A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | |
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1 | Totals ==> | 83 | 0 | 1 | 6 | 4 | 1 | 3 | 14 | 0 | 0 | 0 | 0 | 0 | 110 | |||||||||||
2 | Ok | ? | BP | BSI | BSQ | IF | IG | OI | WU | EU | XX | RV | Scope | Answer | Explanation | ID | Formula | Expected | ||||||||
3 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G (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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G (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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | G(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 | 1 | F(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 | 1 | G(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 | 1 | F(X(Red)) | R_1E0ztwRbCQeEjAn | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
30 | 1 | F(Red&&XG!Red) | R_d6w1dXzacJ9KN0Z | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
31 | 1 | F(Red && X(G(!Red))) | R_3MuS1ttcj8sdoRv | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
32 | 1 | G (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 | 1 | F(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 | 1 | F(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 | 1 | F(Red && X(G(!Red))) | R_33wl4yU4sEzJKu4 | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
39 | 1 | F(Red) && G(red => X(G(!red))) | R_3iWIMn2gWx1V4Lp | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
40 | 1 | F(Red) | R_W7oqYTh5ZL9V9vP | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
41 | 1 | X(F(Red) U G(!Red)) | R_3e8mdHJtEsNstwp | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | |||||||||||||||||||||
42 | 1 | 1 | (F(Red) => G(!Red)) | R_1i3xVhhSYFfFwDR | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | ||||||||||||||||||||
43 | 1 | F(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 | 1 | 1 | X(F(Red)) | R_3KSFgYqXtEshyWa | Red in exactly one state, not necessarily the first | (!r) U (r & X(G(!r))) | ||||||||||||||||||||
47 | 1 | G(Red && X(Red) => X(X(!Red))) | R_10pfB7n4SRWFEiA | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
48 | 1 | G((Red && X(Red)) => X(X(!Red))) | R_1d6RMi3t0gkcM5M | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
49 | 1 | G(¬(Red && X(Red) && X(X(Red)))) | R_e8QLXoeqrle4xS9 | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
50 | 1 | G(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 | 1 | G(!(Red&&XRed&&XXRed)) | R_d6w1dXzacJ9KN0Z | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
53 | 1 | G((Red && X(Red)) => !X(X(Red))) | R_3MuS1ttcj8sdoRv | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
54 | 1 | G ((red && Xred) => XX!red ) | R_1hEGqpvvTZegzQ7 | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
55 | 1 | G(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 | 1 | G((Red && X(Red)) => XX(!Red)) | R_332amsBlozpU5n8 | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
57 | 1 | G(!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 | 1 | G (red => (X !red || XX !red)) | R_0Vg19zBXa3hIGzf | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
60 | 1 | G((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 | 1 | G((Red && X(Red) => X(X(!Red))) | R_W7oqYTh5ZL9V9vP | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
63 | 1 | G(Red => X(!Red) || X(X(!Red))) | R_3e8mdHJtEsNstwp | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
64 | 1 | G(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 | 1 | G((Red && X(Red)) => X(X(!Red))) | R_6F2ykLOE4e1S4IF | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
66 | 1 | G((red && Xred) => XX!red) | R_sb9MnVHZ3rBbcuR | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
67 | 1 | G((red && Xred) => XX!red) | R_3GB8QvZ8WJ7imO7 | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
68 | 1 | G(!(Red => X(Red) && XX(Red))) | R_3KSFgYqXtEshyWa | Red cannot stay on 3 states in a row | !F(r & Xr & XXr) | |||||||||||||||||||||
69 | 1 | G(Red => F(Blue)) | R_10pfB7n4SRWFEiA | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
70 | 1 | G(Red => F(Blue)) | R_1d6RMi3t0gkcM5M | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
71 | 1 | G(Red => F(Blue)) | R_e8QLXoeqrle4xS9 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
72 | 1 | G(Red=>F(Blue)) | R_z5PVfNBIPKX5S4F | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
73 | 1 | G(Red=>Blue || F(Blue)) | R_1E0ztwRbCQeEjAn | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
74 | 1 | G(Red=>FBlue) | R_d6w1dXzacJ9KN0Z | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
75 | 1 | G(Red => F(Blue)) | R_3MuS1ttcj8sdoRv | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
76 | 1 | G (red => Fblue) | R_1hEGqpvvTZegzQ7 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
77 | 1 | G(Red => F(Blue)) | R_3gO868rLSy0R2Ep | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
78 | 1 | G(X(Red) => (X(Blue) || F(Blue))) | R_332amsBlozpU5n8 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
79 | 1 | G(Red => F Blue) | R_QcBt5TnllV1Ynq9 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
80 | 1 | G(Red => F(Blue)) | R_2t50ks4XN0wxwLl | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
81 | 1 | G( red => F blue) | R_0Vg19zBXa3hIGzf | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
82 | 1 | G(Red => F(Blue)) | R_33wl4yU4sEzJKu4 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
83 | 1 | G(red => F(blue)) | R_3iWIMn2gWx1V4Lp | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
84 | 1 | G(Red => F(Blue)) | R_W7oqYTh5ZL9V9vP | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
85 | 1 | G(Red => F(Blue)) | R_3e8mdHJtEsNstwp | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
86 | 1 | Red => (Blue || F(Blue)) | R_1i3xVhhSYFfFwDR | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
87 | 1 | G(Red => F(Blue)) | R_6F2ykLOE4e1S4IF | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
88 | 1 | G(red => F blue) | R_sb9MnVHZ3rBbcuR | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
89 | 1 | G(red => F blue) | R_3GB8QvZ8WJ7imO7 | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
90 | 1 | G(Red => F(Blue)) | R_3KSFgYqXtEshyWa | Whenever Red, then Blue then or later | G(r ==> F(b)) | |||||||||||||||||||||
91 | 1 | Red U (G(!Red)) | R_10pfB7n4SRWFEiA | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
92 | 1 | F(G(!Red)) | R_1d6RMi3t0gkcM5M | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
93 | 1 | Red U G(!Red) | R_e8QLXoeqrle4xS9 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
94 | 1 | F(R => X(G(!R))) | R_z5PVfNBIPKX5S4F | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
95 | 1 | Red U (G(!Red)) | R_1E0ztwRbCQeEjAn | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
96 | 1 | RedU(G!Red) | R_d6w1dXzacJ9KN0Z | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
97 | 1 | F(G(!Red)) | R_3MuS1ttcj8sdoRv | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
98 | 1 | red U G!red | R_1hEGqpvvTZegzQ7 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
99 | 1 | Red U G(!Red) | R_3gO868rLSy0R2Ep | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
100 | 1 | F(G(!Red)) | R_332amsBlozpU5n8 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
101 | 1 | Red U (G !Red) | R_QcBt5TnllV1Ynq9 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
102 | 1 | Red 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 | 1 | FG(!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 | 1 | Red U G(!Red) | R_33wl4yU4sEzJKu4 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
105 | 1 | red U G(!Red) | R_3iWIMn2gWx1V4Lp | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
106 | 1 | Red U (G(!Red)) | R_W7oqYTh5ZL9V9vP | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
107 | 1 | G(Red) U G(!Red) | R_3e8mdHJtEsNstwp | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
108 | 1 | G(F(Red)) U (G(!Red)) | R_1i3xVhhSYFfFwDR | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
109 | 1 | F(Red) && G(Red => X(U(!Red))) | R_6F2ykLOE4e1S4IF | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
110 | 1 | red U G(!red) | R_sb9MnVHZ3rBbcuR | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
111 | 1 | red U G(!red) | R_3GB8QvZ8WJ7imO7 | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) | |||||||||||||||||||||
112 | 1 | F(G(!Red)) | R_3KSFgYqXtEshyWa | r for zero or more, then !r forevermore | (r U !r) & (G(!r ==> G(!r))) |