1. CSCI1600: Embedded and Real Time Software
Lecture 9: Modeling II: Discrete Systems
Steven Reiss, Fall 2017
Should provide automata for the two/three different train problems.

2. Self-Driving Cars 15-Point Checklist
point-federal-checklist-for-self-driving-cars.html
Lecture 8: Modeling Discrete Systems
2/24/2019

3. Embedded Systems Are sets of tasks If we want to understand the system
The task is the primary abstraction to be used
If we want to understand the system
We need to understand the tasks
We need to understand the interactions
Between tasks
With the environment (real world)
Should we model the whole system
Or should we just model the individual tasks
Lecture 8: Modeling Discrete Systems
2/24/2019

4. How to Model a Task English description Formal mathematics
Typically used first
Imprecise, hard to check, incomplete
Formal mathematics
Very precise
Difficult to understand and write (correctly)
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
Lecture 8: Modeling Discrete Systems
2/24/2019

5. 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
Also called a finite state machine
Lecture 8: Modeling Discrete Systems
2/24/2019

6. Basic Finite State Automata
What language does this recognize?
((a*b)a*cd(bd)*a)*(a*b)*a*c
Lecture 8: Modeling Discrete Systems
2/24/2019

7. Problem Want to automatically trigger switchD
Want to automatically trigger switch
Only once if possible (not continually)
When train goes from R to L
What does sensing look like (at A, B, C, D)
Events: A, 𝐴 , B, 𝐵 , C, 𝐶 , D, 𝐷
When should you trigger the switch
What does the train look like to the sensor
Triggers: c,d,c’, d’ – what is the expected sequence of events and when should you trigger
Students should try to do this (use white board?)
Lecture 8: Modeling Discrete Systems
2/24/2019

8. Problem Can only trigger one switch at a time Is it a FSA?
Switch trigger
Should be momentary (>100ms, <500ms)
What does this task do?
How many tasks should it be?
Different approaches
Is it a FSA?
Queue-based approach is one way
How is a queue implemented?
Another is a simple set of flags, one per switch and we cycle through to find next one to trigger
How do you prevent 2 trains from entering a block simultaneously from both ends going in opposite directions?
Lecture 8: Modeling Discrete Systems
2/24/2019

9. Problem Problem: when is the train on which block ComplexitiesD A B
Problem
Problem: when is the train on which block
When is train completely on A/C or B or D side of switch
Complexities
Handling initial conditions
Handling reversing directions
Students should try to do this
Lecture 8: Modeling Discrete Systems
2/24/2019

10. Issues with Basic FSA Need to specify actions
Semi-external events: timers
Internal events from other tasks
Conditional events
Multiple FSA’s in parallel (multiple tasks)
Counters and other variables
State space blowup
Lecture 8: Modeling Discrete Systems
2/24/2019

11. Actions: Moore vs Mealy Machine
Lecture 8: Modeling Discrete Systems
2/24/2019

12. Moore vs. Mealy Which is more useful? Are they equivalent?
Lecture 8: Modeling Discrete Systems
2/24/2019

13. 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
Is the result still a finite state machine?
Lecture 8: Modeling Discrete Systems
2/24/2019

14. 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
Disallow
Lecture 8: Modeling Discrete Systems
2/24/2019

15. Extended State Machines
What does this do?
Lecture 8: Modeling Discrete Systems
2/24/2019

16. Extended State Machines
What does this do?
Lecture 8: Modeling Discrete Systems
2/24/2019

17. Periodic Automata Specify a Period Extended automata
Action taken every period
Not on timeout
Not when events occur
Extended automata
Variables, actions
Good model for Arduino tasks
What does this do

18. Periodic Automata Period = 100 ms What does this do
Lecture 8: Modeling Discrete Systems
2/24/2019

19. Statecharts David Harel (80’s) Part of UML Extended FSM notation
Lecture 8: Modeling Discrete Systems
2/24/2019

20. Meta States Hierarchical Automata Start states Stop states
Enter States
Lecture 8: Modeling Discrete Systems
2/24/2019

21. Homework Read Chapter 4 Exercises 4.3, 4.5, 4.7
Lecture 8: Modeling Discrete Systems
2/24/2019