ABCDEFGHIJKLMNOPQRSTUVWXYZAAABAC
1
Totals ==>10500000001020000108
2
Ok?BPBSI
BSQ
IFIGOIWUEU
LenX
Last
SeqX
RV
Scope
AnswerExplanationIDFormulaTraceExpected
3
1Yes
Red is true at last.
R_3zr1TPsbL8Fh01g
G(F(r)){r} {} {} {r}Yes
4
1Yes
R_7t8OynItMvsY3qS
G(F(r)){r} {} {} {r}Yes
5
1Yes
Red is on in the last state, so for every state F(Red) is true.
R_5pl5ovreUYilD5z
G(F(r)){r} {} {} {r}Yes
6
1Yes
R_6ffI4bTyX5zoEHh
G(F(r)){r} {} {} {r}Yes
7
1Yes
R_4mVF8KOBt6MErhn
G(F(r)){r} {} {} {r}Yes
8
1Yes
R_2pKyoW6gWKFoQnZ
G(F(r)){r} {} {} {r}Yes
9
1Yes
R_1kn76aEhDPLve1a
G(F(r)){r} {} {} {r}Yes
10
1Yes
R_5PdIR5FnMDzrVUu
G(F(r)){r} {} {} {r}Yes
11
1Yes
R_3p46SBAhKNhlNvS
G(F(r)){r} {} {} {r}Yes
12
1Yes
R_47BVZHw0XbaticF
G(F(r)){r} {} {} {r}Yes
13
1Yes
R_51nrC3cVmGQGCbZ
G(F(r)){r} {} {} {r}Yes
14
1Yes
This is equivalent to the last state satisfying that the Red light is on, which is the case.
R_2rjQI459Ka4U504
G(F(r)){r} {} {} {r}Yes
15
1Yes
R_10WMbhmzVMMfCQ9
G(F(r)){r} {} {} {r}Yes
16
1Yes
R_3p2LrOwAHaKfYYG
G(F(r)){r} {} {} {r}Yes
17
1Yes
R_2EPSIkVcvTwusZ1
G(F(r)){r} {} {} {r}Yes
18
1Yes
R_6ZBMLj5oxGtGYyV
G(F(r)){r} {} {} {r}Yes
19
1Yes
R_7gRsvfLpsHGFun8
G(F(r)){r} {} {} {r}Yes
20
1Yes
R_2wQrFCdtVBTz165
G(F(r)){r} {} {} {r}Yes
21
1No
Red is required to become false eventually (before the end of the trace).
R_3zr1TPsbL8Fh01g
r U (!r){r} {r} {r}No
22
1No
R_7t8OynItMvsY3qS
r U (!r){r} {r} {r}No
23
1No
!Red is never satisfied.
R_5pl5ovreUYilD5z
r U (!r){r} {r} {r}No
24
1No
R_6ffI4bTyX5zoEHh
r U (!r){r} {r} {r}No
25
1No
R_4mVF8KOBt6MErhn
r U (!r){r} {r} {r}No
26
1No
R_2pKyoW6gWKFoQnZ
r U (!r){r} {r} {r}No
27
1No
R_1kn76aEhDPLve1a
r U (!r){r} {r} {r}No
28
1No
R_5PdIR5FnMDzrVUu
r U (!r){r} {r} {r}No
29
1No
R_3p46SBAhKNhlNvS
r U (!r){r} {r} {r}No
30
1No
R_47BVZHw0XbaticF
r U (!r){r} {r} {r}No
31
1No
R_51nrC3cVmGQGCbZ
r U (!r){r} {r} {r}No
32
1No
!Red holds for no state in the above trace.
R_2rjQI459Ka4U504
r U (!r){r} {r} {r}No
33
1No
No, because Red remains on for the whole trace.
R_10WMbhmzVMMfCQ9
r U (!r){r} {r} {r}No
34
1Yes
R_3p2LrOwAHaKfYYG
r U (!r){r} {r} {r}No
35
1No
R_2EPSIkVcvTwusZ1
r U (!r){r} {r} {r}No
36
1No
R_6ZBMLj5oxGtGYyV
r U (!r){r} {r} {r}No
37
1No
The second part of the until needs to be satisfied for the until to be true.,
R_7gRsvfLpsHGFun8
r U (!r){r} {r} {r}No
38
1No
R_2wQrFCdtVBTz165
r U (!r){r} {r} {r}No
39
1Yes
In the last state weak next read hold, so the whole formula holds.
R_3zr1TPsbL8Fh01g
F(!X(r)){r} {r}Yes
40
1Yes
R_7t8OynItMvsY3qS
F(!X(r)){r} {r}Yes
41
1Yes
In the last state, !X(Red) is satisfied because there is no next state.
R_5pl5ovreUYilD5z
F(!X(r)){r} {r}Yes
42
1Yes
R_6ffI4bTyX5zoEHh
F(!X(r)){r} {r}Yes
43
1Yes
R_4mVF8KOBt6MErhn
F(!X(r)){r} {r}Yes
44
1Yes
In the final state, !X(Red) is true because there is no next state.
R_2pKyoW6gWKFoQnZ
F(!X(r)){r} {r}Yes
45
1Yes
R_1kn76aEhDPLve1a
F(!X(r)){r} {r}Yes
46
1Yes
X (Red) is false at state 2.
R_5PdIR5FnMDzrVUu
F(!X(r)){r} {r}Yes
47
1Yes
R_3p46SBAhKNhlNvS
F(!X(r)){r} {r}Yes
48
1No
R_47BVZHw0XbaticF
F(!X(r)){r} {r}Yes
49
1Yes
R_51nrC3cVmGQGCbZ
F(!X(r)){r} {r}Yes
50
1Yes
Holds, as after the last state, there is no following state (i.e. trace finishes).
R_2rjQI459Ka4U504
F(!X(r)){r} {r}Yes
51
1Yes
Yes, because the strong next condition is immediately false for state 2 , thus the negative condition is satisfied!
R_10WMbhmzVMMfCQ9
F(!X(r)){r} {r}Yes
52
1No
R_3p2LrOwAHaKfYYG
F(!X(r)){r} {r}Yes
53
1Yes
R_2EPSIkVcvTwusZ1
F(!X(r)){r} {r}Yes
54
1Yes
R_6ZBMLj5oxGtGYyV
F(!X(r)){r} {r}Yes
55
1Yes
In the last state, X(\phi) is false for any \phi ==> X(Red) is false and therefore !X(Red) is true at the last state which renders the eventually true as well.
R_7gRsvfLpsHGFun8
F(!X(r)){r} {r}Yes
56
1Yes
The negation of X in LTLf is, WX. So every non-empty trace is accepted
R_2wQrFCdtVBTz165
F(!X(r)){r} {r}Yes
57
1No
The formula requires that eventually after the first state Red becomes false.
R_3zr1TPsbL8Fh01g
F(X(!r)){r} {r}No
58
1No
R_7t8OynItMvsY3qS
F(X(!r)){r} {r}No
59
1No
There is no state where its successor exists and has not Red on.
R_5pl5ovreUYilD5z
F(X(!r)){r} {r}No
60
1No
R_6ffI4bTyX5zoEHh
F(X(!r)){r} {r}No
61
1No
R_4mVF8KOBt6MErhn
F(X(!r)){r} {r}No
62
1No
R_2pKyoW6gWKFoQnZ
F(X(!r)){r} {r}No
63
1No
R_1kn76aEhDPLve1a
F(X(!r)){r} {r}No
64
1No
X (!Red) is always false.
R_5PdIR5FnMDzrVUu
F(X(!r)){r} {r}No
65
1No
R_3p46SBAhKNhlNvS
F(X(!r)){r} {r}No
66
1No
R_47BVZHw0XbaticF
F(X(!r)){r} {r}No
67
1No
R_51nrC3cVmGQGCbZ
F(X(!r)){r} {r}No
68
1No
It does not hold, as after the last state, there is no following state, hence !Red cannot hold there.
R_2rjQI459Ka4U504
F(X(!r)){r} {r}No
69
1No
No. For state 1 it is not satisfied because Red is on in next state. For state 2 is not satisfied because there is no next state.
R_10WMbhmzVMMfCQ9
F(X(!r)){r} {r}No
70
1No
R_3p2LrOwAHaKfYYG
F(X(!r)){r} {r}No
71
1No
R_2EPSIkVcvTwusZ1
F(X(!r)){r} {r}No
72
1No
R_6ZBMLj5oxGtGYyV
F(X(!r)){r} {r}No
73
1No
Here, we know that at states 1 X(!Red) is false, as state 2 is red. Moreover, at state 2, X(Red) is false as well - as at the last state X(\phi) is false for any \phi.
R_7gRsvfLpsHGFun8
F(X(!r)){r} {r}No
74
1No
Normal interpretation of strong next in LTL
R_2wQrFCdtVBTz165
F(X(!r)){r} {r}No
75
1Yes
Red is satisfied at last.
R_3zr1TPsbL8Fh01g
F(G(r)){} {} {} {r}Yes
76
1Yes
R_7t8OynItMvsY3qS
F(G(r)){} {} {} {r}Yes
77
1Yes
In the last state, G(Red) is true.
R_5pl5ovreUYilD5z
F(G(r)){} {} {} {r}Yes
78
1Yes
R_6ffI4bTyX5zoEHh
F(G(r)){} {} {} {r}Yes
79
1Yes
R_4mVF8KOBt6MErhn
F(G(r)){} {} {} {r}Yes
80
1Yes
R_2pKyoW6gWKFoQnZ
F(G(r)){} {} {} {r}Yes
81
1Yes
R_1kn76aEhDPLve1a
F(G(r)){} {} {} {r}Yes
82
1Yes
R_5PdIR5FnMDzrVUu
F(G(r)){} {} {} {r}Yes
83
1Yes
R_3p46SBAhKNhlNvS
F(G(r)){} {} {} {r}Yes
84
1Yes
R_47BVZHw0XbaticF
F(G(r)){} {} {} {r}Yes
85
1Yes
R_51nrC3cVmGQGCbZ
F(G(r)){} {} {} {r}Yes
86
1Yes
This is equivalent to the last state satisfying that the Red light is on, which is the case.
R_2rjQI459Ka4U504
F(G(r)){} {} {} {r}Yes
87
1Yes
R_10WMbhmzVMMfCQ9
F(G(r)){} {} {} {r}Yes
88
1Yes
R_3p2LrOwAHaKfYYG
F(G(r)){} {} {} {r}Yes
89
1Yes
R_2EPSIkVcvTwusZ1
F(G(r)){} {} {} {r}Yes
90
1Yes
R_6ZBMLj5oxGtGYyV
F(G(r)){} {} {} {r}Yes
91
1Yes
At state 4, G(Red) is true and as every state is succeeded (or the same as) state 4, this is true.
R_7gRsvfLpsHGFun8
F(G(r)){} {} {} {r}Yes
92
1Yes
R_2wQrFCdtVBTz165
F(G(r)){} {} {} {r}Yes
93
1Yes
Within the trace first we meet Red and then Blue.
R_3zr1TPsbL8Fh01g
F(r & F(b)){b} {r} {r} {b}Yes
94
1Yes
R_7t8OynItMvsY3qS
F(r & F(b)){b} {r} {r} {b}Yes
95
1Yes
Red & F(Blue) is satisfied by state 2, because Blue is satisfied by state 4.
R_5pl5ovreUYilD5z
F(r & F(b)){b} {r} {r} {b}Yes
96
1Yes
R_6ffI4bTyX5zoEHh
F(r & F(b)){b} {r} {r} {b}Yes
97
1Yes
R_4mVF8KOBt6MErhn
F(r & F(b)){b} {r} {r} {b}Yes
98
1Yes
R_2pKyoW6gWKFoQnZ
F(r & F(b)){b} {r} {r} {b}Yes
99
1Yes
R_1kn76aEhDPLve1a
F(r & F(b)){b} {r} {r} {b}Yes
100
1Yes
R_5PdIR5FnMDzrVUu
F(r & F(b)){b} {r} {r} {b}Yes
101
1Yes
R_3p46SBAhKNhlNvS
F(r & F(b)){b} {r} {r} {b}Yes
102
1Yes
R_47BVZHw0XbaticF
F(r & F(b)){b} {r} {r} {b}Yes
103
1Yes
R_51nrC3cVmGQGCbZ
F(r & F(b)){b} {r} {r} {b}Yes
104
1Yes
Holds, because in our trace, we can find a state (in fact, actually, 2 states, the second and the third ones)where the Red light is on, and after that state, there exists a state where the Blue light is on too ( the last state).
R_2rjQI459Ka4U504
F(r & F(b)){b} {r} {r} {b}Yes
105
1Yes
R_10WMbhmzVMMfCQ9
F(r & F(b)){b} {r} {r} {b}Yes
106
1Yes
R_3p2LrOwAHaKfYYG
F(r & F(b)){b} {r} {r} {b}Yes
107
1Yes
R_2EPSIkVcvTwusZ1
F(r & F(b)){b} {r} {r} {b}Yes
108
1Yes
R_6ZBMLj5oxGtGYyV
F(r & F(b)){b} {r} {r} {b}Yes
109
1Yes
At state 2, Red is true and F(Blue) is true,
R_7gRsvfLpsHGFun8
F(r & F(b)){b} {r} {r} {b}Yes
110
1Yes
R_2wQrFCdtVBTz165
F(r & F(b)){b} {r} {r} {b}Yes
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263