Real-Time Reactive System - CCS with Time Delays

Transcription

1 Real-Time Reactive System - CCS with Time Delays Wai Leung Sze (Stephen) Swansea University VINO 18th July 2011

2 Overview Introduction of real-time reactive system Describing the real-time reactive system Timed CCS (TCCS)

3 Introduction of Real-Time Reactive System

4 What is Real-Time Reactive System A real-time (reactive) system is a system whose correct behaviour depends on a) the logical order in which the events are performed b) and timing of the events. Example: the air-bag system in a car Expected Behaviour: inflate the air bags in case of a car crash Order: when the car is crashed Time: at that moment (within 50milliseconds)

5 What is Real-Time Reactive System Another Example: control program loop read the sensors values at regular intervals depending on the sensors values, trigger the relevant actuators forever Control programs are usually non-terminating The idling mode : during the time between consecutive reading of values of the sensors

6 Describing the Real-Time Reactive System

7 Our Real-Time Reactive System A light switch: If the switch is off, and is pressed once, then the light will turn on. If the switch is pressed again soon after the light was turned on, then the light becomes brighter. Otherwise, the light is turned off by the next button press. The light is also turned off by a button press when it is bright.

8 Our Real-Time Reactive System CCS: def Off = press.light def Bright = press.off def Light = press.off + press.bright

9 Our Real-Time Reactive System CCS: def Off = press.light def Bright = press.off def Light = τ.press.off + press.bright

10 Our Real-Time Reactive System Timed CCS: def Off = press.light def Bright = press.off def Light = ε(1.4).τ.press.off + press.bright In general: ε(d), where d is a non-negative real number that specifies the amount of time delay.

11 Timed Labelled Transition System (TLTS)

12 Timed Labelled Transition System (TLTS) Additive: Without Delay: Deterministic:

13 Timed CCS (TCCS)

14 The Syntax Everything remains the same as CCS, but one extra prefix: ε(d) where d is a non-negative real number. Note: ε(0).p is the same as P

15 The Syntax Everything remains the same as CCS, but one extra prefix: ε(d) where d is a non-negative real number. Note: ε(0).p is the same as P Remark: In the rest of the book, only guarded expressions are considered.

16 Exercise Consider the following Timed CCS expression, Which constants are guarded and which are not?

17 Exercise Consider the following Timed CCS expression, Which constants are guarded and which are not? Answer: First K1 - guarded K2 - not guarded First K3 - guarded Second K2 - not guarded K4 - guarded Second K3 - not guarded Overall: not guarded

18 SOS Rules for Timed CCS SOS rules for TCCS includes all rule from CSS plus the following: means ε(0).p is the same as P SOS rules for timed CCS

19 Exercise Answer is given on the board SOS rules for timed CCS

20 Parallel Composition Suppose we now have a fast user of the light switch: Synchronize with the light switch in Off State: The whole system is delayed by 0.3

21 Parallel Composition Two possible actions: a) to perform press immediately b) wait for the time delay ε(1.1) and perform the action τ

22 Maximal-Progress Assumption It is the design decision of TCCS that evolution of processes must obey this assumption If a process is ready to perform an action that is entirely under its control immediately then it will do so without further delay Therefore, is the right action.

23 Parallel Composition SOS Rule Parallel composition SOS rule for TCCS The predicate NoSync(P, Q, d) means that no synchronization between P and Q becomes available within a time delay of d (not including d)

24 Summary Introduction of real-time reactive system Describing the real-time reactive system Timed CCS (TCCS)

25 Thank you

26 Acknowledgement Luca Aceto, Anna Ingólfsdóttir, Kim Larsen and Jirí Srba: Reactive Systems - Modelling, Specification and Verification