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 | AA | AB | AC | AD | AE | AF | AG | AH | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | Totals ==> | 121 | 10 | 2 | 0 | 0 | 0 | 3 | 0 | 0 | 6 | 0 | 0 | 0 | 2 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 144 | |||||||||||
2 | Ok | ? | BP | BSI | BSQ | CyG | EU | TSU | BU | IF | IG | IPfx | OI | LenX | SeqX | Last | WU | WF | SG | RV | Scope | Answer | Explanation | ID | Formula | Expected | ||||||||
3 | 1 | It is equivalent to F(!Red): eventually Red becomes false. | R_3zr1TPsbL8Fh01g | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
4 | 1 | The red light is off in some state. | R_7t8OynItMvsY3qS | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
5 | 1 | Either there is no state with the Red light on, or Red will be off after being on. | R_5pl5ovreUYilD5z | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
6 | 1 | There is a state which is not red | R_6ffI4bTyX5zoEHh | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
7 | 1 | only satisfied if !Red is true in some state (equivalent to F !Red) | R_4mVF8KOBt6MErhn | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
8 | 1 | Eventually, a red light must be followed (in >=0 states) by no red light. | R_2pKyoW6gWKFoQnZ | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
9 | 1 | The Red light is off on some state in the infinite trace. | R_1kn76aEhDPLve1a | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
10 | 1 | There is a state where Red being on implies that after zero or more states it becomes off. | R_5PdIR5FnMDzrVUu | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
11 | 1 | There must be at least one state where when Red is on, then there is at least one state where Red is off. | R_3p46SBAhKNhlNvS | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
12 | 1 | Eventually, a Red light being on will imply that it will eventually turn off | R_47BVZHw0XbaticF | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
13 | 1 | If the Red light is on in the first state then it will eventually turn off. | R_51nrC3cVmGQGCbZ | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
14 | 1 | Eventually, if the Red light is on, then eventually, it will be switched off. | R_2rjQI459Ka4U504 | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
15 | 1 | It will eventually be true that if Red is on, then eventually the Red will be off. | R_10WMbhmzVMMfCQ9 | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
16 | 1 | there is at least one state in which red is on, and after this state there is at least one state in which Red is off | R_3p2LrOwAHaKfYYG | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
17 | 1 | Eventually, we have a state where Red is true and there exists a future state where Red is False. | R_2EPSIkVcvTwusZ1 | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
18 | 1 | Eventually, the red light will be on and, sometime eventually after that, the red light will be off. | R_6ZBMLj5oxGtGYyV | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
19 | 1 | There is a state in the future, such that if in that state the Red light is on, then there is a state where it is off after that as well. | R_7gRsvfLpsHGFun8 | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
20 | 1 | Eventually if Red is on the there must exist a point in the futere included the current one where Red turns off. (if in the first state Red is of it is already satisfied) | R_2wQrFCdtVBTz165 | F(r => F(!r)) | if red, must have !red in future | |||||||||||||||||||||||||||||
21 | 1 | Red is true all along the trace and eventually Blue also becomes true. | R_3zr1TPsbL8Fh01g | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
22 | 1 | Red light is always on and blue light turns on in some state. | R_7t8OynItMvsY3qS | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
23 | 1 | Red is always on and Blue is on in at least one state. | R_5pl5ovreUYilD5z | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
24 | 1 | All states are red and there exists a state that is blue as well | R_6ffI4bTyX5zoEHh | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
25 | 1 | red always holds and blue holds at some point | R_4mVF8KOBt6MErhn | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
26 | 1 | The red light must be on until the blue light is on, AND the red light must always be on. | R_2pKyoW6gWKFoQnZ | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
27 | 1 | The Red light is on in every state, and the Blue light is on in some state | R_1kn76aEhDPLve1a | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
28 | 1 | Red is always on and, at least in one state, Blue is on. | R_5PdIR5FnMDzrVUu | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
29 | 1 | Blue is on at one state, and Red is on in every state before and after it. | R_3p46SBAhKNhlNvS | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
30 | 1 | Red is always on and blue will eventually turn on | R_47BVZHw0XbaticF | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
31 | 1 | The Blue light eventually turns on and the Red light was always on before that state. Moreover, the Green light is always on. | R_51nrC3cVmGQGCbZ | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
32 | 1 | It is the case that the Red light is on forever and the Blue light is off until a certain state, where the Blue light will be turned on. | R_2rjQI459Ka4U504 | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
33 | 1 | Blue is on for some state and Red is on for every state in the trace. | R_10WMbhmzVMMfCQ9 | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
34 | 1 | 1 | Red is always on and Blue is never on | R_3p2LrOwAHaKfYYG | (r U b) & G(r) | always r, eventually b | ||||||||||||||||||||||||||||
35 | 1 | We always have Red to be true, and we must have Blue to be true in some future state. | R_2EPSIkVcvTwusZ1 | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
36 | 1 | The red light is always on. At some point, the blue light will be on. | R_6ZBMLj5oxGtGYyV | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
37 | 1 | Globally red is true and at some point blue is true as well. | R_7gRsvfLpsHGFun8 | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
38 | 1 | Red is on until Blue is on, and Red is always on. | R_2wQrFCdtVBTz165 | (r U b) & G(r) | always r, eventually b | |||||||||||||||||||||||||||||
39 | 1 | Red is true at the beginning and Blue is false next. | R_3zr1TPsbL8Fh01g | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
40 | 1 | Red light is on in this state and blue light is off in the next state. | R_7t8OynItMvsY3qS | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
41 | 1 | Red is on in the first state, and in the second state Blue is not on. | R_5pl5ovreUYilD5z | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
42 | 1 | First state is red, and the next one is not blue | R_6ffI4bTyX5zoEHh | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
43 | 1 | red holds in state 1 and blue must not hold in state 2. | R_4mVF8KOBt6MErhn | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
44 | 1 | The red light is on initially, AND the following state has no blue light. | R_2pKyoW6gWKFoQnZ | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
45 | 1 | In the first state, the Red light is on and in the second state, the Blue light is off | R_1kn76aEhDPLve1a | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
46 | 1 | Red is on at the initial state and Blue is off at the next state. | R_5PdIR5FnMDzrVUu | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
47 | 1 | Red is on in the initial state, and there doesn't exist a next state which is blue. | R_3p46SBAhKNhlNvS | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
48 | 1 | Red is on in the current state and blue is off in the next state | R_47BVZHw0XbaticF | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
49 | 1 | The Red light is on in the first state and Blue is off in the second state. | R_51nrC3cVmGQGCbZ | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
50 | 1 | It is the case that, in the first state, the Red light is on and in the next state, the Blue light will be off. | R_2rjQI459Ka4U504 | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
51 | 1 | Red is on in the initial state and Blue is off in the next state. | R_10WMbhmzVMMfCQ9 | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
52 | 1 | Red is on in the initial state and Blue is not on in the state after | R_3p2LrOwAHaKfYYG | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
53 | 1 | Current state has Red to be true and the next state to have Blue to be false. | R_2EPSIkVcvTwusZ1 | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
54 | 1 | At some state in the trace, the red light is on and, in the next state, the blue light is not on. | R_6ZBMLj5oxGtGYyV | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
55 | 1 | The current state is red and in the next state blue is false. | R_7gRsvfLpsHGFun8 | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
56 | 1 | Red is on at the first state, and in the next state Blue is off. | R_2wQrFCdtVBTz165 | r & !X(b) | r now, !b next | |||||||||||||||||||||||||||||
57 | not english | 1 | Always(if Red then next not Red and then Red again). | R_3zr1TPsbL8Fh01g | G(r => X(!r & X(r))) | whenever r, off/on evermore | ||||||||||||||||||||||||||||
58 | 1 | Whenever red light turns on, it is off in the next state and on again in the state after. | R_7t8OynItMvsY3qS | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
59 | 1 | At every state, if Red is on then in the next state Red is not on and in the state after that Red is on again. | R_5pl5ovreUYilD5z | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
60 | 1 | Every appearance of red is followed by a state which is not red and then a red state | R_6ffI4bTyX5zoEHh | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
61 | 1 | whenever red holds, it must not hold in the next state and must hold in the state after the next state. this is the same as saying, either red never holds or, it holds at some point in the trace and from that point on red alternates between true and false. | R_4mVF8KOBt6MErhn | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
62 | 1 | Always, a red light is immediately followed by no red light, which is immediately followed by a red light. | R_2pKyoW6gWKFoQnZ | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
63 | 1 | Whenever the Red light is on, it is off in the next state, and on again in the state after that. This amounts to: From the first time the Red light is on (if any), the Red light is on in exactly every other state | R_1kn76aEhDPLve1a | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
64 | 1 | Whenever the red light is on, it is off at the next state and back on at the state after that. | R_5PdIR5FnMDzrVUu | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
65 | 1 | In every state, when Red is on, then there must exist a next state where Red is off and the next state of that state is Red. | R_3p46SBAhKNhlNvS | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
66 | 1 | Globally, Red being on implies that it will be off in the next state and back on in the one after | R_47BVZHw0XbaticF | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
67 | 1 | If the Red light is on in a state, then it is off in the next state and on again in the state after that. | R_51nrC3cVmGQGCbZ | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
68 | 1 | It is always the case that, whenever the Red light is on in a state, then in the next state, the Red light is off, and the Red light is back on in the state following that. | R_2rjQI459Ka4U504 | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
69 | 1 | Whenever the Red light is on, the Red light is off in the next state and again on in the next of the next state. | R_10WMbhmzVMMfCQ9 | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
70 | 1 | Once Red is on at least once, then it alternates between being on and off in subsequent states | R_3p2LrOwAHaKfYYG | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
71 | 1 | Always, whenever we have Red to be true, the next state has Red to be false and the next to next state has Red to be true. | R_2EPSIkVcvTwusZ1 | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
72 | 1 | Whenever the red light is on, in the next state the red light is off and in the state after that the red light is on again. So, the red light alternates on and off. | R_6ZBMLj5oxGtGYyV | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
73 | 1 | Whenever there red light is on, it is off in the next state and on in the state that follows. | R_7gRsvfLpsHGFun8 | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
74 | 1 | Whenever Red is on, then in the next state Red turns off and in the next REd is on again. | R_2wQrFCdtVBTz165 | G(r => X(!r & X(r))) | whenever r, off/on evermore | |||||||||||||||||||||||||||||
75 | 1 | Same | R_3zr1TPsbL8Fh01g | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
76 | 1 | same | R_7t8OynItMvsY3qS | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
77 | 1 | Either there is no state with the Red light on, or Red will be off after being on. | R_5pl5ovreUYilD5z | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
78 | 1 | Same | R_6ffI4bTyX5zoEHh | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
79 | 1 | same | R_4mVF8KOBt6MErhn | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
80 | 1 | same | R_2pKyoW6gWKFoQnZ | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
81 | 1 | Pretty much the same, the Red light is off on some state in the finite trace | R_1kn76aEhDPLve1a | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
82 | 1 | same | R_5PdIR5FnMDzrVUu | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
83 | 1 | There must be at least one state where when Red is on, then there is at least one state where Red is off. | R_3p46SBAhKNhlNvS | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
84 | 1 | Finally, if Red holds, then eventually, Red does not hold. | R_47BVZHw0XbaticF | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
85 | 1 | same | R_51nrC3cVmGQGCbZ | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
86 | 1 | Eventually, if the Red light is on, then eventually, it will be switched off in a finite number of steps. | R_2rjQI459Ka4U504 | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
87 | 1 | Same. | Eventually has the same meaning in both. | R_10WMbhmzVMMfCQ9 | F(r => F(!r)) | same | ||||||||||||||||||||||||||||
88 | 1 | Same | R_3p2LrOwAHaKfYYG | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
89 | 1 | Same | R_2EPSIkVcvTwusZ1 | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
90 | 1 | Eventually, the red light will be on and, sometime eventually after that, the red light will be off. | R_6ZBMLj5oxGtGYyV | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
91 | 1 | Same | R_7gRsvfLpsHGFun8 | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
92 | 1 | Same as LTL. | R_2wQrFCdtVBTz165 | F(r => F(!r)) | same | |||||||||||||||||||||||||||||
93 | 1 | Same | R_3zr1TPsbL8Fh01g | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
94 | 1 | Same | R_7t8OynItMvsY3qS | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
95 | 1 | Red is always on and Blue is on in at least one state. | R_5pl5ovreUYilD5z | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
96 | 1 | Same | R_6ffI4bTyX5zoEHh | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
97 | 1 | same | R_4mVF8KOBt6MErhn | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
98 | 1 | same | R_2pKyoW6gWKFoQnZ | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
99 | 1 | Same | R_1kn76aEhDPLve1a | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
100 | 1 | same | R_5PdIR5FnMDzrVUu | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
101 | 1 | Blue is on at one state, and Red is on in every state before and after it. | R_3p46SBAhKNhlNvS | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
102 | 1 | Red is always on and blue will eventually turn on | R_47BVZHw0XbaticF | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
103 | 1 | same | R_51nrC3cVmGQGCbZ | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
104 | 1 | It is the case that the Red light is on in every state and the Blue light is off until a certain state, where the Blue light will be turned on. | R_2rjQI459Ka4U504 | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
105 | 1 | Same. | R_10WMbhmzVMMfCQ9 | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
106 | 1 | Same | R_3p2LrOwAHaKfYYG | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
107 | 1 | Same | R_2EPSIkVcvTwusZ1 | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
108 | 1 | The red light is on at every state. The blue light is on for some state in the trace. | R_6ZBMLj5oxGtGYyV | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
109 | 1 | Same. | R_7gRsvfLpsHGFun8 | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
110 | 1 | Same as LTL. | R_2wQrFCdtVBTz165 | (r U b) & G(r) | r for all states, b for some | |||||||||||||||||||||||||||||
111 | 1 | Red is true at the beginning and if there exist a next instant Blue is false in it. | R_3zr1TPsbL8Fh01g | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
112 | 1 | Red light is on in this state. If the trace is of length more than 1 then blue light is off in the next state. | R_7t8OynItMvsY3qS | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
113 | 1 | Red is on in the first state, and either the trace has only one state or Blue is off in the second state. | R_5pl5ovreUYilD5z | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
114 | 1 | First state is red, and either this state is the last state, or the next one is not blue (if it exists). | R_6ffI4bTyX5zoEHh | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
115 | 1 | Red must hold in state 1 and EITHER the trace has length 1 OR blue holds in state 2. | R_4mVF8KOBt6MErhn | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
116 | 1 | The red light is on initially, AND there is no next state OR the next state is not blue | R_2pKyoW6gWKFoQnZ | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
117 | 1 | In the first state, the Red light is on. In addition, either there is no second state (the trace has length 1) or in the second state the Blue light is off | R_1kn76aEhDPLve1a | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
118 | 1 | Red is on at the initial state and either a next state exists on which Blue is off, or a next state doesn't exist and the trace is automatically satisfying. In other words, all traces of length 1 where Red is on at the initial state satisfy this formula. | R_5PdIR5FnMDzrVUu | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
119 | 1 | Red is on in the initial state, and there doesn't exist a next state which is blue. | R_3p46SBAhKNhlNvS | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
120 | 1 | Red is on in the current state and blue is off in the next state | R_47BVZHw0XbaticF | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
121 | 1 | The Red light is on in the first state and either there is no second state or the blue light is off in the second state. | R_51nrC3cVmGQGCbZ | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
122 | 1 | It is the case that, in the first state, the Red light is on and either there is no further state (i.e. the trace ends after the first state) or, if there is a second state, then Blue light is off in this state. | R_2rjQI459Ka4U504 | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
123 | 1 | Red is on in the initial state and if there exists a next state, Blue is off in it. | Because the negative condition is before the strong next, the meaning of the formula is similar in both. | R_10WMbhmzVMMfCQ9 | r & !X(b) | r now, if next !b | ||||||||||||||||||||||||||||
124 | 1 | As long as the trace is 2 or more states long then it is satisfiable with the same behavior | R_3p2LrOwAHaKfYYG | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
125 | 1 | Current state has Red to be true and the next state either does not exist or it exists and Blue is false in that state. | R_2EPSIkVcvTwusZ1 | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
126 | 1 | There is a state where the red light is on, and, if the next state exists, the blue light is not on in it. | I am not 100% sure of the implications of !X. I assume here that it means that X may not exist, and in that case, !X is satisfied. | R_6ZBMLj5oxGtGYyV | r & !X(b) | r now, if next !b | ||||||||||||||||||||||||||||
127 | 1 | The current state is red and if there is a next state, then blue needs to be false. | R_7gRsvfLpsHGFun8 | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
128 | 1 | Red is on at the first state. Trace of length 1 where Red is on satisfies the formula. Any other trace of length greater or equal to two, the definition is the same as LTL. | R_2wQrFCdtVBTz165 | r & !X(b) | r now, if next !b | |||||||||||||||||||||||||||||
129 | 1 | Same. | R_3zr1TPsbL8Fh01g | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
130 | 1 | Red light is never on. | R_7t8OynItMvsY3qS | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
131 | 1 | This formula is only satisfied if the Red is never on. | R_5pl5ovreUYilD5z | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
132 | 1 | There is no red states | If there was a red state in the finite trace, then from that point we would must have an alternating sequence of red and not red states. For the last red state in sequence (which is the very last state, or the one before) one of the X expressions will fail | R_6ffI4bTyX5zoEHh | G(r => X(!r & X(r))) | never r | ||||||||||||||||||||||||||||
133 | 1 | EITHER red never holds OR (same as LTL) it holds at some point in the trace and from that point on red alternates between true and false. However, the 2nd possibility can never be satisfied by a finite trace. | R_4mVF8KOBt6MErhn | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
134 | 1 | same (so cannot be satisfied by a finite trace) | R_2pKyoW6gWKFoQnZ | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
135 | 1 | No finite traces where the Red light is on satisfy this formula, so the formula in LTLf amounts to the Red light is always off | R_1kn76aEhDPLve1a | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
136 | 1 | Every state where the Red light is on is followed by a state where Red is off and by another state where it is on again. Therefore, no trace of length at most 2 can satisfy this formula. | R_5PdIR5FnMDzrVUu | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
137 | 1 | In every state, when Red is on, then there must exist a next state where Red is off and the next state of that state is Red. This can not be satisfied by LTLf since there is not next state for the last state. | R_3p46SBAhKNhlNvS | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
138 | 1 | Globally, Red being on implies that it will be off in the next state and back on in the one after. No finite traces satisfy this | R_47BVZHw0XbaticF | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
139 | 1 | The Red light never turns on. | R_51nrC3cVmGQGCbZ | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
140 | 1 | For every state, if Red light is on, then in the next state, the Red light is off, and the Red light is back on in the state following that. No finite traces satisfy the formula. | R_2rjQI459Ka4U504 | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
141 | 1 | Every state where Red is on, must be followed by a state with Red off and then by a state with Red on. A finite trace can satisfy the formula only if there is no state where Red is on. | R_10WMbhmzVMMfCQ9 | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
142 | 1 | this is not possible over finite traces | R_3p2LrOwAHaKfYYG | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
143 | 1 | Same as above, but the only finite traces that can satisfy it do not have Red to be true. This is because once Red is true, it starts alternating forever and a finite trace will cause the implication to be false as X(State) gives false if we are at the last state of the finite trace. | R_2EPSIkVcvTwusZ1 | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
144 | 1 | This cannot be expressed without an infinite trace as it demands the existence of a next state for all states. | R_6ZBMLj5oxGtGYyV | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
145 | 1 | Whenever the red light is on, there needs to be a next state where it is off and a third successor state, where it is on again. But then, this also holds for that state ==> thus this formula is not satisfiable over finite traces. | R_7gRsvfLpsHGFun8 | G(r => X(!r & X(r))) | never r | |||||||||||||||||||||||||||||
146 | 1 | The traces satisfying the formula are the ones where Red is always off, independently from the size (empty trace included). Then it is the same as LTL with the checking of the last poit of the trace. | R_2wQrFCdtVBTz165 | G(r => X(!r & X(r))) | never r |