Timed Patterns: From TCOZ to Timed Automata

1. Timed Patterns: From TCOZ to Timed Automata J.S. Dong, P. Hao, S.C. Qin, J. Sun National University of Singapore Y. Wang Uppsala University

2. Outline Outline • Motivation • Introduction on TCOZ and TA • Composable Timed Patterns • Projection from TCOZ to TA • Case study: Railway Crossing System • Conclusion & Future Work

3. Motivation • TCOZ: • Powerful notation for modeling the state, process and timing aspects of complex real-time systems. • Lacking of tool support for verification. • TA: • Well-developed tool support • Lacking of high level composable graphical patterns to support systematic design for complex real-time systems

4. Our Approach • Define and map TCOZ constructs into composable TA graphical patterns • For TA, a possible set of composable graphic patterns can be defined based on the semantics of TCOZ constructs.

5. Our Approach • Based on the TA patterns, a set of transformation rules are given for projecting TCOZ models into TA models • For TCOZ, TA‘s tool support can be reused to check timing properties.

6. TCOZ • Integration of Object-Z with Timed CSP • Features • A Model of Time • Communication Interface—Channels, Sensors and actuators • Active objects • Network Topologies

8. Timed Automata • A timed automaton A is a tuple < S, S0, Σ, C, E >, where • S is a finite set of states • S0 is a set of initial states and a subset of S • Σ is a set of labels • C is a finite set of clocks, and • E, a subset of S×S×Σ×2C×Φ(C), is the set of transitions. An edge <s, s’, a, λ,δ> represents a transition from state s to state s’ on input symbol a. The set λgives the clocks to be reset with this transition, and δis a clock constraint over C.

9. A Gate Automaton

10. Tools for Timed Automata • Uppaal • Developed by Uppsala University, Sweden and Aalborg University, Denmark • Kronos • Developed by Verimag,France • Timed COSPAN • Developed by Bell Labs,USA

11. Definitions

12. Sequential Composition Pattern

13. Deadline Pattern

14. WaitUntil Pattern

15. Recursion Pattern

16. Composing TA Patterns Task ‘A’ is repeated every t0 time units provided that A is guaranteed to terminate before t0 time units

17. Rules for Translating Dynamic Information

18. Rules for Translating Static Information • In TCOZ, each object is translated as an automaton • Each operation schema is translated as an atomic state • Init operation schema is used to identify the initial state in the corresponding automaton

19. Tool Support

20. Case Study: The Railway Crossing System

24. Model Checking with UPPAAL

25. Conclusion • Provide a proficient interchange media for transforming TCOZ specification into TA models • Provide a reusable high level library that may facilitate a systematical engineering process when using TA alone to design timed systems • Build up the semantic link between TCOZ and TA • Developed a translation tool from TCOZ to TA

26. Future Work • Encode the TA patterns to assist building TA models in a more systematical way. • Integration of Timed Automata and Z language and relevant tool support.

27. Thanks!