#+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.

The main motivations for rewriting this tool were:
  - support for PSL formulas in addition to LTL
  - more statistics (like counting the number of logical transitions
    represented by each physical edge), output in a format that
    can be more easily be post-processed,
  - more precise time measurement (LBTT was only precise to
    1/100 of a second, reporting most times as "0.00s").

Although =ltlcross= performs the same sanity checks as LBTT, it does
not implement any of the interactive features of LBTT.  Essentially
=ltlcross= will report problems, but you will be on your own to
investigate and fix them.

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
    will be denoted =P0=, =N0=, =P1=, =N1=, =P2=, =N2=.
  - Build the products of these automata with a random state-space (the same
    state-space for all translations).
  - Perform sanity checks between all these automata to detect any problem.
  - 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
:   %N,%T                      the output automaton as a Never claim, or in
:                              LBTT's format

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

=ltlcross= can only read two kinds of output:
  - 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
    should be indicated using =%N=.
  - [[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=.

Of course all configured tools need not the same =%= sequences.

* 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.

The following compare =ltl2tgba=, =spin=, and =lbt= on three random
formula (where =W= and =M= operators have been removed because they
are not supported by =spin= and =lbt=).

#+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
-: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)))))))' >'lck-o0-eGEYaZ'
Running [P1]: spin -f '([](((p0) U ((p0) && ([](p1)))) V (([](p1)) || ((p0) U ((p0) && ([](p1)))))))' >'lck-o1-nYpFBX'
Running [P2]: lbt < 'lck-i0-fGdZQ0' >'lck-o2-CPs23V'
Running [N0]: ltl2tgba -s '(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))' >'lck-o0-kXiZZS'
Running [N1]: spin -f '(!([](((p0) U ((p0) && ([](p1)))) V (([](p1)) || ((p0) U ((p0) && ([](p1))))))))' >'lck-o1-7ILLzR'
Running [N2]: lbt < 'lck-i0-9KG0wU' >'lck-o2-CcMCaQ'
Performing sanity checks and gathering statistics...

-:2: (!((G(F(p0))) -> (F(p1))))
Running [P0]: ltl2tgba -s '(!((G(F(p0))) -> (F(p1))))' >'lck-o0-IOckzW'
Running [P1]: spin -f '(!((<>(p1)) || (!([](<>(p0))))))' >'lck-o1-tsT3RZ'
Running [P2]: lbt < 'lck-i1-5TJXmT' >'lck-o2-5E9jb3'
Running [N0]: ltl2tgba -s '(G(F(p0))) -> (F(p1))' >'lck-o0-M3XRO9'
Running [N1]: spin -f '(<>(p1)) || (!([](<>(p0))))' >'lck-o1-6nxqfd'
Running [N2]: lbt < 'lck-i1-4hS5u6' >'lck-o2-vNItGg'
Performing sanity checks and gathering statistics...

no problem detected
#+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
"formula", "tool",  "states", "edges", "transitions", "acc", "scc", "nondetstates", "nondeterministic", "time", "product_states", "product_transitions", "product_scc"
"(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))", "ltl2tgba -s %f >%N", 3, 5, 9, 1, 3, 2, 1, 0.0453898, 401, 5136, 3
"(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))", "spin -f %s >%N", 6, 13, 18, 1, 3, 6, 1, 0.0108596, 995, 14384, 5
"(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1)))))))", "lbt < %L >%T", 8, 41, 51, 1, 3, 8, 1, 0.00343479, 1389, 42998, 5
"(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))", "ltl2tgba -s %f >%N", 4, 10, 16, 1, 3, 0, 0, 0.0437875, 797, 16340, 3
"(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))", "spin -f %s >%N", 7, 24, 63, 1, 4, 6, 1, 0.0061535, 1400, 64668, 4
"(!(G(((p0) U ((p0) & (G(p1)))) R ((G(p1)) | ((p0) U ((p0) & (G(p1))))))))", "lbt < %L >%T", 39, 286, 614, 3, 28, 33, 1, 0.00384434, 7592, 602204, 4400
"(!((G(F(p0))) -> (F(p1))))", "ltl2tgba -s %f >%N", 2, 4, 4, 1, 1, 0, 0, 0.0416853, 398, 4198, 1
"(!((G(F(p0))) -> (F(p1))))", "spin -f %s >%N", 2, 3, 5, 1, 1, 1, 1, 0.00325558, 398, 5227, 1
"(!((G(F(p0))) -> (F(p1))))", "lbt < %L >%T", 5, 10, 15, 1, 4, 5, 1, 0.00299424, 409, 6401, 12
"(G(F(p0))) -> (F(p1))", "ltl2tgba -s %f >%N", 3, 5, 11, 1, 3, 1, 1, 0.0422192, 600, 11663, 3
"(G(F(p0))) -> (F(p1))", "spin -f %s >%N", 3, 5, 14, 1, 3, 1, 1, 0.00293655, 600, 14840, 3
"(G(F(p0))) -> (F(p1))", "lbt < %L >%T", 11, 18, 54, 2, 11, 5, 1, 0.0030133, 1253, 26891, 457
#+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.

If we had used the option =--json=results.json= instead of
=--cvs=results.csv=, the file =results.json= would have contained the
following [[http://www.json.org/][JSON]] output.

#+BEGIN_SRC sh :results verbatim :exports results
cat results.json
#+END_SRC
#+RESULTS:
#+begin_example
{
  "tools": [
    "ltl2tgba -s %f >%N",
    "spin -f %s >%N",
    "lbt < %L >%T"
  ],
  "inputs": [
    "(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))"
  ],
  "fields": [
    "input", "tool", "states", "edges", "transitions", "acc", "scc", "nondetstates", "nondeterministic", "time", "product_states", "product_transitions", "product_scc"
  ],
  "results": [
    [ 0, 0, 3, 5, 9, 1, 3, 2, 1, 0.0431589, 401, 5136, 3 ],
    [ 0, 1, 6, 13, 18, 1, 3, 6, 1, 0.0104812, 995, 14384, 5 ],
    [ 0, 2, 8, 41, 51, 1, 3, 8, 1, 0.00321619, 1389, 42998, 5 ],
    [ 1, 0, 4, 10, 16, 1, 3, 0, 0, 0.0443761, 797, 16340, 3 ],
    [ 1, 1, 7, 24, 63, 1, 4, 6, 1, 0.00623927, 1400, 64668, 4 ],
    [ 1, 2, 39, 286, 614, 3, 28, 33, 1, 0.00386306, 7592, 602204, 4400 ],
    [ 2, 0, 2, 4, 4, 1, 1, 0, 0, 0.0414639, 398, 4198, 1 ],
    [ 2, 1, 2, 3, 5, 1, 1, 1, 1, 0.00327304, 398, 5227, 1 ],
    [ 2, 2, 5, 10, 15, 1, 4, 5, 1, 0.00322862, 409, 6401, 12 ],
    [ 3, 0, 3, 5, 11, 1, 3, 1, 1, 0.0432979, 600, 11663, 3 ],
    [ 3, 1, 3, 5, 14, 1, 3, 1, 1, 0.00296043, 600, 14840, 3 ],
    [ 3, 2, 11, 18, 54, 2, 11, 5, 1, 0.00295457, 1253, 26891, 457 ]
  ]
}
#+end_example

Here the =fields= table describes the columns of the =results= table,
and the =input= and =tool= columns contains indices relative to the
=inputs= and =tools= table.  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.

JSON data can be easily processed in any language.  For instance the
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).

#+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
results = { t:[] for t in range(0, len(data["tools"])) }
for l in data["results"]:
  results[l[1]].append(l)
# Average columns for each tools, and display them as a table
print("%-18s &" % "tool", "count &",
      " & ".join(data["fields"][2:]), "\\\\")
for i in range(0, len(data["tools"])):
  c = len(results[i])
  sums = ["%6.2f" % (sum([x[j] for x in results[i]])/c)
          for j in datacols]
  print("%-18s & %3d & " % (data["tools"][i], c),
        " & ".join(sums), "\\\\")
#+END_SRC
#+RESULTS:
: tool               & count & states & edges & transitions & acc & scc & nondetstates & nondeterministic & time & product_states & product_transitions & product_scc \\
: ltl2tgba -s %f >%N &   4 &    3.00 &   6.00 &  10.00 &   1.00 &   2.50 &   0.75 &   0.50 &   0.04 & 549.00 & 9334.25 &   2.50 \\
: spin -f %s >%N     &   4 &    4.50 &  11.25 &  25.00 &   1.00 &   2.75 &   3.50 &   1.00 &   0.01 & 848.25 & 24779.75 &   3.25 \\
: lbt < %L >%T       &   4 &   15.75 &  88.75 & 183.50 &   1.75 &  11.50 &  12.75 &   1.00 &   0.00 & 2660.75 & 169623.50 & 1218.50 \\

The script =bench/ltl2tgba/sum.py= is a more evolved version of the
above script that generates two kinds of LaTeX tables.

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.

* 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:

    : error: P0*N1 is nonempty
    : error: P1*N0 is nonempty
    : error: P1*N1 is nonempty
    : error: P1*N2 is nonempty
    : error: P1*N3 is nonempty
    : error: P1*N4 is nonempty
    : error: P1*N5 is nonempty
    : error: P1*N6 is nonempty
    : error: P1*N7 is nonempty
    : error: P1*N8 is nonempty
    : error: P1*N9 is nonempty
    : error: P2*N1 is nonempty
    : error: P3*N1 is nonempty
    : error: P4*N1 is nonempty
    : error: P5*N1 is nonempty
    : error: P6*N1 is nonempty
    : error: P7*N1 is nonempty
    : error: P8*N1 is nonempty
    : error: P9*N1 is nonempty

    In this example, translator number =1= looks clearly faulty
    (at least the other 9 translators do not contradict each other).

  - 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

  - 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

The above checks are the same that are performed by [[http://www.tcs.hut.fi/Software/lbtt/][LBTT]].

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.

# Local variables:
# eval: (setenv "PATH" (concat "../../src/bin" path-separator (getenv "PATH")))
# eval: (org-babel-do-load-languages 'org-babel-load-languages '((sh . t) (dot . t) (python . t)))
# eval: (setq org-confirm-babel-evaluate nil)
# eval: (setq org-babel-python-command "/usr/bin/python3")
# End:

#  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