex system design specification, analysis and synthesis

et al. 2021

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The envisioned platform's robustness would allow for domain-agnostic cherry-picking and assembling of constructs and transforms. A roadmap for bridging the gap between theory and practice, including particular applications for systems engineering, was published by the US National Institute of Standards and Technology (NIST) [48]. State-of-the-art applications of Category Theory in systems analysis, engineering, and design include:…”

Section: Category Theory Applications In Systems Engineering Analysimentioning

confidence: 99%

Category-Theoretic Formulation of Model-Based Systems Architecting: The Concept-Model-Graph-View-Concept Transformation Cycle

Mordecai¹,

Fairbanks²,

Crawley³

2021

Preprint

View full text Add to dashboard Cite

We introduce the Concept-Model-Graph-View-Concept (CMGVC) transformation cycle. The CMGVC cycle facilitates coherent architecture analysis, reasoning, insight, and decision-making based on conceptual models that are transformed into a common, robust graph data structure (GDS). The GDS is then transformed into multiple views on 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). CMGVC applies the rigorous foundations of Category Theory, a mathematical framework of representations and transformations. The CMGVC architecture is superior to direct transformations and language-coupled common representations. We demonstrate the CMGVC cycle to transform a conceptual system architecture model built with the Object Process Modeling Language (OPM) into dual graphs and a decision support matrix (DSM) that stimulates system architecture insight.

show abstract

Workshop on applied category theory:

Cited by 7 publications

References 15 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

Category-Theoretic Formulation of Model-Based Systems Architecting: The Concept-Model-Graph-View-Concept Transformation Cycle

Contact Info

Product

Resources

About