ltlcross.org 34 KB
 Alexandre Duret-Lutz committed Apr 09, 2013 1 2 3 #+TITLE: =ltlcross= #+EMAIL spot@lrde.epita.fr #+OPTIONS: H:2 num:nil toc:t  Alexandre Duret-Lutz committed Feb 06, 2014 4 #+LINK_UP: tools.html  Alexandre Duret-Lutz committed Apr 09, 2013 5 6 7 8 9 10  =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.  Alexandre Duret-Lutz committed Aug 26, 2013 11 The main differences are:  Alexandre Duret-Lutz committed Apr 09, 2013 12  - support for PSL formulas in addition to LTL  Alexandre Duret-Lutz committed Apr 27, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 18  - statistics output in a format that can be more easily be post-processed,  Alexandre Duret-Lutz committed Apr 09, 2013 19  - more precise time measurement (LBTT was only precise to  Alexandre Duret-Lutz committed Aug 26, 2013 20 21  1/100 of a second, reporting most times as "0.00s"), - support for deterministic Rabin or Streett automata written in  Alexandre Duret-Lutz committed Nov 11, 2013 22  [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]],  Alexandre Duret-Lutz committed Aug 26, 2013 23 24  - additional intersection checks with the complement of any deterministic automaton produced by a translator.  Alexandre Duret-Lutz committed Apr 09, 2013 25 26  Although =ltlcross= performs the same sanity checks as LBTT, it does  Alexandre Duret-Lutz committed Apr 27, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 30 31 problems, maybe with a conterexample, but you will be on your own to investigate and fix them.  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 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.  Alexandre Duret-Lutz committed Apr 09, 2013 40  - Build the products of these automata with a random state-space (the same  Alexandre Duret-Lutz committed May 13, 2013 41 42  state-space for all translations). (If the =--products=N= option is given, =N= products are performed instead.)  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 63 64 : %N,%T,%D the output automaton as a Never claim, in LBTT's : or in LTL2DSTAR's format  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 101 =ltlcross= can only read three kinds of output:  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Aug 26, 2013 105 106  should be indicated using =%N=. The newer syntax introduced by Spin 6.24, using =do= instead of =if=, is also supported.  Alexandre Duret-Lutz committed Apr 09, 2013 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=.  Alexandre Duret-Lutz committed Aug 26, 2013 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.  Alexandre Duret-Lutz committed Nov 22, 2013 121  This kind of output (Rabin or Streett) should be indicated with =%D=.  Alexandre Duret-Lutz committed Aug 26, 2013 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='  Alexandre Duret-Lutz committed Nov 11, 2013 129 130  - '=ltl3ba -S -f %s >%N=' - '=ltl3ba -S -M -f %s >%N=' (more deterministic output)  Alexandre Duret-Lutz committed Aug 26, 2013 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='  Alexandre Duret-Lutz committed Aug 31, 2014 139  - '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %L %D='  Alexandre Duret-Lutz committed Aug 26, 2013 140  (deterministic Rabin output)  Alexandre Duret-Lutz committed Aug 31, 2014 141  - '=ltl2dstar --automata=streett --ltl2nba=spin:path/to/ltl2tgba@-sD  Alexandre Duret-Lutz committed Nov 22, 2013 142  %L %D=' (deterministic Streett output)  Alexandre Duret-Lutz committed Aug 31, 2014 143  - '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %L - | dstar2tgba  Alexandre Duret-Lutz committed Aug 26, 2013 144  -s >%N=' (external conversion from Rabin to Büchi done by  Alexandre Duret-Lutz committed Nov 22, 2013 145  =dstar2tgba= for more reduction of the Büchi automaton than  Alexandre Duret-Lutz committed Aug 26, 2013 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)  Alexandre Duret-Lutz committed Nov 22, 2013 150  - '=ltl3dra -f %s >%D='  Alexandre Duret-Lutz committed Apr 09, 2013 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.  Alexandre Duret-Lutz committed May 13, 2013 158 159 ** CSV or JSON output (or both!)  Alexandre Duret-Lutz committed Nov 11, 2013 160 161 The following compare =ltl2tgba=, =spin=, and =lbt= on two random formulas (where =W= and =M= operators have been rewritten away because  Alexandre Duret-Lutz committed Apr 27, 2013 162 they are not supported by =spin= and =lbt=).  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Nov 22, 2013 183 184 185 186 187 188 189 -:1: (G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))) Running [P0]: ltl2tgba -s '(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))' >'lcr-o0-I7yemj' Running [P1]: spin -f '([](((p0) U ((p0) && ([](p1)))) V (([](p1)) || ((p0) U ((p0) && ([](p1)))))))' >'lcr-o1-VFo8q2' Running [P2]: lbt < 'lcr-i0-SYp5lA' >'lcr-o2-GIQcxL' Running [N0]: ltl2tgba -s '(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))' >'lcr-o0-jppaKd' Running [N1]: spin -f '(!([](((p0) U ((p0) && ([](p1)))) V (([](p1)) || ((p0) U ((p0) && ([](p1))))))))' >'lcr-o1-7v46UW' Running [N2]: lbt < 'lcr-i0-8AoGDu' >'lcr-o2-PzOH6F'  Alexandre Duret-Lutz committed Apr 09, 2013 190 191 Performing sanity checks and gathering statistics...  Alexandre Duret-Lutz committed Nov 22, 2013 192 193 194 195 196 197 198 -:2: (!((G(F(p0))) -> (F(p1)))) Running [P0]: ltl2tgba -s '(!((G(F(p0))) -> (F(p1))))' >'lcr-o0-J9i0Ac' Running [P1]: spin -f '(!((<>(p1)) || (!([](<>(p0))))))' >'lcr-o1-N2NUTX' Running [P2]: lbt < 'lcr-i1-T8OQlr' >'lcr-o2-xaj9cJ' Running [N0]: ltl2tgba -s '(G(F(p0))) -> (F(p1))' >'lcr-o0-YfWgQf' Running [N1]: spin -f '(<>(p1)) || (!([](<>(p0))))' >'lcr-o1-cpcHd1' Running [N2]: lbt < 'lcr-i1-vqYHwu' >'lcr-o2-WCqqBM'  Alexandre Duret-Lutz committed Apr 09, 2013 199 200 Performing sanity checks and gathering statistics...  Alexandre Duret-Lutz committed Apr 27, 2013 201 No problem detected.  Alexandre Duret-Lutz committed Apr 09, 2013 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  Alexandre Duret-Lutz committed Nov 22, 2013 211 212 213 214 215 216 217 218 219 220 221 222 223 "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" "(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))","ltl2tgba -s %f >%N","ok",0,0.0315577,3,5,9,1,3,2,0,1,0,2,1,0,1,0,401,5168,3 "(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))","spin -f %s >%N","ok",0,0.00750061,6,13,18,1,3,2,0,0,1,6,1,0,0,1,999,14414,5 "(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))","lbt < %L >%T","ok",0,0.0022915,8,41,51,1,3,2,0,0,1,8,1,0,0,1,1397,43175,5 "(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))","ltl2tgba -s %f >%N","ok",0,0.0296025,4,10,16,1,3,1,1,0,1,0,0,0,0,1,797,16411,3 "(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))","spin -f %s >%N","ok",0,0.00388934,7,24,63,1,4,2,1,0,1,6,1,0,0,1,1400,64822,4 "(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))","lbt < %L >%T","ok",0,0.00268385,39,286,614,3,28,26,1,0,1,33,1,0,0,1,7583,600472,4394 "(!((G(F(p0))) -> (F(p1))))","ltl2tgba -s %f >%N","ok",0,0.0248804,2,4,4,1,1,0,0,0,1,0,0,0,0,1,399,4130,1 "(!((G(F(p0))) -> (F(p1))))","spin -f %s >%N","ok",0,0.0019908,2,3,5,1,1,0,0,0,1,1,1,0,0,1,399,5174,1 "(!((G(F(p0))) -> (F(p1))))","lbt < %L >%T","ok",0,0.00197792,5,10,15,1,4,3,0,0,1,5,1,0,0,1,407,6333,9 "(G(F(p0))) -> (F(p1))","ltl2tgba -s %f >%N","ok",0,0.0256492,3,5,11,1,3,1,1,1,0,1,1,0,1,0,600,11305,3 "(G(F(p0))) -> (F(p1))","spin -f %s >%N","ok",0,0.00185036,3,5,14,1,3,1,1,1,0,1,1,0,1,0,600,14397,3 "(G(F(p0))) -> (F(p1))","lbt < %L >%T","ok",0,0.00209399,11,18,54,2,11,9,1,1,0,5,1,0,1,0,1245,25838,449  Alexandre Duret-Lutz committed Apr 09, 2013 224 225 #+end_example  Alexandre Duret-Lutz committed Nov 22, 2013 226 227 228 229 230 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.  Alexandre Duret-Lutz committed Apr 09, 2013 231   Alexandre Duret-Lutz committed May 13, 2013 232 233 234 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.  Alexandre Duret-Lutz committed Apr 09, 2013 235 236 237 238 239 240 241  #+BEGIN_SRC sh :results verbatim :exports results cat results.json #+END_SRC #+RESULTS: #+begin_example {  Alexandre Duret-Lutz committed Apr 27, 2013 242  "tool": [  Alexandre Duret-Lutz committed Apr 09, 2013 243 244 245 246  "ltl2tgba -s %f >%N", "spin -f %s >%N", "lbt < %L >%T" ],  Alexandre Duret-Lutz committed Apr 27, 2013 247  "formula": [  Alexandre Duret-Lutz committed Nov 22, 2013 248 249 250 251  "(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))", "(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))", "(!((G(F(p0))) -> (F(p1))))", "(G(F(p0))) -> (F(p1))"  Alexandre Duret-Lutz committed Apr 09, 2013 252  ],  Alexandre Duret-Lutz committed Apr 27, 2013 253  "fields": [  Alexandre Duret-Lutz committed Nov 22, 2013 254  "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"  Alexandre Duret-Lutz committed Apr 09, 2013 255  ],  Alexandre Duret-Lutz committed Apr 27, 2013 256  "inputs": [ 0, 1 ],  Alexandre Duret-Lutz committed Apr 09, 2013 257  "results": [  Alexandre Duret-Lutz committed Nov 22, 2013 258 259 260 261 262 263 264 265 266 267 268 269  [ 0,0,"ok",0,0.0315577,3,5,9,1,3,2,0,1,0,2,1,0,1,0,401,5168,3 ], [ 0,1,"ok",0,0.00750061,6,13,18,1,3,2,0,0,1,6,1,0,0,1,999,14414,5 ], [ 0,2,"ok",0,0.0022915,8,41,51,1,3,2,0,0,1,8,1,0,0,1,1397,43175,5 ], [ 1,0,"ok",0,0.0296025,4,10,16,1,3,1,1,0,1,0,0,0,0,1,797,16411,3 ], [ 1,1,"ok",0,0.00388934,7,24,63,1,4,2,1,0,1,6,1,0,0,1,1400,64822,4 ], [ 1,2,"ok",0,0.00268385,39,286,614,3,28,26,1,0,1,33,1,0,0,1,7583,600472,4394 ], [ 2,0,"ok",0,0.0248804,2,4,4,1,1,0,0,0,1,0,0,0,0,1,399,4130,1 ], [ 2,1,"ok",0,0.0019908,2,3,5,1,1,0,0,0,1,1,1,0,0,1,399,5174,1 ], [ 2,2,"ok",0,0.00197792,5,10,15,1,4,3,0,0,1,5,1,0,0,1,407,6333,9 ], [ 3,0,"ok",0,0.0256492,3,5,11,1,3,1,1,1,0,1,1,0,1,0,600,11305,3 ], [ 3,1,"ok",0,0.00185036,3,5,14,1,3,1,1,1,0,1,1,0,1,0,600,14397,3 ], [ 3,2,"ok",0,0.00209399,11,18,54,2,11,9,1,1,0,5,1,0,1,0,1245,25838,449 ]  Alexandre Duret-Lutz committed Apr 09, 2013 270 271 272 273  ] } #+end_example  Alexandre Duret-Lutz committed Apr 27, 2013 274 275 276 277 278 279 280 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.  Alexandre Duret-Lutz committed Apr 09, 2013 281 282  JSON data can be easily processed in any language. For instance the  Alexandre Duret-Lutz committed Nov 22, 2013 283 284 285 286 287 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.  Alexandre Duret-Lutz committed Apr 09, 2013 288 289 290 291 292  #+BEGIN_SRC python :results output :exports both #!/usr/bin/python3 import json data = json.load(open('results.json'))  Alexandre Duret-Lutz committed Nov 22, 2013 293 datacols = range(4, len(data["fields"]))  Alexandre Duret-Lutz committed Apr 09, 2013 294 # Index results by tool  Alexandre Duret-Lutz committed Apr 27, 2013 295 results = { t:[] for t in range(0, len(data["tool"])) }  Alexandre Duret-Lutz committed Apr 09, 2013 296 297 for l in data["results"]: results[l[1]].append(l)  Alexandre Duret-Lutz committed Apr 27, 2013 298 # Average columns for each tool, and display them as a table  Alexandre Duret-Lutz committed Nov 22, 2013 299 print("%-18s & count & %s \\\\" % ("tool", " & ".join(data["fields"][4:])))  Alexandre Duret-Lutz committed Apr 27, 2013 300 for i in range(0, len(data["tool"])):  Alexandre Duret-Lutz committed Apr 09, 2013 301  c = len(results[i])  Alexandre Duret-Lutz committed Apr 27, 2013 302  sums = ["%6.1f" % (sum([x[j] for x in results[i]])/c)  Alexandre Duret-Lutz committed Apr 09, 2013 303  for j in datacols]  Alexandre Duret-Lutz committed Apr 27, 2013 304 305  print("%-18s & %3d & %s \\\\" % (data["tool"][i], c, " & ".join(sums)))  Alexandre Duret-Lutz committed Apr 09, 2013 306 307 #+END_SRC #+RESULTS:  Alexandre Duret-Lutz committed Nov 22, 2013 308 309 310 311 : 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 & product_states & product_transitions & product_scc \\ : ltl2tgba -s %f >%N & 4 & 0.0 & 3.0 & 6.0 & 10.0 & 1.0 & 2.5 & 1.0 & 0.5 & 0.5 & 0.5 & 0.8 & 0.5 & 0.0 & 0.5 & 0.5 & 549.2 & 9253.5 & 2.5 \\ : spin -f %s >%N & 4 & 0.0 & 4.5 & 11.2 & 25.0 & 1.0 & 2.8 & 1.2 & 0.5 & 0.2 & 0.8 & 3.5 & 1.0 & 0.0 & 0.2 & 0.8 & 849.5 & 24701.8 & 3.2 \\ : lbt < %L >%T & 4 & 0.0 & 15.8 & 88.8 & 183.5 & 1.8 & 11.5 & 10.0 & 0.5 & 0.2 & 0.8 & 12.8 & 1.0 & 0.0 & 0.2 & 0.8 & 2658.0 & 168954.5 & 1214.2 \\  Alexandre Duret-Lutz committed Apr 09, 2013 312   Alexandre Duret-Lutz committed Apr 09, 2013 313 314 The script =bench/ltl2tgba/sum.py= is a more evolved version of the above script that generates two kinds of LaTeX tables.  Alexandre Duret-Lutz committed Apr 09, 2013 315 316 317 318  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  Alexandre Duret-Lutz committed Nov 22, 2013 319 320 321 322 323 324 325 326 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.  Alexandre Duret-Lutz committed Apr 09, 2013 327   Alexandre Duret-Lutz committed May 13, 2013 328 329 330 331 332 333 334 ** 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.  Alexandre Duret-Lutz committed Nov 22, 2013 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 =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  Alexandre Duret-Lutz committed Nov 22, 2013 351 equal to "=ok=". (You may instruct =ltlcross= not to output lines with  Alexandre Duret-Lutz committed Nov 22, 2013 352 353 such missing data with the option =--omit-missing=.)  Alexandre Duret-Lutz committed Nov 22, 2013 354 355 356 357 358 359 360 361 362 363 364 365 366 The columns =in_type=, =in_states=, =in_edges=, =in_transitions=, =in_acc=, and =in_scc= are only output if one of the translator produces Rabin or Streett automata (i.e., if =%D= is used to specify one output filename for any translator). In that case these columns give the type (DRA or DSA) of the produced automaton, as well as its size (states, edges, transitions, number of acceptance pairs, and number of SCCs). This input automaton is then converted by =ltlcross= into a TGBA before being checked the result of other translators, and all the following columns are measures of that converted automaton. (Aside from parsing them and converting them to TGBA, Spot has no support for Rabin automata and Streett automata.) =states=, =edges=, =transitions=, =acc= are size measures for the  Alexandre Duret-Lutz committed May 13, 2013 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 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. 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.  Alexandre Duret-Lutz committed Nov 22, 2013 459 460 461 462 463 464 465 466 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.  Alexandre Duret-Lutz committed Nov 22, 2013 467 468 469 470 471 472 473 474 475 476 477 478 479 ** 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 configurations, and the strings =ltl2tgba -s --small %f >%N= and =ltl2tgba -s --deter %f >%N= appear verbatim in the output: #+BEGIN_SRC sh :results verbatim :exports both ltlcross -f a -f Ga 'ltl2tgba -s --small %f >%N' 'ltl2tgba -s --deter %f >%N' --csv #+END_SRC #+RESULTS:  Alexandre Duret-Lutz committed Nov 22, 2013 480 481 482 483 484 485 486 487 488 : "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 >%N","ok",0,0.0274533,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4092,2 : "(a)","ltl2tgba -s --deter %f >%N","ok",0,0.0274613,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4092,2 : "(!(a))","ltl2tgba -s --small %f >%N","ok",0,0.0271082,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4098,2 : "(!(a))","ltl2tgba -s --deter %f >%N","ok",0,0.0263196,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4098,2 : "(G(a))","ltl2tgba -s --small %f >%N","ok",0,0.0232094,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2023,1 : "(G(a))","ltl2tgba -s --deter %f >%N","ok",0,0.0253393,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2023,1 : "(!(G(a)))","ltl2tgba -s --small %f >%N","ok",0,0.023919,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8166,2 : "(!(G(a)))","ltl2tgba -s --deter %f >%N","ok",0,0.0235093,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8166,2  Alexandre Duret-Lutz committed Nov 22, 2013 489 490 491 492 493 494 495 496 497 498 499 500  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 ltlcross -f a -f Ga '{small} ltl2tgba -s --small %f >%N' '{deter} ltl2tgba -s --deter %f >%N' --csv #+END_SRC #+RESULTS:  Alexandre Duret-Lutz committed Nov 22, 2013 501 502 503 504 505 506 507 508 509 : "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",0,0.0310046,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4092,2 : "(a)","deter","ok",0,0.0292434,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4092,2 : "(!(a))","small","ok",0,0.027431,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4098,2 : "(!(a))","deter","ok",0,0.0259028,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4098,2 : "(G(a))","small","ok",0,0.0245275,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2023,1 : "(G(a))","deter","ok",0,0.0245139,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2023,1 : "(!(G(a)))","small","ok",0,0.0241781,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8166,2 : "(!(G(a)))","deter","ok",0,0.0235059,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8166,2  Alexandre Duret-Lutz committed Nov 22, 2013 510   Alexandre Duret-Lutz committed Apr 09, 2013 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 * 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:  Alexandre Duret-Lutz committed Jul 29, 2013 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544  : 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}  Alexandre Duret-Lutz committed Apr 09, 2013 545 546  In this example, translator number =1= looks clearly faulty  Alexandre Duret-Lutz committed Jul 29, 2013 547 548 549 550 551 552  (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{...}=.  Alexandre Duret-Lutz committed Apr 09, 2013 553   Alexandre Duret-Lutz committed Aug 26, 2013 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571  - 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.  Alexandre Duret-Lutz committed Apr 09, 2013 572 573 574 575 576 577 578 579  - 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  Alexandre Duret-Lutz committed May 13, 2013 580 581 582 583 584  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.  Alexandre Duret-Lutz committed Apr 09, 2013 585 586 587 588 589 590 591 592 593 594 595  - 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  Alexandre Duret-Lutz committed May 13, 2013 596 597 598 599  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.  Alexandre Duret-Lutz committed Aug 26, 2013 600 601 602 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=.  Alexandre Duret-Lutz committed Apr 09, 2013 603 604 605 606 607 608 609 610 611 612  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=  Alexandre Duret-Lutz committed Aug 21, 2014 613 614 615 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  Alexandre Duret-Lutz committed Apr 09, 2013 616 617 618 619 620 621 622 623 624 625 626 627 628 629 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  Alexandre Duret-Lutz committed Aug 21, 2014 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 ** =--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=. #+BEGIN_SRC sh :export code :eval no randltl -n -1 --tree-size 10..25 a b c | ltlcross --save-bogus=bugs.ltl 'ltl2tgba --lbtt %f >%T' 'ltl3ba -f %s >%N' #+END_SRC You can periodically check the contents of =bugs.ltl=, and then run =ltlcross= only on those formulas to look at the problems: #+BEGIN_SRC sh :export code :eval no ltlcross -F bugs.ltl 'ltl2tgba --lbtt %f >%T' 'ltl3ba -f %s >%N' #+END_SRC  Alexandre Duret-Lutz committed Apr 09, 2013 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 ** =--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  Thibaud Michaud committed Oct 06, 2014 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 ** =--grind=FILENAME= This argument tells =ltlcross= that, when an error is detected, it should try to find a smaller formula that still exhibit the bug. This is the procedure used: - Internally list the mutations of the bogus formula and sort them by length (as =ltlgrind --sort= would do) - Process every mutation until one is found that exhibit the bug - Repeat the process with this formula, and again until a formula is found for which no mutation exhibit the bug - Output that last formula in FILENAME Every bogus formula found during the process will be saved if =--save-bogus=FILENAME= is provided. Example: #+BEGIN_SRC sh :exports both :results verbatim ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %T" \ --save-bogus=bogus \ --grind=bogus-grind #+END_SRC #+RESULTS: #+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)