ltlcross.org 28.8 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
#+TITLE: =ltlcross=
#+EMAIL spot@lrde.epita.fr
#+OPTIONS: H:2 num:nil toc:t
#+LINK_UP: file:tools.html

=ltlcross= is a tool for cross-comparing the output of LTL-to-Büchi
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
21
    1/100 of a second, reporting most times as "0.00s"),
  - support for deterministic Rabin or Streett automata written in
22
    [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]],
23
24
  - additional intersection checks with the complement of any
    deterministic automaton produced by a translator.
25
26

Although =ltlcross= performs the same sanity checks as LBTT, it does
27
28
29
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
30
31
problems, maybe with a conterexample, but you will be on your own to
investigate and fix them.
32
33
34
35
36

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
37
38
39
    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.
40
  - Build the products of these automata with a random state-space (the same
41
42
    state-space for all translations).  (If the =--products=N= option is given,
    =N= products are performed instead.)
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
  - 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
ltlcross --help | sed -n '/character sequences:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
:   %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
:   %N,%T,%D                   the output automaton as a Never claim, in LBTT's
:                              or in LTL2DSTAR's format
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100

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
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%N' 'spin -f %s >%N'
#+END_SRC
#+RESULTS:

When =ltlcross= executes these commands, =%s= will be replaced
by the formula in Spin's syntax, and =%N= will be replaced by a
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
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%N' 'spin -f %s >%N' 2>&1
#+END_SRC
#+RESULTS:
#+begin_example
([](<>(a)))
Running [P0]: ltl2tgba -s '([](<>(a)))' >'lck-o0-iDGV6y'
Running [P1]: spin -f '([](<>(a)))' >'lck-o1-sA3FYp'
Running [N0]: ltl2tgba -s '(!([](<>(a))))' >'lck-o0-1ClVQg'
Running [N1]: spin -f '(!([](<>(a))))' >'lck-o1-wyErP7'
Performing sanity checks and gathering statistics...

(X((a) U (b)))
Running [P0]: ltl2tgba -s '(X((a) U (b)))' >'lck-o0-ex1BYY'
Running [P1]: spin -f '(X((a) U (b)))' >'lck-o1-UNE8dQ'
Running [N0]: ltl2tgba -s '(!(X((a) U (b))))' >'lck-o0-coM8tH'
Running [N1]: spin -f '(!(X((a) U (b))))' >'lck-o1-eHPoQy'
Performing sanity checks and gathering statistics...

no problem detected
#+end_example

101
=ltlcross= can only read three kinds of output:
102
103
104
  - Never claims (only if they are restricted to representing an
    automaton using =if=, =goto=, and =skip= statements) such as those
    output by [[http://spinroot.com/][=spin=]], [[http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/][=ltl2ba=]], [[http://sourceforge.net/projects/ltl3ba/][=ltl3ba=]], or =ltl2tgba --spin=.  These
105
106
    should be indicated using =%N=.  The newer syntax introduced by
    Spin 6.24, using =do= instead of =if=, is also supported.
107
108
109
110
  - [[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
    --lbtt=.  These should be indicated using =%T=.
111
112
113
114
115
116
117
118
119
120
  - [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dsar='s format]], which support deterministic Rabin or Streett
    automata.  After =ltlcross= reads such input, it immediately
    convert it into a Büchi automaton.  Rabin automata are converted
    to (degeneralized) Büchi automata and the conversion will preserve
    the determinism anytime a deterministic Büchi automaton exists for
    that property (this determinism is good for the complemented
    intersection check discussed below).  Streett automata are
    converted to non-deterministic TGBA, where generalized acceptance
    conditions are used to reduce the size of the automaton you would
    get by the classical conversion from Streett to Büchi.
121
    This kind of output (Rabin or Streett) should be indicated with =%D=.
122
123
124
125
126
127
128

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

  - '=spin -f %s >%N='
  - '=ltl2ba -f %s >%N='
129
130
  - '=ltl3ba -S -f %s >%N='
  - '=ltl3ba -S -M -f %s >%N=' (more deterministic output)
131
132
133
134
135
136
137
138
  - '=modella -r12 -g -e %L %T='
  - '=/path/to/script4lbtt.py %L %T=' (script supplied by [[http://www.ti.informatik.uni-kiel.de/~fritz/][ltl2nba]] for
    its interface with LBTT)
  - '=ltl2tgba -s %s >%N=' (smaller output, Büchi automaton)
  - '=ltl2tgba -s -D %s >%N=' (more deterministic output, Büchi automaton)
  - '=ltl2tgba --lbtt %s >%T=' (smaller output, TGBA)
  - '=ltl2tgba --lbtt -D %s >%T=' (more deterministic output, TGBA)
  - '=lbt <%L >%T='
139
  - '=ltl2dstar --ltl2nba=spin:path/tp/ltl2tgba@-sD %L %D='
140
141
    (deterministic Rabin output)
  - '=ltl2dstar --automata=streett --ltl2nba=spin:path/tp/ltl2tgba@-sD
142
    %L %D=' (deterministic Streett output)
143
144
  - '=ltl2dstar --ltl2nba=spin:path/tp/ltl2tgba@-sD %L - | dstar2tgba
    -s >%N=' (external conversion from Rabin to Büchi done by
145
    =dstar2tgba= for more reduction of the Büchi automaton than
146
147
148
149
    what =ltlcross= would provide)
  - '=java -jar Rabinizer.jar -ltl2dstar %F %D; mv %D.dst %D=' (Rabinizer
    uses the last =%D= argument as a prefix to which it always append =.dst=,
    so we have to rename =%D.dst= as =%D= so that =ltlcross= can find the file)
150
  - '=ltl3dra -f %s >%D='
151
152
153
154
155
156
157

* 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.

158
159
** CSV or JSON output (or both!)

160
161
The following compare =ltl2tgba=, =spin=, and =lbt= on two random
formulas (where =W= and =M= operators have been rewritten away because
162
they are not supported by =spin= and =lbt=).
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182

#+BEGIN_SRC sh :results verbatim :exports code
randltl -n 2 a b |
ltlfilt --remove-wm |
ltlcross --csv=results.csv \
         'ltl2tgba -s %f >%N' \
         'spin -f %s >%N' \
         'lbt < %L >%T'
#+END_SRC
#+RESULTS:

#+BEGIN_SRC sh :results verbatim :exports results
randltl -n 2 a b c | ltlfilt --remove-wm |
ltlcross --csv=results.csv --json=results.json \
         'ltl2tgba -s %f >%N' \
         'spin -f %s >%N' \
         'lbt < %L >%T' --csv=results.csv 2>&1
#+END_SRC
#+RESULTS:
#+begin_example
183
184
185
186
187
188
189
-:1: (G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))
Running [P0]: ltl2tgba -s '(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))' >'lck-o0-HcRzrd'
Running [P1]: spin -f '([]((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) V ((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) || (X(p1)))))' >'lck-o1-Sir9YC'
Running [P2]: lbt < 'lck-i0-W7LdjO' >'lck-o2-ZACV3b'
Running [N0]: ltl2tgba -s '(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))' >'lck-o0-KoveKk'
Running [N1]: spin -f '(!([]((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) V ((((p0) && (<>(p1))) U ((p1) U ((p1) && ((!(p2)) V (p0))))) || (X(p1))))))' >'lck-o1-xxXdfU'
Running [N2]: lbt < 'lck-i0-tcO4oL' >'lck-o2-QQUs0t'
190
191
Performing sanity checks and gathering statistics...

192
193
194
195
196
197
198
-:2: (!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))
Running [P0]: ltl2tgba -s '(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))' >'lck-o0-qlcvic'
Running [P1]: spin -f '(!((!(p1)) || (!(((!([]((p0) || (<>(p1))))) && ((p0) || (X(p1)))) || (([]((p0) || (<>(p1)))) && (!((p0) || (X(p1)))))))))' >'lck-o1-fEBqz3'
Running [P2]: lbt < 'lck-i1-sint9k' >'lck-o2-6oY4RU'
Running [N0]: ltl2tgba -s '((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))' >'lck-o0-6PQGuD'
Running [N1]: spin -f '(!(p1)) || (!(((!([]((p0) || (<>(p1))))) && ((p0) || (X(p1)))) || (([]((p0) || (<>(p1)))) && (!((p0) || (X(p1)))))))' >'lck-o1-1l4NVu'
Running [N2]: lbt < 'lck-i1-iEEnbM' >'lck-o2-a2Toum'
199
200
Performing sanity checks and gathering statistics...

201
No problem detected.
202
203
204
205
206
207
208
209
210
#+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
211
212
213
214
215
216
217
218
219
220
221
222
223
"formula", "tool",  "states", "edges", "transitions", "acc", "scc", "nonacc_scc", "terminal_scc", "weak_scc", "strong_scc", "nondetstates", "nondeterministic", "terminal_aut", "weak_aut", "strong_aut", "time", "product_states", "product_transitions", "product_scc"
"(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "ltl2tgba -s %f >%N", 7, 27, 42, 1, 1, 0, 0, 0, 1, 5, 1, 0, 0, 1, 0.162927, 1333, 20565, 3
"(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "spin -f %s >%N", 55, 957, 1723, 1, 1, 0, 0, 0, 1, 55, 1, 0, 0, 1, 3.83261, 10791, 866615, 37
"(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))", "lbt < %L >%T", 167, 5656, 10744, 3, 2, 1, 0, 0, 1, 167, 1, 0, 0, 1, 0.0365079, 32258, 5318535, 96
"(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "ltl2tgba -s %f >%N", 11, 28, 72, 1, 10, 6, 1, 2, 1, 1, 1, 0, 0, 1, 0.0628941, 2163, 36722, 594
"(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "spin -f %s >%N", 23, 113, 331, 1, 14, 9, 1, 1, 3, 20, 1, 0, 0, 1, 0.101343, 4567, 171114, 1193
"(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))", "lbt < %L >%T", 157, 2414, 5957, 3, 109, 103, 1, 1, 4, 133, 1, 0, 0, 1, 0.0197828, 30811, 3020266, 19147
"(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "ltl2tgba -s %f >%N", 6, 12, 21, 1, 5, 3, 0, 1, 1, 1, 1, 0, 0, 1, 0.0509422, 806, 15638, 9
"(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "spin -f %s >%N", 11, 21, 47, 1, 8, 6, 0, 1, 1, 7, 1, 0, 0, 1, 0.0102468, 1217, 36416, 20
"(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))", "lbt < %L >%T", 17, 45, 100, 2, 13, 11, 0, 1, 1, 14, 1, 0, 0, 1, 0.00346881, 1744, 57783, 347
"((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "ltl2tgba -s %f >%N", 7, 14, 28, 1, 6, 3, 1, 1, 1, 2, 1, 0, 0, 1, 0.0503676, 1006, 19822, 10
"((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "spin -f %s >%N", 17, 43, 102, 1, 13, 10, 1, 1, 1, 12, 1, 0, 0, 1, 0.0474604, 2449, 70190, 256
"((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))", "lbt < %L >%T", 23, 68, 154, 2, 19, 16, 1, 1, 1, 18, 1, 0, 0, 1, 0.0037305, 2236, 73111, 640
224
225
226
227
228
229
#+end_example

This can be loaded in any spreadsheet 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.

230
231
232
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.
233
234
235
236
237
238
239

#+BEGIN_SRC sh :results verbatim :exports results
cat results.json
#+END_SRC
#+RESULTS:
#+begin_example
{
240
  "tool": [
241
242
243
244
    "ltl2tgba -s %f >%N",
    "spin -f %s >%N",
    "lbt < %L >%T"
  ],
245
246
247
248
249
  "formula": [
    "(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1)))))",
    "(!(G((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) R ((((p0) & (F(p1))) U ((p1) U ((p1) & ((!(p2)) R (p0))))) | (X(p1))))))",
    "(!(((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))))",
    "((!(G((p0) | (F(p1))))) <-> ((p0) | (X(p1)))) -> (!(p1))"
250
  ],
251
252
  "fields":  [
  "formula", "tool", "states", "edges", "transitions", "acc", "scc", "nonacc_scc", "terminal_scc", "weak_scc", "strong_scc", "nondetstates", "nondeterministic", "terminal_aut", "weak_aut", "strong_aut", "time", "product_states", "product_transitions", "product_scc"
253
  ],
254
  "inputs":  [ 0, 1 ],
255
  "results": [
256
257
258
259
260
261
262
263
264
265
266
267
    [ 0, 0, 7, 27, 42, 1, 1, 0, 0, 0, 1, 5, 1, 0, 0, 1, 0.162927, 1333, 20565, 3 ],
    [ 0, 1, 55, 957, 1723, 1, 1, 0, 0, 0, 1, 55, 1, 0, 0, 1, 3.83261, 10791, 866615, 37 ],
    [ 0, 2, 167, 5656, 10744, 3, 2, 1, 0, 0, 1, 167, 1, 0, 0, 1, 0.0365079, 32258, 5318535, 96 ],
    [ 1, 0, 11, 28, 72, 1, 10, 6, 1, 2, 1, 1, 1, 0, 0, 1, 0.0628941, 2163, 36722, 594 ],
    [ 1, 1, 23, 113, 331, 1, 14, 9, 1, 1, 3, 20, 1, 0, 0, 1, 0.101343, 4567, 171114, 1193 ],
    [ 1, 2, 157, 2414, 5957, 3, 109, 103, 1, 1, 4, 133, 1, 0, 0, 1, 0.0197828, 30811, 3020266, 19147 ],
    [ 2, 0, 6, 12, 21, 1, 5, 3, 0, 1, 1, 1, 1, 0, 0, 1, 0.0509422, 806, 15638, 9 ],
    [ 2, 1, 11, 21, 47, 1, 8, 6, 0, 1, 1, 7, 1, 0, 0, 1, 0.0102468, 1217, 36416, 20 ],
    [ 2, 2, 17, 45, 100, 2, 13, 11, 0, 1, 1, 14, 1, 0, 0, 1, 0.00346881, 1744, 57783, 347 ],
    [ 3, 0, 7, 14, 28, 1, 6, 3, 1, 1, 1, 2, 1, 0, 0, 1, 0.0503676, 1006, 19822, 10 ],
    [ 3, 1, 17, 43, 102, 1, 13, 10, 1, 1, 1, 12, 1, 0, 0, 1, 0.0474604, 2449, 70190, 256 ],
    [ 3, 2, 23, 68, 154, 2, 19, 16, 1, 1, 1, 18, 1, 0, 0, 1, 0.0037305, 2236, 73111, 640 ]
268
269
270
271
  ]
}
#+end_example

272
273
274
275
276
277
278
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.
279
280

JSON data can be easily processed in any language.  For instance the
281
282
283
284
285
following Python3 script averages each column 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.
286
287
288
289
290
291
292

#+BEGIN_SRC python :results output :exports both
#!/usr/bin/python3
import json
data = json.load(open('results.json'))
datacols = range(2, len(data["fields"]))
# Index results by tool
293
results = { t:[] for t in range(0, len(data["tool"])) }
294
295
for l in data["results"]:
  results[l[1]].append(l)
296
297
298
# Average columns for each tool, and display them as a table
print("%-18s & count & %s \\\\" % ("tool", " & ".join(data["fields"][2:])))
for i in range(0, len(data["tool"])):
299
  c = len(results[i])
300
  sums = ["%6.1f" % (sum([x[j] for x in results[i]])/c)
301
          for j in datacols]
302
303
  print("%-18s & %3d & %s \\\\" % (data["tool"][i], c,
        " & ".join(sums)))
304
305
#+END_SRC
#+RESULTS:
306
307
308
309
: tool               & count & states & edges & transitions & acc & scc & nonacc_scc & terminal_scc & weak_scc & strong_scc & nondetstates & nondeterministic & terminal_aut & weak_aut & strong_aut & time & product_states & product_transitions & product_scc \\
: ltl2tgba -s %f >%N &   4 &    7.0 &   20.0 &   40.0 &    1.0 &    5.0 &    3.0 &    0.0 &    1.0 &    1.0 &    2.0 &    1.0 &    0.0 &    0.0 &    1.0 &    0.1 & 1327.0 & 23186.0 &  154.0 \\
: spin -f %s >%N     &   4 &   26.0 &  283.0 &  550.0 &    1.0 &    9.0 &    6.0 &    0.0 &    0.0 &    1.0 &   23.0 &    1.0 &    0.0 &    0.0 &    1.0 &    1.0 & 4756.0 & 286083.0 &  376.0 \\
: lbt < %L >%T       &   4 &   91.0 & 2045.0 & 4238.0 &    2.0 &   35.0 &   32.0 &    0.0 &    0.0 &    1.0 &   83.0 &    1.0 &    0.0 &    0.0 &    1.0 &    0.0 & 16762.0 & 2117423.0 & 5057.0 \\
310

Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
311
312
The script =bench/ltl2tgba/sum.py= is a more evolved version of the
above script that generates two kinds of LaTeX tables.
313
314
315
316
317
318
319
320
321

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
time) are not represented in the CSV or JSON files.  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.

322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
** 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.

=states=, =edged=, =transitions=, =acc= are size measures for the
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.

=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.)

Finally, =product_states=, =product_transitions=, and =product_scc=
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.

428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
* Detecting problems

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:

444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
    : 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}
462
463

    In this example, translator number =1= looks clearly faulty
464
465
466
467
468
469
    (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{...}=.
470

471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
  - Complemented intersection check.  If $P_i$ and $P_j$ are
    deterministic, we =ltlcross= builds their complements, $Comp(P_i)$
    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.

    This check is only done for deterministic automata, because
    complementation is cheap is that case.  When validating a
    translator with =ltlcross=, we highly recommend to include a
    translator with good deterministic output to augment test
    coverage.  Using '=ltl2tgba -lD %f >%T=' will produce
    deterministic automata for all obligation properties and many
    recurrence properties.  Using '=ltl2dstar
    --ltl2nba=spin:pathto/ltl2tgba@-sD %L %D=' is more expansive, but
    it will produce a deterministic Büchi automaton whenever one
    exists.

489
490
491
492
493
494
495
496
  - 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

497
498
499
500
501
    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.

502
503
504
505
506
507
508
509
510
511
512
  - 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

513
514
515
516
    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.

517
518
519
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=.
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563

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=

The =--stop-on-error= 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
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).

#+BEGIN_SRC sh :export code :eval no
randltl -n -1 --tree-size 10..25 a b c | ltlcross --stop-on-error 'ltl2tgba --lbtt %f >%T' 'ltl3ba -f %s >%N'
#+END_SRC

** =--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