Class 13: State Machines

cs2102: Discrete Mathematics
University of Virginia, Fall 2016

See course site for notes:
https://uvacs2102.github.io

Transcript

1. Class 13: State Machines cs2102: Discrete Mathematics | F16 uvacs2102.github.io David Evans | University of Virginia Return Exam 1 Today No problem set due this week! PS6 is due Friday, Oct 21.
2. Plan State Machines Invariant Principle Exam 1 Read this week: MCS Chapter 6
3. State Machine
4. Example = , = → , → ) =
5. M =
6. State Machine M = (, : × , ) ∈ )
7. State Machine M = (, : × , ) ∈ ) What does it mean if is total?
8. State Machine M = (, : × , ) ∈ ) What does it mean if is not a function?
9. State Machine M = (, : × , ) ∈ ) What does it mean if is surjective?
10. = = ) = Counter = (, : × , ) ∈ )
11. Is your computer a state machine?
14. Modeling as State Machine
15. Modeling as State Machine How accurate is this model? How useful is this model?
17. State Machine Executions
18. State Machine Executions The execution of a state machine, = (, ⊆ ×, ) ∈ ) is a (possibly infinite) sequence of states, () , 3 , … , 5 ) that:
19. Two Steps Forward, One Step Back = ℕ =
20. Two Steps Forward, One Step Back = =
21. Exam 1
22. 65% of class >= 87 90% of class >= 75
23. Problem Areas 0 1 2 3 4 5 6 7 8 >=8 100% 40% 56% 54% 28% 44% 42% 37% 33% >=6 100% 46% 57% 55% 51% 53% 52% 41% 40%
24. Biggest Issues • To prove by induction, need to state a predicate with an induction variable • If a set is empty, any predicate is true for all elements of that set ∷= whatever is here must use n (and that is what you are doing induction on)
25. Returning Exam 1 Group 1 Group 2 Group 3 Group 4 aa6.. (Aaron) dav.. (Daniel) kaw.. (Kevin) rcb.. (Rachel) ac5.. (Allison) dc7.. (David) khl.. (Kenny) rel.. (Rashid) … … … … cwf… (Chris) jxp.. (John) pv.. (Phoenix) zw4.. (Mike)
26. Charge Read MCS Chapter 6 PS6 will be posted later, Due Oct 21