ABCDEFGHIJKLMNOPQRSTUVWXYZ
1
Totals ==>830164131400000110
2
Ok?BPBSIBSQIFIGOIWUEUXXRV
Scope
AnswerExplanationIDFormulaExpected
3
1G(Red => X(!Red) && X(X(Red))
R_10pfB7n4SRWFEiA
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
4
1G(Red => (X(!Red) && X(X(Red))))
R_1d6RMi3t0gkcM5M
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
5
1G(Red => (!X(Red) && X(X(Red))))
R_e8QLXoeqrle4xS9
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
6
1G(R =>(X(!Red) && X(X(Red)))
R_z5PVfNBIPKX5S4F
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
7
1G(Red =>X(!Red) && X(X(Red)))
R_1E0ztwRbCQeEjAn
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
8
1G(Red=>(X!Red&&XXRed))
R_d6w1dXzacJ9KN0Z
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
9
1G(Red => X(!Red) && X(X(Red)))
R_3MuS1ttcj8sdoRv
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
10
1G (red => (X!red && XXred))
R_1hEGqpvvTZegzQ7
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
11
1G(Red => (X(!Red) && X(X(Red))))
Same as last question in part 2
R_3gO868rLSy0R2Ep
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
12
1G(Red => (X(!Red) && XX(Red)))
R_332amsBlozpU5n8
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
13
1G(Red => ( X(!Red) && X(X(Red)))
R_QcBt5TnllV1Ynq9
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
14
1G(Red => (X(!Red) && X(X(Red))))
R_2t50ks4XN0wxwLl
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
15
1G (red => ((X !red) && (XX red))
R_0Vg19zBXa3hIGzf
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
16
1G(Red => (X(!Red) && X(X(Red))))
R_33wl4yU4sEzJKu4
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
17
1G(red => (X(!red) && X(X(red))))
R_3iWIMn2gWx1V4Lp
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
18
1G(Red => (X(!Red) && X(X(Red)))
R_W7oqYTh5ZL9V9vP
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
19
1G(Red => X(!Red) && X(X(Red)))
R_3e8mdHJtEsNstwp
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
20
1G(Red => X(!Red) && X(X(Red)))
R_1i3xVhhSYFfFwDR
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
21
1G(Red => X(!Red) && X(X(Red)))
R_6F2ykLOE4e1S4IF
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
22
1G(red => (X !red && XX red))
R_sb9MnVHZ3rBbcuR
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
23
1G(red => (X !red && XX red))
R_3GB8QvZ8WJ7imO7
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
24
1G(Red => X(!Red) && XX(Red))
R_3KSFgYqXtEshyWa
Whenever Red, it is off in the next state and on again in the state after that.
G(r ==> X(!r) & XX(r))
25
1!Red U (Red && X(G(!Red))
R_10pfB7n4SRWFEiA
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
26
1F(X(Red))
R_1d6RMi3t0gkcM5M
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
27
1(!Red U (Red & X(G(!Red))))
R_e8QLXoeqrle4xS9
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
28
1G(F(R) => X(G(!R))) && F(R)
R_z5PVfNBIPKX5S4F
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
29
1F(X(Red))
R_1E0ztwRbCQeEjAn
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
30
1F(Red&&XG!Red)
R_d6w1dXzacJ9KN0Z
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
31
1F(Red && X(G(!Red)))
R_3MuS1ttcj8sdoRv
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
32
1G (red => XG!red)
R_1hEGqpvvTZegzQ7
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
33
1(!Red) U (Red && X(G(!Red)))
This forces the red light to be off until a red state is reached with all following states not red
R_3gO868rLSy0R2Ep
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
34
1F(Red) && (Red => X(G(!Red)))
R_332amsBlozpU5n8
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
35
1!Red U (Red && X(G(!Red)))
R_QcBt5TnllV1Ynq9
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
36
1F(Red) && !(F(Red && F(Red))
There must be at least one state with the Red light on. \\ There must not be more than one state with the Red light on.
R_2t50ks4XN0wxwLl
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
37
interesting!1
This is inexpressible in LTL. There's no way of saying, from a certain point in time, something holds. For example, we can't say !red U (red && (from here onwards !red)).
R_0Vg19zBXa3hIGzf
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
38
1F(Red && X(G(!Red)))
R_33wl4yU4sEzJKu4
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
39
1F(Red) && G(red => X(G(!red)))
R_3iWIMn2gWx1V4Lp
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
40
1F(Red)
R_W7oqYTh5ZL9V9vP
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
41
1X(F(Red) U G(!Red))
R_3e8mdHJtEsNstwp
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
42
11(F(Red) => G(!Red))
R_1i3xVhhSYFfFwDR
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
43
1F(Red) && G(Red => X(G(!Red)))
R_6F2ykLOE4e1S4IF
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
44
1(!red) U (red && X(G(!red)) \\ G(red => X(G(!red))) && F(red)
R_sb9MnVHZ3rBbcuR
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
45
1(!red) U (red && X(G(!red)))
R_3GB8QvZ8WJ7imO7
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
46
11X(F(Red))
R_3KSFgYqXtEshyWa
Red in exactly one state, not necessarily the first
(!r) U (r & X(G(!r)))
47
1G(Red && X(Red) => X(X(!Red)))
R_10pfB7n4SRWFEiA
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
48
1G((Red && X(Red)) => X(X(!Red)))
R_1d6RMi3t0gkcM5M
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
49
1G(¬(Red && X(Red) && X(X(Red))))
R_e8QLXoeqrle4xS9
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
50
1G(Red && X(Red) => X(X(Red)))
R_z5PVfNBIPKX5S4F
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
51
1!Red || X(!Red) || X(X(!Red))
R_1E0ztwRbCQeEjAn
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
52
1G(!(Red&&XRed&&XXRed))
R_d6w1dXzacJ9KN0Z
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
53
1G((Red && X(Red)) => !X(X(Red)))
R_3MuS1ttcj8sdoRv
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
54
1G ((red && Xred) => XX!red )
R_1hEGqpvvTZegzQ7
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
55
1G(Red && X(Red) => X(X(!Red)))
Reading this as "It is always the case that the red light cannot stay on for three states in a row"
R_3gO868rLSy0R2Ep
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
56
1G((Red && X(Red)) => XX(!Red))
R_332amsBlozpU5n8
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
57
1G(!Red || X(!Red) || X(X(!Red)))
On 3 consecutive states at least one is not Red
R_QcBt5TnllV1Ynq9
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
58
1!(F(Red && X(Red) && X(X(Red))))
There must not be a state such that three states starting from there have the Red light on.
R_2t50ks4XN0wxwLl
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
59
1G (red => (X !red || XX !red))
R_0Vg19zBXa3hIGzf
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
60
1G((Red && X(Red)) => X(X(!Red)))
R_33wl4yU4sEzJKu4
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
61
1!F(red && X(red) && X(X(red)))
R_3iWIMn2gWx1V4Lp
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
62
1G((Red && X(Red) => X(X(!Red)))
R_W7oqYTh5ZL9V9vP
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
63
1G(Red => X(!Red) || X(X(!Red)))
R_3e8mdHJtEsNstwp
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
64
1G(Red => X(!Red) || Red && X(Red) => X(X(!Red)))
R_1i3xVhhSYFfFwDR
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
65
1G((Red && X(Red)) => X(X(!Red)))
R_6F2ykLOE4e1S4IF
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
66
1G((red && Xred) => XX!red)
R_sb9MnVHZ3rBbcuR
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
67
1G((red && Xred) => XX!red)
R_3GB8QvZ8WJ7imO7
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
68
1G(!(Red => X(Red) && XX(Red)))
R_3KSFgYqXtEshyWa
Red cannot stay on 3 states in a row
!F(r & Xr & XXr)
69
1G(Red => F(Blue))
R_10pfB7n4SRWFEiA
Whenever Red, then Blue then or later
G(r ==> F(b))
70
1G(Red => F(Blue))
R_1d6RMi3t0gkcM5M
Whenever Red, then Blue then or later
G(r ==> F(b))
71
1G(Red => F(Blue))
R_e8QLXoeqrle4xS9
Whenever Red, then Blue then or later
G(r ==> F(b))
72
1G(Red=>F(Blue))
R_z5PVfNBIPKX5S4F
Whenever Red, then Blue then or later
G(r ==> F(b))
73
1G(Red=>Blue || F(Blue))
R_1E0ztwRbCQeEjAn
Whenever Red, then Blue then or later
G(r ==> F(b))
74
1G(Red=>FBlue)
R_d6w1dXzacJ9KN0Z
Whenever Red, then Blue then or later
G(r ==> F(b))
75
1G(Red => F(Blue))
R_3MuS1ttcj8sdoRv
Whenever Red, then Blue then or later
G(r ==> F(b))
76
1G (red => Fblue)
R_1hEGqpvvTZegzQ7
Whenever Red, then Blue then or later
G(r ==> F(b))
77
1G(Red => F(Blue))
R_3gO868rLSy0R2Ep
Whenever Red, then Blue then or later
G(r ==> F(b))
78
1G(X(Red) => (X(Blue) || F(Blue)))
R_332amsBlozpU5n8
Whenever Red, then Blue then or later
G(r ==> F(b))
79
1G(Red => F Blue)
R_QcBt5TnllV1Ynq9
Whenever Red, then Blue then or later
G(r ==> F(b))
80
1G(Red => F(Blue))
R_2t50ks4XN0wxwLl
Whenever Red, then Blue then or later
G(r ==> F(b))
81
1G( red => F blue)
R_0Vg19zBXa3hIGzf
Whenever Red, then Blue then or later
G(r ==> F(b))
82
1G(Red => F(Blue))
R_33wl4yU4sEzJKu4
Whenever Red, then Blue then or later
G(r ==> F(b))
83
1G(red => F(blue))
R_3iWIMn2gWx1V4Lp
Whenever Red, then Blue then or later
G(r ==> F(b))
84
1G(Red => F(Blue))
R_W7oqYTh5ZL9V9vP
Whenever Red, then Blue then or later
G(r ==> F(b))
85
1G(Red => F(Blue))
R_3e8mdHJtEsNstwp
Whenever Red, then Blue then or later
G(r ==> F(b))
86
1Red => (Blue || F(Blue))
R_1i3xVhhSYFfFwDR
Whenever Red, then Blue then or later
G(r ==> F(b))
87
1G(Red => F(Blue))
R_6F2ykLOE4e1S4IF
Whenever Red, then Blue then or later
G(r ==> F(b))
88
1G(red => F blue)
R_sb9MnVHZ3rBbcuR
Whenever Red, then Blue then or later
G(r ==> F(b))
89
1G(red => F blue)
R_3GB8QvZ8WJ7imO7
Whenever Red, then Blue then or later
G(r ==> F(b))
90
1G(Red => F(Blue))
R_3KSFgYqXtEshyWa
Whenever Red, then Blue then or later
G(r ==> F(b))
91
1Red U (G(!Red))
R_10pfB7n4SRWFEiA
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
92
1F(G(!Red))
R_1d6RMi3t0gkcM5M
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
93
1Red U G(!Red)
R_e8QLXoeqrle4xS9
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
94
1F(R => X(G(!R)))
R_z5PVfNBIPKX5S4F
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
95
1Red U (G(!Red))
R_1E0ztwRbCQeEjAn
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
96
1RedU(G!Red)
R_d6w1dXzacJ9KN0Z
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
97
1F(G(!Red))
R_3MuS1ttcj8sdoRv
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
98
1red U G!red
R_1hEGqpvvTZegzQ7
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
99
1Red U G(!Red)
R_3gO868rLSy0R2Ep
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
100
1F(G(!Red))
R_332amsBlozpU5n8
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
101
1Red U (G !Red)
R_QcBt5TnllV1Ynq9
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
102
1Red U !(F(Red))
At the state where the Red light switches off, there will be no state in the future that has the Red light on.
R_2t50ks4XN0wxwLl
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
103
1FG(!red)
The "red light on for zero or more states" part is irrelevant. All we care about is that the red light turns off and stays off, hence FG(!red)
R_0Vg19zBXa3hIGzf
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
104
1Red U G(!Red)
R_33wl4yU4sEzJKu4
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
105
1red U G(!Red)
R_3iWIMn2gWx1V4Lp
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
106
1Red U (G(!Red))
R_W7oqYTh5ZL9V9vP
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
107
1G(Red) U G(!Red)
R_3e8mdHJtEsNstwp
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
108
1G(F(Red)) U (G(!Red))
R_1i3xVhhSYFfFwDR
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
109
1F(Red) && G(Red => X(U(!Red)))
R_6F2ykLOE4e1S4IF
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
110
1red U G(!red)
R_sb9MnVHZ3rBbcuR
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
111
1red U G(!red)
R_3GB8QvZ8WJ7imO7
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))
112
1F(G(!Red))
R_3KSFgYqXtEshyWa
r for zero or more, then !r forevermore
(r U !r) & (G(!r ==> G(!r)))