1. EECE 396-1 Hybrid and Embedded Systems: Computation T. John Koo, Ph.D. Institute for Software Integrated Systems Department of Electrical Engineering and Computer Science Vanderbilt University 300 Featheringill Hall January 22, 2004 john.koo@vanderbilt.edu http://www.vuse.vanderbilt.edu/~kootj

2. 2 Hybrid System A system built from atomic discrete components and continuous components by parallel and serial composition, arbitrarily nested. The behaviors and interactions of components are governed by models of computation (MOCs). Discrete Components Finite State Machine (FSM) Discrete Event (DE) Synchronous Data Flow (SDF) Continuous Components Ordinary Differential Equation (ODE) Partial Differential Equation (PDE)

3. 3 Modeling: Finite State Machine

4. 4 Topics Relations Binary Relation Relation Properties Equivalent Relation Alphabets Strings Language Finite Automata Deterministic Finite Automata Non- Deterministic Finite Automata Ref: D. L. Johnson, Elements of Logic via Numbers and Sets, Springer, 1998. Harry R. Lewis and Christos H. Papadimitrious, Elements of The Theory of Computation, Prentice Hall, 1998.

5. 5 Relations

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7. 7

8. 8

9. 9 Alphabets

10. 10 Deterministic Finite Automata

11. 11 Deterministic Finite Automata

12. 12 Deterministic Finite Automata

13. 13 Non-Deterministic Finite Automata

14. 14 Non-Deterministic Finite Automata

15. 15 Non-Deterministic Finite Automata

16. 16 End