ltlcross.org 47.7 KB
Newer Older
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
1
# -*- coding: utf-8 -*-
2
#+TITLE: =ltlcross=
3
4
#+SETUPFILE: setup.org
#+HTML_LINK_UP: tools.html
5

6
=ltlcross= is a tool for cross-comparing the output of LTL-to-automata
7
8
9
10
translators.  It is actually a Spot-based clone of [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]], the
/LTL-to-Büchi Translator Testbench/, that essentially performs the
same sanity checks.

11
The main differences are:
12
  - support for PSL formulas in addition to LTL
13
14
15
16
17
  - more statistics, especially:
    - the number of logical transitions represented by each physical edge,
    - the number of deterministic states and automata
    - the number of SCCs with their various strengths (nonaccepting, terminal, weak, strong)
    - the number of terminal, weak, and strong automata
18
  - statistics output in a format that can be more easily be post-processed,
19
  - more precise time measurement (LBTT was only precise to
20
    1/100 of a second, reporting most times as "0.00s"),
21
  - support for any type of acceptance condition,
22
23
  - additional intersection checks with the complement, allowing
    to check equivalence of automata more precisely.
24
25

Although =ltlcross= performs the same sanity checks as LBTT, it does
26
27
28
not implement any of the interactive features of LBTT.  In our almost
10-year usage of LBTT, we never had to use its interactive features to
understand bugs in our translation.  Therefore =ltlcross= will report
29
30
problems, maybe with a conterexample, but you will be on your own to
investigate and fix them.
31
32
33
34
35

The core of =ltlcross= is a loop that does the following steps:
  - Input a formula
  - Translate the formula and its negation using each configured translator.
    If there are 3 translators, the positive and negative translations
36
37
38
    will be denoted =P0=, =N0=, =P1=, =N1=, =P2=, =N2=.  Optionally
    build complemented automata denoted =Comp(P0)=, =Comp(N0)=, etc.
  - Perform sanity checks between all these automata to detect any problem.
39
  - Build the products of these automata with a random state-space (the same
40
41
    state-space for all translations).  (If the =--products=N= option is given,
    =N= products are performed instead.)
42
43
44
45
46
47
48
49
50
51
52
53
54
  - Gather statistics if requested.

* Formula selection

Formulas to translate should be specified using the [[file:ioltl.org][common input options]].
Standard input is read if no =-f= or =-F= option is given.

* Configuring translators

Each translator should be specified as a string that use some of the
following character sequences:

#+BEGIN_SRC sh :results verbatim :exports results
55
  ltlcross --help | sed -n '/character sequences:/,/^$/p' | sed '1d;$d'
56
57
#+END_SRC
#+RESULTS:
58
:   %%                         a single %
59
60
61
62
:   %f,%s,%l,%w                the formula as a (quoted) string in Spot, Spin,
:                              LBT, or Wring's syntax
:   %F,%S,%L,%W                the formula as a file in Spot, Spin, LBT, or
:                              Wring's syntax
63
64
:   %O                         the automaton is output in HOA, never claim, LBTT,
:                              or ltl2dstar's format
65
66
67
68
69

For instance here is how we could cross-compare the never claims
output by =spin= and =ltl2tgba= for the formulas =GFa= and =X(a U b)=.

#+BEGIN_SRC sh :results verbatim :exports code
70
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%O' 'spin -f %s >%O'
71
72
73
74
#+END_SRC
#+RESULTS:

When =ltlcross= executes these commands, =%s= will be replaced
75
by the formula in Spin's syntax, and =%O= will be replaced by a
76
77
78
79
temporary file into which the output of the translator is redirected
before it is read back by =ltlcross=.

#+BEGIN_SRC sh :results verbatim :exports results
80
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%O' 'spin -f %s >%O' 2>&1
81
82
83
84
#+END_SRC
#+RESULTS:
#+begin_example
([](<>(a)))
85
86
87
88
Running [P0]: ltl2tgba -s '([](<>(a)))' >'lcr-o0-hvzgTC'
Running [P1]: spin -f '([](<>(a)))' >'lcr-o1-iYh45L'
Running [N0]: ltl2tgba -s '(!([](<>(a))))' >'lcr-o0-z6nzjV'
Running [N1]: spin -f '(!([](<>(a))))' >'lcr-o1-8JB5F4'
89
90
91
Performing sanity checks and gathering statistics...

(X((a) U (b)))
92
93
94
95
Running [P0]: ltl2tgba -s '(X((a) U (b)))' >'lcr-o0-rqfB6d'
Running [P1]: spin -f '(X((a) U (b)))' >'lcr-o1-OUNHEn'
Running [N0]: ltl2tgba -s '(!(X((a) U (b))))' >'lcr-o0-qzVvdx'
Running [N1]: spin -f '(!(X((a) U (b))))' >'lcr-o1-eUfHTG'
96
97
Performing sanity checks and gathering statistics...

98
No problem detected.
99
100
#+end_example

101
102
103
104
105
106
107
108
To handle tools that do not support some LTL operators, the character
sequences ~%f~, ~%s~, ~%l~, ~%w~, ~%F~, ~%S~, ~%L~, and ~%W~ can be
"infixed" by a bracketed list of operators to rewrite away.  For
instance if a tool reads LTL formulas from a file in LBT's syntax, but
does not support operators ~M~ (strong until) and ~W~ (weak until),
use ~%[WM]L~ instead of just ~%L~; this way operators ~W~ and ~M~ will
be rewritten using the other supported operators.

109
=ltlcross= can only read four kinds of output:
110
111
  - Never claims (only if they are restricted to representing an
    automaton using =if=, =goto=, and =skip= statements) such as those
112
    output by [[http://spinroot.com/][=spin=]], [[http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/][=ltl2ba=]], [[https://sourceforge.net/projects/ltl3ba/][=ltl3ba=]], or =ltl2tgba --spin=.  The
113
114
    newer syntax introduced by Spin 6.24, using =do= instead of =if=,
    is also supported.
115
116
117
  - [[http://www.tcs.hut.fi/Software/lbtt/doc/html/Format-for-automata.html][LBTT's format]], which supports generalized Büchi automata with
    either state-based acceptance or transition-based acceptance.
    This output is used for instance by [[http://www.tcs.hut.fi/Software/maria/tools/lbt/][=lbt=]], [[http://web.archive.org/web/20080607170403/http://www.science.unitn.it/~stonetta/modella.html][=modella=]], or =ltl2tgba
118
    --lbtt=.
119
  - Non-alternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]] with an acceptance
120
    condition that is is generalized-Büchi or inferior.
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
121
  - [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]], which supports deterministic Rabin or Streett
122
123
124
125
126
    automata.

Files in any of these format should be indicated with =%O=.  (Past
versions of =ltlcross= used different letters for each format, but the
four parsers have been merged into a single one.)
127
128
129
130
131

Of course all configured tools need not use the same =%= sequences.
The following list shows some typical configurations for some existing
tools:

132
133
134
135
  - '=spin -f %s >%O='
  - '=ltl2ba -f %s >%O='
  - '=ltl3ba -M0 -f %s >%O=' (less deterministic output, can be smaller)
  - '=ltl3ba -M1 -f %s >%O=' (more deterministic output)
136
  - '=modella -r12 -g -e %[MWei^]L %O='
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
137
  - '=/path/to/script4lbtt.py %L %O=' (script supplied by [[http://web.archive.org/web/20070214050826/http://estragon.ti.informatik.uni-kiel.de/~fritz/][ltl2nba]] for
138
    its interface with LBTT)
139
140
141
142
  - '=ltl2tgba -s %f >%O=' (smaller output, Büchi automaton)
  - '=ltl2tgba -s -D %f >%O=' (more deterministic output, Büchi automaton)
  - '=ltl2tgba -H %f >%O=' (smaller output, TGBA)
  - '=ltl2tgba -H -D %f >%O=' (more deterministic output, TGBA)
143
  - '=lbt <%L >%O='
144
  - '~ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD
145
    --output-format=hoa %[MW]L %O~' deterministic Rabin output in HOA, as
146
147
    supported since version 0.5.2 of =ltl2dstar=.
  - '~ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD --automata=streett
148
    --output-format=hoa %[MW]L %O~' deterministic Streett output in HOA,
149
    as supported since version 0.5.2 of =ltl2dstar=.
150
  - '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %[MW]L %O=' (Rabin
151
152
    output in DSTAR format, as supported in older versions of
    =ltl2dstar=.
153
  - '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %L - | dstar2tgba
154
    -s >%O=' (external conversion from Rabin to Büchi done by
155
156
    =dstar2tgba= for more reduction of the Büchi automaton than what
    =ltlcross= would provide)
157
  - '=java -jar Rabinizer.jar -ltl2dstar %[MW]F %O; mv %O.dst %O=' (Rabinizer
158
159
    uses the last =%O= argument as a prefix to which it always append =.dst=,
    so we have to rename =%O.dst= as =%O= so that =ltlcross= can find the file)
160
  - '~java -jar rabinizer3.1.jar -in=formula -silent -out=std -format=hoa -auto=tr %[MWR]f >%O~'
161
    (rabinizer 3.1 can output automata in the HOA format)
162
  - '=ltl3dra -f %s >%O=' (The HOA format is the default for =ltl2dra=.)
163

164
165
166
167
168
169
170
171
172
173
174
175
To simplify the use of some of the above tools, a set of predefined
shorthands are available.  Those can be listed with the
=--list-shorthands= option.

#+BEGIN_SRC sh :results verbatim :exports both
ltlcross --list-shorthands
#+END_SRC
#+RESULTS:
#+begin_example
If a COMMANDFMT does not use any %-sequence, and starts with one of
the following words, then the string on the right is appended.

176
177
  lbt          <%L>%O
  ltl2ba       -f %s>%O
178
  ltl2dstar    --output-format=hoa %[MW]L %O
179
180
  ltl2tgba     -H %f>%O
  ltl3ba       -f %s>%O
181
182
  ltl3dra      -f %s>%O
  modella      %[MWei^]L %O
183
  spin         -f %s>%O
184
185
186
187
188

Any {name} and directory component is skipped for the purpose of
matching those prefixes.  So for instance
  '{DRA} ~/mytools/ltl2dstar-0.5.2'
will changed into
189
  '{DRA} ~/mytools/ltl2dstar-0.5.2 --output-format=hoa %[MR]L %O'
190
191
192
#+end_example

What this implies is that running =ltlcross ltl2ba ltl3ba ...= is
193
the same as running =ltlcross 'ltl2ba -f %s>%O' 'ltl3ba -f %s>%O' ...=
194
195
196

Because only the prefix of the actual command is checked, you can
still specify some options.  For instance =ltlcross 'ltl2tgba -D' ...=
197
is short for =ltlcross 'ltl2tgba -D -H %F>%O' ...=
198

199
200
201
202
203
204
* Getting statistics

Detailed statistics about the result of each translation, and the
product of that resulting automaton with the random state-space, can
be obtained using the =--csv=FILE= or =--json=FILE= option.

205
206
** CSV or JSON output (or both!)

207
The following compare =ltl2tgba=, =spin=, and =lbt= on three random
208
formulas (where =W= and =M= operators have been rewritten away because
209
they are not supported by =spin= and =lbt=).
210
211

#+BEGIN_SRC sh :results verbatim :exports code
212
randltl -n 3 a b |
213
214
ltlfilt --remove-wm |
ltlcross --csv=results.csv \
215
216
217
         'ltl2tgba -s %f >%O' \
         'spin -f %s >%O' \
         'lbt < %L >%O'
218
219
220
221
#+END_SRC
#+RESULTS:

#+BEGIN_SRC sh :results verbatim :exports results
222
randltl -n 3 a b | ltlfilt --remove-wm |
223
ltlcross --csv=results.csv --json=results.json \
224
225
226
         'ltl2tgba -s %f >%O' \
         'spin -f %s >%O' \
         'lbt < %L >%O' --csv=results.csv 2>&1
227
228
229
#+END_SRC
#+RESULTS:
#+begin_example
230
231
232
233
234
235
236
-:1: (0)
Running [P0]: ltl2tgba -s '(0)' >'lcr-o0-HUCuLR'
Running [P1]: spin -f '(false)' >'lcr-o1-OEpUm3'
Running [P2]: lbt < 'lcr-i0-KCU1eG' >'lcr-o2-jzzGYe'
Running [N0]: ltl2tgba -s '(1)' >'lcr-o0-ppQ4cC'
Running [N1]: spin -f '(true)' >'lcr-o1-0OiIVN'
Running [N2]: lbt < 'lcr-i0-KZxSAq' >'lcr-o2-EcBREZ'
237
238
Performing sanity checks and gathering statistics...

239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
-:2: (!((1) U (F(!(p0)))))
Running [P0]: ltl2tgba -s '(!((1) U (F(!(p0)))))' >'lcr-o0-3dS2an'
Running [P1]: spin -f '(!((true) U (<>(!(p0)))))' >'lcr-o1-SJop2y'
Running [P2]: lbt < 'lcr-i1-jbIWpb' >'lcr-o2-hBEeUK'
Running [N0]: ltl2tgba -s '(1) U (F(!(p0)))' >'lcr-o0-Hku1E8'
Running [N1]: spin -f '(true) U (<>(!(p0)))' >'lcr-o1-8sslEk'
Running [N2]: lbt < 'lcr-i1-M3MCMW' >'lcr-o2-f6kaEw'
Performing sanity checks and gathering statistics...

-:3: (1) U ((G(p0)) | (F(p1)))
Running [P0]: ltl2tgba -s '(1) U ((G(p0)) | (F(p1)))' >'lcr-o0-0Mu0SU'
Running [P1]: spin -f '(true) U (([](p0)) || (<>(p1)))' >'lcr-o1-Vhkn66'
Running [P2]: lbt < 'lcr-i2-tc2zLI' >'lcr-o2-iOQjkj'
Running [N0]: ltl2tgba -s '(!((1) U ((G(p0)) | (F(p1)))))' >'lcr-o0-eveiNH'
Running [N1]: spin -f '(!((true) U (([](p0)) || (<>(p1)))))' >'lcr-o1-7hg46T'
Running [N2]: lbt < 'lcr-i2-XwPNyv' >'lcr-o2-GuXns6'
255
256
Performing sanity checks and gathering statistics...

257
No problem detected.
258
259
260
261
262
263
264
265
266
#+end_example

After this execution, the file =results.csv= contains the following:

#+BEGIN_SRC sh :results verbatim :exports results
cat results.csv
#+END_SRC
#+RESULTS:
#+begin_example
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
"formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","ambiguous_aut","product_states","product_transitions","product_scc"
"(0)","ltl2tgba -s %f >%O","ok",0,0.0329577,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,1,0,1
"(0)","spin -f %s >%O","ok",0,0.00219235,2,2,1,1,2,1,1,0,0,0,0,1,0,0,1,1,0,1
"(0)","lbt < %L >%O","ok",0,0.0026317,1,0,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,1
"(1)","ltl2tgba -s %f >%O","ok",0,0.0429693,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,200,4062,1
"(1)","spin -f %s >%O","ok",0,0.00305038,2,2,2,1,2,1,1,0,0,0,0,1,0,0,0,201,4083,2
"(1)","lbt < %L >%O","ok",0,0.00404441,3,3,3,0,3,2,1,0,0,0,0,1,0,0,0,222,4510,23
"(!((1) U (F(!(p0)))))","ltl2tgba -s %f >%O","ok",0,0.041792,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,200,2098,1
"(!((1) U (F(!(p0)))))","spin -f %s >%O","ok",0,0.00278539,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,200,2098,1
"(!((1) U (F(!(p0)))))","lbt < %L >%O","ok",0,0.00347608,2,2,2,0,2,1,0,1,0,0,0,0,1,0,0,201,2110,2
"(1) U (F(!(p0)))","ltl2tgba -s %f >%O","ok",0,0.046218,2,3,4,1,2,1,1,0,0,0,0,1,0,0,0,400,8356,2
"(1) U (F(!(p0)))","spin -f %s >%O","ok",0,0.00292604,2,3,5,1,2,1,1,0,0,1,1,1,0,0,1,400,10436,2
"(1) U (F(!(p0)))","lbt < %L >%O","ok",0,0.00420574,7,13,22,2,7,6,1,0,0,4,1,1,0,0,1,1201,35534,604
"(1) U ((G(p0)) | (F(p1)))","ltl2tgba -s %f >%O","ok",0,0.0395735,3,5,11,1,3,1,1,1,0,1,1,0,1,0,1,600,11104,4
"(1) U ((G(p0)) | (F(p1)))","spin -f %s >%O","ok",0,0.00349485,4,8,24,1,4,2,1,1,0,2,1,0,1,0,1,800,24284,4
"(1) U ((G(p0)) | (F(p1)))","lbt < %L >%O","ok",0,0.00316141,9,17,52,2,9,7,1,1,0,4,1,0,1,0,1,1601,40505,805
"(!((1) U ((G(p0)) | (F(p1)))))","ltl2tgba -s %f >%O","ok",0,0.0352196,2,4,4,1,1,0,0,0,1,0,0,0,0,1,0,398,3919,3
"(!((1) U ((G(p0)) | (F(p1)))))","spin -f %s >%O","ok",0,0.00995492,6,18,17,1,4,2,0,1,1,5,1,0,0,1,1,596,8720,4
"(!((1) U ((G(p0)) | (F(p1)))))","lbt < %L >%O","ok",0,0.0035013,3,6,9,1,2,1,0,0,1,3,1,0,0,1,1,399,5837,4
286
287
#+end_example

288
289
290
291
292
This file can be loaded in any spreadsheet or statistical application.

Although we only supplied 2 random generated formulas, the output
contains 4 formulas because =ltlcross= had to translate the positive
and negative version of each.
293

294
295
296
If we had used the option =--json=results.json= instead of (or in
addition to) =--cvs=results.csv=, the file =results.json= would have
contained the following [[http://www.json.org/][JSON]] output.
297
298
299
300
301
302
303

#+BEGIN_SRC sh :results verbatim :exports results
cat results.json
#+END_SRC
#+RESULTS:
#+begin_example
{
304
  "tool": [
305
306
307
    "ltl2tgba -s %f >%O",
    "spin -f %s >%O",
    "lbt < %L >%O"
308
  ],
309
  "formula": [
310
    "(0)",
311
312
313
314
315
    "(1)",
    "(!((1) U (F(!(p0)))))",
    "(1) U (F(!(p0)))",
    "(1) U ((G(p0)) | (F(p1)))",
    "(!((1) U ((G(p0)) | (F(p1)))))"
316
  ],
317
  "fields":  [
318
  "formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","ambiguous_aut","product_states","product_transitions","product_scc"
319
  ],
320
  "inputs":  [ 0, 1 ],
321
  "results": [
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
    [ 0,0,"ok",0,0.0329577,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,1,0,1 ],
    [ 0,1,"ok",0,0.00219235,2,2,1,1,2,1,1,0,0,0,0,1,0,0,1,1,0,1 ],
    [ 0,2,"ok",0,0.0026317,1,0,0,0,1,1,0,0,0,0,0,1,0,0,1,1,0,1 ],
    [ 1,0,"ok",0,0.0429693,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,200,4062,1 ],
    [ 1,1,"ok",0,0.00305038,2,2,2,1,2,1,1,0,0,0,0,1,0,0,0,201,4083,2 ],
    [ 1,2,"ok",0,0.00404441,3,3,3,0,3,2,1,0,0,0,0,1,0,0,0,222,4510,23 ],
    [ 2,0,"ok",0,0.041792,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,200,2098,1 ],
    [ 2,1,"ok",0,0.00278539,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0,200,2098,1 ],
    [ 2,2,"ok",0,0.00347608,2,2,2,0,2,1,0,1,0,0,0,0,1,0,0,201,2110,2 ],
    [ 3,0,"ok",0,0.046218,2,3,4,1,2,1,1,0,0,0,0,1,0,0,0,400,8356,2 ],
    [ 3,1,"ok",0,0.00292604,2,3,5,1,2,1,1,0,0,1,1,1,0,0,1,400,10436,2 ],
    [ 3,2,"ok",0,0.00420574,7,13,22,2,7,6,1,0,0,4,1,1,0,0,1,1201,35534,604 ],
    [ 4,0,"ok",0,0.0395735,3,5,11,1,3,1,1,1,0,1,1,0,1,0,1,600,11104,4 ],
    [ 4,1,"ok",0,0.00349485,4,8,24,1,4,2,1,1,0,2,1,0,1,0,1,800,24284,4 ],
    [ 4,2,"ok",0,0.00316141,9,17,52,2,9,7,1,1,0,4,1,0,1,0,1,1601,40505,805 ],
    [ 5,0,"ok",0,0.0352196,2,4,4,1,1,0,0,0,1,0,0,0,0,1,0,398,3919,3 ],
    [ 5,1,"ok",0,0.00995492,6,18,17,1,4,2,0,1,1,5,1,0,0,1,1,596,8720,4 ],
    [ 5,2,"ok",0,0.0035013,3,6,9,1,2,1,0,0,1,3,1,0,0,1,1,399,5837,4 ]
340
341
342
343
  ]
}
#+end_example

344
345
346
347
348
349
350
Here the =fields= table describes the columns of the =results= table.
The =inputs= tables lists the columns that are considered as inputs
for the experiments.  The values in the columns corresponding to the
fields =formula= and =tool= contains indices relative to the =formula=
and =tool= tables.  This format is more compact when dealing with lots
of translators and formulas, because they don't have to be repeated on
each line as in the CSV version.
351
352

JSON data can be easily processed in any language.  For instance the
353
354
355
356
357
following Python3 script averages each column (except the first four)
for each tool, and presents the results in a form that can almost be
copied into a LaTeX table (the =%= in the tool names have to be taken
care of).  Note that for simplicity we assume that the first two
columns are inputs, instead of reading the =inputs= field.
358
359
360
361
362

#+BEGIN_SRC python :results output :exports both
#!/usr/bin/python3
import json
data = json.load(open('results.json'))
363
datacols = range(4, len(data["fields"]))
364
# Index results by tool
365
results = { t:[] for t in range(0, len(data["tool"])) }
366
367
for l in data["results"]:
  results[l[1]].append(l)
368
# Average columns for each tool, and display them as a table
369
print("%-18s & count & %s \\\\" % ("tool", " & ".join(data["fields"][4:])))
370
for i in range(0, len(data["tool"])):
371
  c = len(results[i])
372
  sums = ["%6.1f" % (sum([x[j] for x in results[i]])/c)
373
          for j in datacols]
374
375
  print("%-18s & %3d & %s \\\\" % (data["tool"][i], c,
        " & ".join(sums)))
376
377
#+END_SRC
#+RESULTS:
378
379
380
381
: tool               & count & time & states & edges & transitions & acc & scc & nonacc_scc & terminal_scc & weak_scc & strong_scc & nondet_states & nondet_aut & terminal_aut & weak_aut & strong_aut & ambiguous_aut & product_states & product_transitions & product_scc \\
: ltl2tgba -s %f >%O &   6 &    0.0 &    1.7 &    2.5 &    3.5 &    1.0 &    1.5 &    0.5 &    0.5 &    0.3 &    0.2 &    0.2 &    0.2 &    0.5 &    0.3 &    0.2 &    0.3 &  299.8 & 4923.2 &    2.0 \\
: spin -f %s >%O     &   6 &    0.0 &    2.8 &    5.7 &    8.3 &    1.0 &    2.5 &    1.2 &    0.7 &    0.5 &    0.2 &    1.3 &    0.5 &    0.5 &    0.3 &    0.2 &    0.7 &  366.3 & 8270.2 &    2.3 \\
: lbt < %L >%O       &   6 &    0.0 &    4.2 &    6.8 &   14.7 &    0.8 &    4.0 &    3.0 &    0.5 &    0.3 &    0.2 &    1.8 &    0.5 &    0.5 &    0.3 &    0.2 &    0.7 &  604.2 & 14749.3 &  239.8 \\
382

Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
383
384
The script =bench/ltl2tgba/sum.py= is a more evolved version of the
above script that generates two kinds of LaTeX tables.
385
386
387
388

When computing such statistics, you should be aware that inputs for
which a tool failed to generate an automaton (e.g. it crashed, or it
was killed if you used =ltlcross='s =--timeout= option to limit run
389
390
391
392
393
394
395
396
time) will appear as mostly empty lines in the CSV or JSON files,
since most statistics cannot be computed without an automaton...
Those lines with missing data can be omitted with the =--omit-missing=
option (this used to be the default up to Spot 1.2).

However data for bogus automata are still included: as shown below
=ltlcross= will report inconsistencies between automata as errors, but
it does not try to guess who is incorrect.
397

398
399
400
401
402
403
404
** Description of the columns

=formula= and =tool= contain the formula translated and the command
run to translate it.  In the CSV, these columns contain the actual
text.  In the JSON output, these column contains an index into the
=formula= and =tool= table declared separately.

405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
=exit_status= and =exit_code= are used to indicate if the translator
successfully produced an automaton, or if it failed.  On successful
translation, =exit_status= is equal to "=ok=" and =exit_code= is 0.
If the translation took more time than allowed with the =--timeout=
option, =exit_status= will contain "=timeout=" and =exit_code= will be
set to -1.  Other values are used to diagnose various issues: please
check the man-page for =ltlcross= for a list of them.

=time= obviously contains the time used by the translation.  Time is
measured with some high-resolution clock when available (that's
nanosecond accuracy under Linux), but because translator commands are
executed through a shell, it also includes the time to start a shell.
(This extra cost apply identically to all translators, so it is not unfair.)


All the values that follow will be missing if =exit_status= is not
421
equal to "=ok=".  (You may instruct =ltlcross= not to output lines with
422
423
such missing data with the option =--omit-missing=.)

424
=states=, =edges=, =transitions=, =acc= are size measures for the
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
automaton that was translated.  =acc= counts the number of acceptance
sets.  When building (degeneralized) Büchi automata, it will always be
=1=, so its value is meaningful only when evaluating translations to
generalized Büchi automata.  =edges= counts the actual number of edges
in the graph supporting the automaton; an edge (labeled by a Boolean
formula) might actually represent several transitions (each labeled by
assignment of all atomic propositions).  For instance in an automaton
where the atomic proposition are $a$ and $b$, one edge labeled by
$a\lor b$ actually represents three transitions $a b$, $a\bar b$, and
$\bar a b$.

The following picture displays two automata for the LTL formula =a U
b=.  They both have 2 states and 3 edges, however they differ in the
number of transitions (7 versus 8), because the initial self-loop is
more constrained in the first automaton.  A smaller number of
transition is therefore an indication of a more constrained automaton.

#+BEGIN_SRC dot :file edges.png :cmdline -Tpng :exports results
digraph G {
  0 [label="", style=invis, height=0]
  0 -> 1
  1 [label="A1"]
  1 -> 2 [label="b\n"]
  1 -> 1 [label="a & !b\n"]
  2 [label="B1", peripheries=2]
  2 -> 2 [label="1"]

  3 [label="", style=invis, height=0]
  3 -> 4
  4 [label="A2"]
  4 -> 5 [label="b\n"]
  4 -> 4 [label="a\n"]
  5 [label="B2", peripheries=2]
  5 -> 5 [label="1"]
}
#+END_SRC

#+RESULTS:
[[file:edges.png]]


=scc= counts the number of strongly-connected components in the automaton.  These SCCs are
also partitioned on four sets based on their strengths:
- =nonacc_scc= for non-accepting SCCs (such as states A1 and A2 in the
  previous picture)
- =terminal_scc= for SCCs that consist of a single state with an
  accepting self-loop labeled by true (such as states B1 and B2
  in the previous picture)
- =weak_scc= for non-terminal SCCs in which all cycles are accepting
- and =strong_scc= for accepting SCCs in which some cycles are not accepting.

These SCC strengths can be used to compute the strength of the
automaton as a whole:
- an automaton is terminal if it contains only non-accepting or
  terminal SCCs,
- an automaton is weak if it it contains only non-accepting,
  terminal, or weak SCCs,
- an automaton is strong if it contains at least one strong SCC.

This classification is used to fill the =terminal_aut=, =weak_aut=,
=strong_aut= columns with Boolean values.  Only one of these should
contain =1=.  We usually prefer terminal automata over weak automata,
and weak automata over strong automata, because the emptiness check
of terminal (and weak) automata is easier.

=nondetstates= counts the number of non-deterministic states in the
automaton.  =nondeterministic= is a Boolean value indicating if the
automaton is not deterministic.  For instance in the previous picture
showing two automata for =a U b=, the first automaton is deterministic
(these two fields will contain 0), while the second automaton contain
a nondeterministic state (state A2 has two possible successors for the
assignment $ab$) and is therefore not deterministic.

498
499
500
=ambiguous_aut= is a Boolean indicating whether the automaton is
ambiguous, i.e., if there exists a word that can be accepted by at
least two different runs.
501

502
503
504
505
=complete_aut= is a Boolean indicating whether the automaton is
complete.

Columns =product_states=, =product_transitions=, and =product_scc=
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
count the number of state, transitions and strongly-connect components
in the product that has been built between the translated automaton
and a random model.  For a given formula, the same random model is of
course used against the automata translated by all tools.  Comparing
the size of these product might give another indication of the
"conciseness" of a translated automaton.

There is of course a certain "luck factor" in the size of the product.
Maybe some translator built a very dumb automaton, with many useless
states, in which just a very tiny part is translated concisely.  By
luck, the random model generated might synchronize with this tiny part
only, and ignore the part with all the useless states.  A way to
lessen this luck factor is to increase the number of products
performed against the translated automaton.  If option =--products=N=
is used, =N= products are builds instead of one, and the fields
=product_states=, =product_transitions=, and =product_scc= contain
average values.

524
525
526
527
528
529
530
531
If the option =--products=+N= is used (with a =+= in front of the
number), then no average value is computed.  Instead, three columns
=product_states=, =product_transitions=, and =product_scc= are output
for each individual product (i.e., $3\times N$ columns are output).
This might be useful if you want to compute different kind of
statistic (e.g., a median instead of a mean) or if you want to build
scatter plots of all these products.

532
533
534
535
Finally, if the =--automata= option was passed to =ltlcross=, the CSV
or JSON output will contain a column named =automaton= encoding each
produced automaton in the HOA format.

536
537
538
539
540
541
** Changing the name of the translators

By default, the names used in the CSV and JSON output to designate the
translators are the command specified on the command line.

For instance in the following, =ltl2tgba= is run in two
542
543
configurations, and the strings =ltl2tgba -s --small %f >%O= and
=ltl2tgba -s --deter %f >%O= appear verbatim in the output:
544
545

#+BEGIN_SRC sh :results verbatim :exports both
546
ltlcross -f a -f Ga 'ltl2tgba -s --small %f >%O' 'ltl2tgba -s --deter %f >%O' --csv
547
548
#+END_SRC
#+RESULTS:
549
550
551
552
553
554
555
556
557
: "formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","product_states","product_transitions","product_scc"
: "(a)","ltl2tgba -s --small %f >%O","ok",0,0.043876,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(a)","ltl2tgba -s --deter %f >%O","ok",0,0.0432137,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(!(a))","ltl2tgba -s --small %f >%O","ok",0,0.0400653,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(!(a))","ltl2tgba -s --deter %f >%O","ok",0,0.0450417,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(G(a))","ltl2tgba -s --small %f >%O","ok",0,0.0429628,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(G(a))","ltl2tgba -s --deter %f >%O","ok",0,0.0478663,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(!(G(a)))","ltl2tgba -s --small %f >%O","ok",0,0.0436822,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
: "(!(G(a)))","ltl2tgba -s --deter %f >%O","ok",0,0.039919,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
558
559
560
561
562
563
564
565
566

To present these results graphically, or even when analyzing these
data, it might be convenient to give each configured tool a shorter
name.  =ltlcross= supports the specification of such short names by
looking whether the command specification for a translator has the
form "={short name}actual command=".

For instance:
#+BEGIN_SRC sh :results verbatim :exports both
567
ltlcross -f a -f Ga '{small} ltl2tgba -s --small %f >%O' '{deter} ltl2tgba -s --deter %f >%O' --csv
568
569
#+END_SRC
#+RESULTS:
570
571
572
573
574
575
576
577
578
: "formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","product_states","product_transitions","product_scc"
: "(a)","small","ok",0,0.0433468,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(a)","deter","ok",0,0.0429179,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(!(a))","small","ok",0,0.0400513,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(!(a))","deter","ok",0,0.040167,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(G(a))","small","ok",0,0.0447826,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(G(a))","deter","ok",0,0.0439892,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(!(G(a)))","small","ok",0,0.0444007,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
: "(!(G(a)))","deter","ok",0,0.0396312,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
579

580
* Detecting problems
581
582
583
   :PROPERTIES:
   :CUSTOM_ID: checks
   :END:
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598

If a translator exits with a non-zero status code, or fails to output
an automaton =ltlcross= can read, and error will be displayed and the
result of the translation will be discarded.

Otherwise =ltlcross= performs the following checks on all translated
formulas ($P_i$ and $N_i$ designate respectively the translation of
positive and negative formulas by the ith translator).

  - Intersection check: $P_i\otimes N_j$ must be empty for all
    pairs of $(i,j)$.

    A single failing translator might generate a lot of lines of
    the form:

599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
    : error: P0*N1 is nonempty; both automata accept the infinite word
    :        cycle{p0 & !p1}
    : error: P1*N0 is nonempty; both automata accept the infinite word
    :        p0; !p1; cycle{p0 & p1}
    : error: P1*N1 is nonempty; both automata accept the infinite word
    :        p0; cycle{!p1 & !p0}
    : error: P1*N2 is nonempty; both automata accept the infinite word
    :        p0; !p1; cycle{p0 & p1}
    : error: P1*N3 is nonempty; both automata accept the infinite word
    :        p0; !p1; cycle{p0 & p1}
    : error: P1*N4 is nonempty; both automata accept the infinite word
    :        p0; cycle{!p1 & !p0}
    : error: P2*N1 is nonempty; both automata accept the infinite word
    :        p0; !p1; !p0; cycle{!p1 & !p0; p0 & !p1; !p1; !p1; p0 & !p1}
    : error: P3*N1 is nonempty; both automata accept the infinite word
    :        p0; !p1; !p1 & !p0; cycle{p0 & !p1}
    : error: P4*N1 is nonempty; both automata accept the infinite word
    :        p0; !p1; !p1 & !p0; cycle{p0 & !p1}
617
618

    In this example, translator number =1= looks clearly faulty
619
620
621
622
623
624
    (at least the other 4 translators do not contradict each other).

    Examples of infinite words that are accepted by both automata
    always have the form of a lasso: a (possibly empty) finite prefix
    followed by a cycle that should be repeated infinitely often.
    The cycle part is denoted by =cycle{...}=.
625

626
  - Complemented intersection check.  If $P_i$ and $P_j$ are
627
    deterministic, =ltlcross= builds their complements, $Comp(P_i)$
628
629
630
631
632
    and $Comp(P_j)$, and then ensures that $Comp(P_i)\otimes
    Comp(P_j)$ is empty.  If only one of them is deterministic,
    for instance $P_i$, we check that $P_j\otimes Comp(P_i)$ for all
    $j \ne i$; likewise if it's $N_i$ that is deterministic.

633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
    By default this check is only done for deterministic automata,
    because complementation is relatively cheap is that case (at least
    it is cheap for simple acceptance conditions).  Using option
    =--determinize=, =ltlcross= can be instructed to perform
    complementation of non-deterministic automata as well, ensuring
    precise equivalence checks between all automata.  However be aware
    that this determinization + complementation may generate large
    automata.

    When validating a translator with =ltlcross= without using the
    =--determinize= option we highly recommend to include a translator
    with good deterministic output to augment test coverage.  Using
    '=ltl2tgba -lD %f >%O=' will produce deterministic automata for
    all obligation properties and many recurrence properties.  Using
    '=ltl2dstar --ltl2nba=spin:pathto/ltl2tgba@-Ds %L %O=' will
    systematically produce a deterministic Rabin automaton (that
    =ltlcross= can complement easily).
650

651
652
653
654
655
656
657
658
  - Cross-comparison checks: for some state-space $S$,
    all $P_i\otimes S$ are either all empty, or all non-empty.
    Similarly all $N_i\otimes S$ are either all empty, or all non-empty.

    A cross-comparison failure could be displayed as:

    : error: {P0,P2,P3,P4,P5,P6,P7,P8,P9} disagree with {P1} when evaluating the state-space

659
660
661
662
663
    If =--products=N= is used with =N= greater than one, the number of
    the state-space is also printed.  This number is of no use by
    itself, except to explain why you may get multiple disagreement
    between the same sets of automata.

664
665
666
667
668
669
670
    These products tests may sometime catch errors that were not
    captured by the first two tests if one non-deterministic automaton
    recognize less words than what it should.  If the input automata
    are deterministic or the =--determinize= option is used, this test
    is redundant and can be disabled.  (In fact, the =--determinize=
    option implies option =--product=0= to do so.)

671
672
673
674
675
676
677
678
679
680
681
  - Consistency check:

    For each $i$, the products $P_i\otimes S$ and $N_i\otimes S$
    actually cover all states of $S$.  Because $S$ does not have any
    deadlock, any of its infinite path must be accepted by $P_i$ or
    $N_i$ (or both).

    An error in that case is displayed as

    : error: inconsistency between P1 and N1

682
683
684
685
    If =--products=N= is used with =N= greater than one, the number of
    the state-space in which the inconsistency was detected is also
    printed.

686
687
688
689
690
691
692
    This test may catch errors that were not captured by the first two
    tests if one non-deterministic automaton recognize less words than
    what it should.  If the input automata are deterministic or the
    =--determinize= option is used, this test is redundant and can be
    disabled.  (In fact, the =--determinize= option implies option
    =--product=0= to do so.)

693
694
695
The above checks are similar to those that are performed by [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]],
except for the complemented intersection check, which is only done in
=ltlcross=.
696
697
698
699
700
701
702
703
704
705

If any problem was reported during the translation of one of the
formulas, =ltlcheck= will exit with an exit status of =1=.  Statistics
(if requested) are output nonetheless, and include any faulty
automaton as well.

* Miscellaneous options

** =--stop-on-error=

706
707
708
The =--stop-on-error= option will cause =ltlcross= to abort on the
first detected error.  This include failure to start some translator,
read its output, or failure to passe the sanity checks.  Timeouts are
709
710
711
712
713
714
715
716
717
718
allowed.

One use for this option is when =ltlcross= is used in combination with
=randltl= to check translators on an infinite stream of formulas.

For instance the following will cross-compare =ltl2tgba= against
=ltl3ba= until it finds an error, or your interrupt the command, or it
runs out of memory (the hash tables used by =randltl= and =ltlcross=
to remove duplicate formulas will keep growing).

719
#+BEGIN_SRC sh :exports code :eval no
720
randltl -n -1 --tree-size 10..25 a b c | ltlcross --stop-on-error 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
721
722
#+END_SRC

723
724
725
726
727
728
729
730
731
732
733
734
735
** =--save-bogus=FILENAME=

The =--save-bogus=FILENAME= will save any formula for which an error
was detected (either some translation failed, or some problem was
detected using the resulting automata) in =FILENAME=.  Again, timeouts
are not considered to be errors, and therefore not reported in this
file.

The main use for this feature is in conjunction with =randltl='s
generation of random formulas.  For instance the following command
will run the translators on an infinite number of formulas, saving
any problematic formula in =bugs.ltl=.

736
#+BEGIN_SRC sh :exports code :eval no
737
randltl -n -1 --tree-size 10..25 a b c | ltlcross --save-bogus=bugs.ltl 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
738
739
740
741
742
#+END_SRC

You can periodically check the contents of =bugs.ltl=, and then run
=ltlcross= only on those formulas to look at the problems:

743
#+BEGIN_SRC sh :exports code :eval no
744
ltlcross -F bugs.ltl 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
745
746
#+END_SRC

747
** =--grind=FILENAME=
748

749
750
751
This option tells =ltlcross= that, when a problem is detected, it
should try to find a smaller formula that still exhibits the
problem.
752

753
754
755
756
757
758
759
Here is the procedure used:
   - internally list the mutations of the bogus formula and sort
     them by length (as [[file:ltlgrind.org][=ltlgrind --sort=]] would do)
   - process every mutation until one is found that exhibit the bug
   - repeat the process with this new formula, and again until a formula
     is found for which no mutation exhibit the bug
   - output that last formula in =FILENAME=
760

761
762
763
764
765
If =--save-bogus=OTHERFILENAME= is provided, every bogus formula found
during the process will be saved in =OTHERFILENAME=.

Example:
#+BEGIN_SRC sh :exports code :results verbatim
766
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %O" \
767
768
769
  --save-bogus=bogus \
  --grind=bogus-grind
#+END_SRC
770
#+BEGIN_SRC sh :exports results :results verbatim
771
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %O" \
772
773
774
  --save-bogus=bogus --grind=bogus-grind 2>&1
true
#+END_SRC
775
#+RESULTS:
776
777
#+begin_example
| & G ! p0 | ! p1 F ! p2 & & p1 G p2 F p0
778
779
Running [P0]: modella 'lcr-i0-1XJw2X' 'lcr-o0-p2nbUW'
Running [N0]: modella 'lcr-i0-lSPMMV' 'lcr-o0-3xEoFU'
780
781
782
783
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
       cycle{!p0 & !p1}

784
785
786
787
Trying to find a bogus mutation of (G!b & (!c | F!a)) | (c & Ga & Fb)...
Mutation 1/22: & & p0 G p1 F p2
Running [P0]: modella 'lcr-i1-3PI0CT' 'lcr-o0-GxBDAS'
Running [N0]: modella 'lcr-i1-eOijzR' 'lcr-o0-wkIZxQ'
788
789
Performing sanity checks and gathering statistics...

790
791
792
Mutation 2/22: & G ! p0 | ! p1 F ! p2
Running [P0]: modella 'lcr-i2-6cYUzP' 'lcr-o0-3ihRBO'
Running [N0]: modella 'lcr-i2-6u8pEN' 'lcr-o0-phxZGM'
793
794
Performing sanity checks and gathering statistics...

795
796
797
Mutation 3/22: | G ! p0 & & p1 G p2 F p0
Running [P0]: modella 'lcr-i3-iwZZML' 'lcr-o0-LMB2SK'
Running [N0]: modella 'lcr-i3-r2g9ZJ' 'lcr-o0-HEfh7I'
798
799
800
801
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
       cycle{!p0 & !p1}

802
803
804
805
Trying to find a bogus mutation of G!b | (c & Ga & Fb)...
Mutation 1/16: t
Running [P0]: modella 'lcr-i4-R8PbkI' 'lcr-o0-6ts7wH'
Running [N0]: modella 'lcr-i4-cv7EKG' 'lcr-o0-vVmdYF'
806
807
Performing sanity checks and gathering statistics...

808
809
810
Mutation 2/16: G ! p0
Running [P0]: modella 'lcr-i5-ZO3HcF' 'lcr-o0-UiydrE'
Running [N0]: modella 'lcr-i5-gOseGD' 'lcr-o0-CL4fVC'
811
812
Performing sanity checks and gathering statistics...

813
Mutation 3/16: & & p0 G p1 F p2
814
815
816
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

817
818
819
Mutation 4/16: | G ! p0 & p1 F p0
Running [P0]: modella 'lcr-i6-QTDjtB' 'lcr-o0-tFpmKA'
Running [N0]: modella 'lcr-i6-1lnX1z' 'lcr-o0-TWWyjz'
820
821
822
823
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
       cycle{!p0 & !p1}

824
825
Trying to find a bogus mutation of G!b | (c & Fb)...
Mutation 1/10: t
826
827
828
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

829
Mutation 2/10: G ! p0
830
831
832
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

833
834
835
Mutation 3/10: & p0 F p1
Running [P0]: modella 'lcr-i7-CJTWjx' 'lcr-o0-DKbNEw'
Running [N0]: modella 'lcr-i7-tSts1v' 'lcr-o0-CGbWov'
836
837
Performing sanity checks and gathering statistics...

838
839
840
Mutation 4/10: | p0 G ! p1
Running [P0]: modella 'lcr-i8-6dtbPu' 'lcr-o0-gLnsfu'
Running [N0]: modella 'lcr-i8-Xn6gGt' 'lcr-o0-U7966s'
841
842
Performing sanity checks and gathering statistics...

843
844
845
Mutation 5/10: | G ! p0 F p0
Running [P0]: modella 'lcr-i9-Vh7hAs' 'lcr-o0-eYZt3r'
Running [N0]: modella 'lcr-i9-I6dfxr' 'lcr-o0-DoY00q'
846
847
Performing sanity checks and gathering statistics...

848
849
850
Mutation 6/10: | ! p0 & p1 F p0
Running [P0]: modella 'lcr-i10-j7fVvq' 'lcr-o0-aChQ0p'
Running [N0]: modella 'lcr-i10-bnpgwp' 'lcr-o0-KV3G1o'
851
852
Performing sanity checks and gathering statistics...

853
854
855
Mutation 7/10: | G p1 & p0 F p1
Running [P0]: modella 'lcr-i11-uUhFyo' 'lcr-o0-OlrF5n'
Running [N0]: modella 'lcr-i11-XHjeDn' 'lcr-o0-0CINan'
856
857
Performing sanity checks and gathering statistics...

858
859
860
Mutation 8/10: | & p0 p1 G ! p0
Running [P0]: modella 'lcr-i12-a7eJLm' 'lcr-o0-RUZFmm'
Running [N0]: modella 'lcr-i12-dobiYl' 'lcr-o0-LuVUzl'
861
862
Performing sanity checks and gathering statistics...

863
864
865
Mutation 9/10: | G ! p0 & p0 F p0
Running [P0]: modella 'lcr-i13-nFQYdl' 'lcr-o0-Mq84Rk'
Running [N0]: modella 'lcr-i13-CnPRwk' 'lcr-o0-7f4Fbk'
866
867
868
869
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
       cycle{!p0}

870
871
Trying to find a bogus mutation of G!c | (c & Fc)...
Mutation 1/7: t
872
873
874
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

875
Mutation 2/7: G ! p0
876
877
878
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

879
880
881
Mutation 3/7: & p0 F p0
Running [P0]: modella 'lcr-i14-KsKPgj' 'lcr-o0-Qo3UXi'
Running [N0]: modella 'lcr-i14-FVPvFi' 'lcr-o0-Zh06mi'
882
883
Performing sanity checks and gathering statistics...

884
885
886
Mutation 4/7: | p0 G ! p0
Running [P0]: modella 'lcr-i15-JB045h' 'lcr-o0-EIL4Oh'
Running [N0]: modella 'lcr-i15-sYY8yh' 'lcr-o0-KVOdjh'
887
888
Performing sanity checks and gathering statistics...

889
Mutation 5/7: | G ! p0 F p0
890
891
892
warning: This formula or its negation has already been checked.
         Use --allow-dups if it should not be ignored.

893
894
895
Mutation 6/7: | ! p0 & p0 F p0
Running [P0]: modella 'lcr-i16-hoqdSg' 'lcr-o0-xghJEg'
Running [N0]: modella 'lcr-i16-5JvOrg' 'lcr-o0-SUdVeg'
896
897
Performing sanity checks and gathering statistics...

898
899
900
Mutation 7/7: | & p0 F p0 G p0
Running [P0]: modella 'lcr-i17-BNo92f' 'lcr-o0-0T8nRf'
Running [N0]: modella 'lcr-i17-J5v5Ff' 'lcr-o0-MOyNuf'
901
902
Performing sanity checks and gathering statistics...

903
Smallest bogus mutation found for (G!b & (!c | F!a)) | (c & Ga & Fb) is G!c | (c & Fc).
904
905
906
907

error: some error was detected during the above runs.
       Check file bogus for problematic formulas.
#+end_example
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924

#+BEGIN_SRC sh :exports both :results verbatim
cat bogus
#+END_SRC

#+RESULTS:
: (G!b & (!c | F!a)) | (c & Ga & Fb)
: G!b | (c & Ga & Fb)
: G!b | (c & Fb)
: G!c | (c & Fc)

#+BEGIN_SRC sh :exports both :results verbatim
cat bogus-grind
#+END_SRC

#+RESULTS:
: G!c | (c & Fc)
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943

** =--no-check=

The =--no-check= option disables all sanity checks, and only use the supplied
formulas in their positive form.

When checks are enabled, the negated formulas are intermixed with the
positives ones in the results.  Therefore the =--no-check= option can
be used to gather statistics about a specific set of formulas.


#  LocalWords:  ltlcross num toc LTL Büchi LBTT Testbench PSL SRC sed
#  LocalWords:  automata LBT LBTT's ltl tgba GFa lck iDGV sA FYp BYY
#  LocalWords:  ClVQg wyErP UNE dQ coM tH eHPoQy goto ba lbt modella
#  LocalWords:  lbtt csv json randltl ltlfilt wm eGEYaZ nYpFBX fGdZQ
#  LocalWords:  CPs kXiZZS ILLzR wU CcMCaQ IOckzW tsT RZ TJXmT jb XRO
#  LocalWords:  nxqfd hS vNItGg acc scc nondetstates nondeterministic
#  LocalWords:  cvs LaTeX datacols len ith otimes ltlcheck eval setq
#  LocalWords:  setenv concat getenv
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
** =--verbose=

The verbose option can be useful to troubleshoot problems or simply
follow the list of transformations and tests performed by =ltlcross=.

For instance here is what happens if we try to cross check =ltl2tgba=
and =ltl3ba= on the formula =FGa=.

#+BEGIN_SRC sh :results verbatim :exports code
ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose
#+END_SRC

#+BEGIN_SRC sh :results verbatim :exports results
ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose 2>&1
#+END_SRC

#+RESULTS:
#+begin_example
F(G(a))
Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-vfVUzt'
Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-IiXGfZ'
Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-T02eWu'
Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-0DpXF0'
Performing sanity checks and gathering statistics...
info: complementing non-deterministic automata via determinization...
info:   P0	(2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets)	Comp(P0)
info:   P1	(2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets)	Comp(P1)
info: getting rid of any Fin acceptance...
info:	Comp(P0)	(2 st.,4 ed.,2 sets) -> (3 st.,7 ed.,2 sets)
info:	Comp(N0)	(1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
info:	Comp(P1)	(2 st.,4 ed.,2 sets) -> (4 st.,9 ed.,2 sets)
info:	Comp(N1)	(2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
info: check_empty P0*N0
info: check_empty Comp(N0)*Comp(P0)
info: check_empty P0*N1
info: check_empty P1*N0
info: check_empty P1*N1
info: check_empty Comp(N1)*Comp(P1)

No problem detected.
#+end_example

First =FGa= and its negations =!FGa= are translated with the two
tools, resulting in four automata: to positive automata =P0= and =P1=
for =FGa=, and two negative automata =N0= and =N1=.

=ltlcross= then proceeds to compute the complement of these four
automata.  Since =P0= and =P1= are nondeterministic and the
=--determinize= option was given, a first pass determinize and
complete these two automata, creating =Comp(P0)= and =Comp(P1)=.

Apparently =N0= and =N1= are already deterministic, so their
complement could be obtained by just complementing their acceptance
condition (this is not written -- we only deduce so because they do
not appear in the list of automata that had to be determinized).

Now that =ltlcross= has four complemented automata, it has to make
sure they use only =Inf= acceptance because that is what our emptiness
check procedure can handle.  So there is a new pass over all automata,
rewriting them to get rid of any =Fin= acceptance.

After this preparatory work, it is time for actually comparing these
automata.  Together, the tests =P0*N0= and =Comp(N0)*Comp(P0)= ensure
that the automaton =N0= is really the complement of =P0=.  Similarly
=P1*N1= and =Comp(N1)*Comp(P1)= ensure that =N1= is the complement of
=P1=.  Finally =P0*N1= and =P1*N0= ensure that =P1= is equivalent to
=P0= and =N1= is equivalent to =N0=.



Note that if we had not used the =--determinize= option, the procedure
would look slightly more complex:

#+BEGIN_SRC sh :results verbatim :exports code
ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose
#+END_SRC

#+BEGIN_SRC sh :results verbatim :exports results
ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose 2>&1
#+END_SRC

#+RESULTS:
#+begin_example
F(G(a))
Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-YvMdzU'
Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-Ixj7RI'
Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-uBbTbx'
Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-eo0fzl'
Performing sanity checks and gathering statistics...
info: getting rid of any Fin acceptance...
info:	Comp(N0)	(1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
info:	Comp(N1)	(2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
info: check_empty P0*N0
info: check_empty P0*N1
info: check_empty Comp(N0)*N1
info: check_empty P1*N0
info: check_empty Comp(N1)*N0
info: check_empty P1*N1
info: building state-space #0/1 of 200 states with seed 0
info: state-space has 4136 edges
info: building product between state-space and P0 (2 st., 3 ed.)
info:   product has 400 st., 8298 ed.
info:               2 SCCs
info: building product between state-space and P1 (2 st., 3 ed.)
info:   product has 400 st., 8298 ed.
info:               2 SCCs
info: building product between state-space and N0 (1 st., 2 ed.)
info:   product has 200 st., 4136 ed.
info:               1 SCCs
info: building product between state-space and N1 (2 st., 4 ed.)
info:   product has 400 st., 8272 ed.
info:               1 SCCs
info: cross_check {P0,P1}, state-space #0/1
info: cross_check {N0,N1}, state-space #0/1
info: consistency_check (P0,N0), state-space #0/1
info: consistency_check (P1,N1), state-space #0/1

No problem detected.
#+end_example

In this case, =ltlcross= does not have any complement automaton for
=P0= and =P1=, so it cannot make sure that =P0= and =P1= are
equivalent.  If we imagine for instance that =P0= has an empty
language, we can see that the six =check_empty= tests would still
succeed.

So =ltlcross= builds a random state-space of 200 states, synchronize
it with the four automata, and then performs additional checks
(=cross_check= and =consistency_check=) on these products as described
[[#checks][earlier]].  While these additional checks do not make a proof that =P0=
and =P1= are equivalent, they can catch some problems, and would
easily catch the case of an automaton with an empty language by
mistake.