1. CSCI1600: Embedded and Real Time Software Lecture 7: Modeling II: Discrete Systems Steven Reiss, Fall 2015

2. Embedded Systems  Are sets of tasks  The task is the primary abstraction to be used  If we want to understand the system  We want to model it  Should we model the whole system  Or should we just model the individual tasks

3. How to Model a Task  English description  Typically used first  Imprecise, hard to check, incomplete  Formal mathematics  Very precise  Difficult to understand  Hard to express external events  Formal diagrams  Combine formal math with understanding  Diagrams make it easier to comprehend what is there  Provide a framework for the math and understanding

4. Modeling Control Systems  Control oriented systems  Typically respond to external stimuli  Reaction based on previous interactions  These determine the state of the system  Stimulus moves system to a new state  Control is state-oriented  Natural model is finite state automata

5. Basic Finite State Automata

6. Problem  Want to automatically trigger switch  When train goes from R to L  What does sensing look like  What does train look like  When should you trigger the switch C D AB

7. Problem  Can only trigger one switch at a time  Switch trigger  Should be momentary (>100ms, <500ms)  What does this task do?  How many tasks should it be?  Is it a FSA?

8. Problem  Problem: when is the train on which block  When is train completely on A/C or B or D side of switch  Handling initial conditions  Handling reversing directions C D A B

9. Issues with Basic FSA  Need to specify actions  Semi-external events: timers  Internal events from other automata  Conditional events  Multiple FSA’s in parallel  Counters and other variables  State space blowup

10. Actions: Moore vs Mealy Machine

11. Moore vs. Mealy  Which is more useful?  Are they equivalent?

12. Extended State Machines  Each arc has condition/action  To traverse arc, condition must hold  When traversing arc, action is taken  There are a finite set of (bounded) variables  Conditions can reference these  Condition can be  Event  Time out  Expression over variables  Combination of the two

13. Extended State Machines  Actions  Can access and change variables  Can be { var = expression; … }  Can do something external  When no condition is true  Stay in same state  When multiple conditions are true  What should be done  Nondeterminism,  Allow priority specification

14. Digital Watch  Four buttons  Chimes, alarms, time, stopwatch, light  How does it work?  Number of states?  Lots of tasks  Specifying each  Specifying their interaction

15. Statecharts  David Harel (80’s)  Part of UML  Extended FSM notation

16. Concurrency  Concurrent FSMs  Same box, dashed line  State of overall is cross-product of states  Can have array (n copies)

17. Hierarchical Automata  Allow abstraction  Can be used to generalize groups of states  Can be used for clustering  Can have multiple levels  What state to goto inside?

18. Start and Stop States  Start states are large dots  Stop states are encircled dots  Hierarchal elements can have internal start states

19. History Mechanism  Keep track of state in nested automata  Circled-H is entry point  Default entry  Can point to start state

20. Delays and Timeouts  Delays cause a state to hold until time has expired  time< in state  Timeouts are automatic events  <time in state  Separate timeout event

21. Homework  Read Chapter 4