Name: Lennart Diego Kahn STUDIENR: 20223228
Exercise 1
A)
B)
One option could be -1,1. Another one could be (-2,0).
C)
I am so sorry, but my brain is simply not able to make a more elegant solution under pressure.
Exercise 2
A) It has 2 reachable states.
B) No, because not all reachable states satisfy
C) No, see B).
D) x + (p - m) < 5 V x + (p - m) > 5
E) x + (p - m) == 6
Exercise 3
A), B)
C)
Input:
- Oi1: x := in1
- Oi2: y := in2
Internal:
-
- Ni y := temp
Output:
- Oo: out0 := x V y
- No: outn := not z
Exercise 4
A) E and F are reachable.
D is not reachable because the guard is x ⇐ 1. if we change it to x ⇐ 4 it is reachable.
B) For E: (A, x = 1, y = 1) ⇒ (B, x = 4, y = 1) ⇒ (C, x = 4, y = 1) ⇒ (E, x = 4, y = 1)
For F: (A, x = 1, y = 1) ⇒ (B, x = 4, y = 1) ⇒ (C, x = 4, y = 1) ⇒ (E, x = 4, y = 1) ⇒ (C, x = 6000, y = 0) ⇒ (F, x = 6000, y = 0)
C) x is never reset that is why x and time are the same.
For E:
For F:
D)
A entry = x = 0 ∧ y = 0
B entry = x = 1 ∧ y = 0
C entry = x = 4 ∧ y = 3
A after delay = x = 3 ∧ y = 3
B after delay = x = 6 ∧ y = 5
C after delay = y = 5
E) D is not reachable because the guard is x ⇐ 1. if we change it to x ⇐ 4 it is becomes reachable.
Exercise 5
A)
If i understand the question correctly it is asking us if it skips any frames.
E<> player.skip_frame returns true.
B)
C) The way i understand the question is that you may ONLY modify device, and MUST make sure that we NEVER hit skip_frame.
man… ive been stuck here for an hour and 7 minutes and just CANNOT get it solved because it seems that device does NOT matter since it can aways move to skip no matter what i do in device, since it can always take the optional transition. If anything we can make sure that when data? runs, that it doesnt skip a frame.
My solution that hopefully scores me more than 0 points.
D)
E)
The current device2 (seen in the screenshot C) seems to already satisfy it.
A<> time <= SECOND && player.buffer <=4000
Exercise 6
A) It is Lipschitz-continuous because there exists a constant 𝐾 such that for all x, v in real k, 𝑓(x) − 𝑓(v) ≤ 𝐾 x − v
B)
C), D), E)
i know this is wrong, but math is just too hard for my brain under exam stress.
I cant even get matplotlib to output anything, which is mainly why im not getting anywhere. I must have missed something blindingly obvious because no matter what i do i get NOTHING from matplotlib.