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Formal Foundations for Real-Time System Design with UML-RT: A Graph-Based Approach

This paper presents a formal calculus for UML-RT specifications to address complexities in real-time system design. It emphasizes the importance of clear visual specifications to avoid fatal ambiguities. The proposed approach utilizes graph construction primitives, connectors, and control- and data-flow models to enable concise and compositional semantics for statecharts. By combining modular specifications of control and data flow, the paper offers a basis for compositional hybrid statecharts and provides a clear foundation for execution and verification tools.

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Formal Foundations for Real-Time System Design with UML-RT: A Graph-Based Approach

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  1. Towards a Calculus for UML-RT Specifications Radu Grosu CIS, Upenn, Philadelphia joint work with M. Broy, B. Selic, Gh. Stefanescu

  2. Motivation • The design of real-time systemsis a difficult task. One has to consider many different aspectslike data, behavior, architecture and distribution. • Moreover it usuallyinvolves people from different engineering disciplines. • The modern SE methods UML and UML-RTrecommend the use of visual specifications. • A formal foundationis needed however, to prohibit ambiguities which may be fatalin this context.

  3. capsule-class has structure behavior controls uses uses uses uses uses uses data-class encoded models c++ or rpl embedded run-time system The Layers of UML-RT Implementation Formal Semantics componentM has strctureM behaviorM controls models uses uses models stateM interaction-graphs implemented flow-graphs

  4. Graph Construction Primitives A C n1 n2 n1 n2 n1 B1 B2 B A A A A B A A A B A identification ramification transposition Operators on nodes A1 A2 A B C visual attachment sequentialcomposition feedback Connectors A A identity

  5. Control- and Data-Flow Models n2 n1 n2 n1 Control-flow model Data-flow model n2 n1 n2 n1

  6. Tightening Sliding A A A A m m C C C B B n m = = C n n D D D m n D p p B B E E Two Feedback Laws

  7. m m m m m m m n n n n m A Graph Transformation = = = = n tightening morphism tightening sliding

  8. Conclusions We showed how to combinemodular specifications of controlanddata-flow. Practical relevance: concise, compositionalsemantics forstatecharts basis forcompositional hybrid statecharts clear foundation forexecution-tools Theoretical relevance: semantics of interactionasmixed graph algebras clear foundation forverification-tools

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