ABCDEFGHIJKLMNOPQRSTUVWXYZAAAB
1
Totals ==>32231551100000100
2
Ok?BPBSIBSQIFIGIPOIWUEUTSUSXRV
Scope
Answer
Explanation
IDFormulaExpected
3
11
In the two next states, there is some point at which the engine is on in the rest of the states
-
R_2V8ftg0MEp4Ubs8
X(X(F(X(E))))
E at 4th state or later
4
1The engine is always on after tail starting at the fourth state.-
R_3HB55PANueKprlM
X(X(F(X(E))))
E at 4th state or later
5
1There is a state after the 2nd state where the engine is on.-
R_bEn5CUcESzA0Y0N
X(X(F(X(E))))
E at 4th state or later
6
1
Starting two states from now, there will eventually be some state where the engine is on in the following state.
-
R_2v92EqnYAvMz4p5
X(X(F(X(E))))
E at 4th state or later
7
1
Eventually, you can always follow the trace to a point where the next state has the engine on.
The two initial Xs don't do much, so I omit them. This is because F is basically an application of an arbitrary number of 'X's
R_3lLHYy05IGVKEsx
X(X(F(X(E))))
E at 4th state or later
8
noopi don't know
generally, I don't have a good feeling of how to use the X operator
R_b9Iqcbski6eXDcR
X(X(F(X(E))))
E at 4th state or later
9
noopI don't Know-
R_Qaiof3VJqdhfB85
X(X(F(X(E))))
E at 4th state or later
10
1
there is a subsequence of frames, excluding the first two frames, where the first frame has the engine on.
-
R_3KpRpBX8YVNs4Gg
X(X(F(X(E))))
E at 4th state or later
11
1Two states forward, there exists a suffix for which the next state has the engine on.-
R_WplTxskwa4dk3Ch
X(X(F(X(E))))
E at 4th state or later
12
1
Starting from two states after the start, the engine is eventually on in the following state.
-
R_1PRjXsiRe02RAu8
X(X(F(X(E))))
E at 4th state or later
13
11
Not sure about this one? The Engine is on in the next state and there is some subsequent state where the Engine is on for 3 states in a row?
-
R_2ZUFGxrSC3ZXGeM
X(X(F(X(E))))
E at 4th state or later
14
wow1
The engine is on in the current state and in the next state. The engine is eventually on again and in the next two states.
-
R_2z5TN4cEAO4EmSf
X(X(F(X(E))))
E at 4th state or later
15
1In the next, next state, eventually in the state after that the engine is on.-
R_1OkTTxT9d1P9iqE
X(X(F(X(E))))
E at 4th state or later
16
wow1
The engine must be on in the second state, and there must be a point after which the engine is on for two consecutive states.
-
R_1pEAmhCygdjC0hg
X(X(F(X(E))))
E at 4th state or later
17
1
After the first three states, the engine is on in the next state at some point in the system.
-
R_32Wmx4NAsQ5tQ0g
X(X(F(X(E))))
E at 4th state or later
18
1in the second state from now, the engine will eventually be on in the following state-
R_24cUoJLuWMdO3rU
X(X(F(X(E))))
E at 4th state or later
19
1
Two states after the initial state, it will eventually be true that the next state will have the engine on.
-
R_1DYHQFLsULDdxzd
X(X(F(X(E))))
E at 4th state or later
20
1The next state of the next state of some state of the next state has an engine on.-
R_3n2fZ76DFeD2wWC
X(X(F(X(E))))
E at 4th state or later
21
1In the next next state, there will eventually be a next state where the engine is on.-
R_3QXxN0o4hm13Q6J
X(X(F(X(E))))
E at 4th state or later
22
1In 2 states, eventually the engine will be on in the next state.-
R_1opqUxjPRpTjVDr
X(X(F(X(E))))
E at 4th state or later
23
1Some state after the second has the engine on.-
R_1NsGgY1vwI9Cv1O
X(X(F(X(E))))
E at 4th state or later
24
noopI don't know-
R_2DOBBusVzcX9lX2
X(X(F(X(E))))
E at 4th state or later
25
noopI really don't know-
R_1In6FleMbf6Kdvg
X(X(F(X(E))))
E at 4th state or later
26
1
In the next next state, there will be a suffix that starts some time after, such that in the next state the engine is on.
-
R_2PdJhdnFu3xDslc
X(X(F(X(E))))
E at 4th state or later
27
noopI don't know.-
R_2YRrACx7A92WPnJ
X(X(F(X(E))))
E at 4th state or later
28
wow1If the engine is on in the first state, it is on in the second, third and fourth state. -
R_2QLp1kb3GO8funU
X(X(F(X(E))))
E at 4th state or later
29
1
After the first 2 states, there is a state where the engine is on, and the state after that state has the engine off.
-
R_1i3PJRO0xu0WEgI
X(X(F(X(E))))
E at 4th state or later
30
1The engine is off in every three states -
R_1Nks8yJ1o65A2K7
X(X(F(X(E))))
E at 4th state or later
31
1Starting in the next state (2), the engine is finally on in the state diagram. -
R_1o5ZIuIDuezOcNI
X(X(F(X(E))))
E at 4th state or later
32
noopI don't know-
R_2fjPwmD0W7yEbi2
X(X(F(X(E))))
E at 4th state or later
33
1For the next state, eventually the Engine will be on. -
R_1o1Gt8hlH9mLuFM
X(X(F(X(E))))
E at 4th state or later
34
1Whenever all states eventually have the engine on, the light is on in all states-
R_2V8ftg0MEp4Ubs8
F(E) ==> G(L)
if ever E, then L always from start
35
1If there's a suffix where the engine is on, the light is always on.-
R_3HB55PANueKprlM
F(E) ==> G(L)
if ever E, then L always from start
36
1If there is some state where the engine is on, the light must always be on.-
R_bEn5CUcESzA0Y0N
F(E) ==> G(L)
if ever E, then L always from start
37
1If the engine eventually turns on, the light will be on in every state.-
R_2v92EqnYAvMz4p5
F(E) ==> G(L)
if ever E, then L always from start
38
1
If the trace ends with the Engine on (or more specifically, the final 'loop' of the trace has the engine on), then the light must be on for the entire trace.
-
R_3lLHYy05IGVKEsx
F(E) ==> G(L)
if ever E, then L always from start
39
1The Engine turning on at some point implies the light is always on-
R_b9Iqcbski6eXDcR
F(E) ==> G(L)
if ever E, then L always from start
40
1for every engine that is only all the following lights must be on-
R_Qaiof3VJqdhfB85
F(E) ==> G(L)
if ever E, then L always from start
41
1If there is a state where the engine is on, the light must be on for all states-
R_3KpRpBX8YVNs4Gg
F(E) ==> G(L)
if ever E, then L always from start
42
1
Whenever there is a suffix of the trace for which Engine holds (i.e., the engine is on in the first state of the suffix), the light will be on in all states.
-
R_WplTxskwa4dk3Ch
F(E) ==> G(L)
if ever E, then L always from start
43
1If the engine is eventually on, the light will always be on.-
R_1PRjXsiRe02RAu8
F(E) ==> G(L)
if ever E, then L always from start
44
1
If there is some subsequent state where the Engine is on, then all of the states following the current one have the light on.
-
R_2ZUFGxrSC3ZXGeM
F(E) ==> G(L)
if ever E, then L always from start
45
1If the engine is eventually on, then the light is always on.-
R_2z5TN4cEAO4EmSf
F(E) ==> G(L)
if ever E, then L always from start
46
1If the Engine is eventually on this implies that for all traces the light is on-
R_1OkTTxT9d1P9iqE
F(E) ==> G(L)
if ever E, then L always from start
47
1If the engine is turned on at some state, the light must be on during all states-
R_1pEAmhCygdjC0hg
F(E) ==> G(L)
if ever E, then L always from start
48
1If the engine is on for some traces of the system, then the light is on at all times.-
R_32Wmx4NAsQ5tQ0g
F(E) ==> G(L)
if ever E, then L always from start
49
todo doublecheck
111the engine will eventually turn on, after which the light will always be on-
R_24cUoJLuWMdO3rU
F(E) ==> G(L)
if ever E, then L always from start
50
1
If eventually, the engine turns on then the light is always on (and possibly has always been on?)
-
R_1DYHQFLsULDdxzd
F(E) ==> G(L)
if ever E, then L always from start
51
1For some state that engine is on, the light is on in all succeeding tails-
R_3n2fZ76DFeD2wWC
F(E) ==> G(L)
if ever E, then L always from start
52
todo doublecheck
11Once the engine light turns on, then the light is always on.-
R_3QXxN0o4hm13Q6J
F(E) ==> G(L)
if ever E, then L always from start
53
1If the engine ever reaches the on state, the light will have been on in all states.-
R_1opqUxjPRpTjVDr
F(E) ==> G(L)
if ever E, then L always from start
54
1If the engine is on in any subsequent state, the light is always on-
R_1NsGgY1vwI9Cv1O
F(E) ==> G(L)
if ever E, then L always from start
55
1If the engine is ever on, then the light is always on-
R_2DOBBusVzcX9lX2
F(E) ==> G(L)
if ever E, then L always from start
56
1If the engine is ever on, the Light is always on-
R_1In6FleMbf6Kdvg
F(E) ==> G(L)
if ever E, then L always from start
57
1Whenever the engine is finally on, the light will be on globally.-
R_2PdJhdnFu3xDslc
F(E) ==> G(L)
if ever E, then L always from start
58
1If eventually the engine is on, then the light is on in all states.-
R_2YRrACx7A92WPnJ
F(E) ==> G(L)
if ever E, then L always from start
59
1If the engine is on in this state, then the light is on in the next state-
R_2QLp1kb3GO8funU
F(E) ==> G(L)
if ever E, then L always from start
60
1
If the engine will ever turn on at any point in the future, the light must be on continuously.
-
R_1i3PJRO0xu0WEgI
F(E) ==> G(L)
if ever E, then L always from start
61
1When the engine is on, so is that light-
R_1Nks8yJ1o65A2K7
F(E) ==> G(L)
if ever E, then L always from start
62
1Whenever the engine eventually is on, the light will globally be on in each state. -
R_1o5ZIuIDuezOcNI
F(E) ==> G(L)
if ever E, then L always from start
63
noopI don't know-
R_2fjPwmD0W7yEbi2
F(E) ==> G(L)
if ever E, then L always from start
64
todo doublecheck
1Eventually the Engine will be on whenever the light is on globally-
R_1o1Gt8hlH9mLuFM
F(E) ==> G(L)
if ever E, then L always from start