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autcross

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autcross is a tool for cross-comparing the output of tools that transform automata. It works similarly to ltlcross except that inputs are automata.

The core of autcross is a loop that does the following steps:

Statistics about the results of each tools can optionally be saved in a CSV file. And in case only those statistics matters, it is also possible to disable the equivalence checks.

Input automata

The input automata can be supplied either on standard input, or in files specified with option -F.

If an input automaton is expressed in the HOA format and has a name, that name will be displayed by autcross when processing the automaton, and will appear in the CSV file if such a file is output.

Specifying the tools to test

Each tool should be specified as a string that uses some of the following character sequences:

%%                         a single %
%H,%S,%L                   filename for the input automaton in (H) HOA, (S)
                           Spin's neverclaim, or (L) LBTT's format
%M, %[val]M                the name of the input automaton, with an optional
                           default value
%O                         filename for the automaton output in HOA, never
                           claim, LBTT, or ltl2dstar's format

For instance we can use autfilt --complement %H >%O to indicate that autfilt reads one file (%H) in the HOA format, and to redirect the output in file so that autcross can find it. The output format is automatically detected, so a generic %O is used for the output file regardless of its format.

Another tool that can complement automata is ltl2dstar, using the syntax ltl2dstar -B --complement-input=yes %H %O. So to compare the results of these two tools we could use:

randaut -B -n 3 a b |
autcross 'autfilt --complement %H >%O' 'ltl2dstar --complement-input=yes -B %H %O'
randaut -B -n 3 a b |
autcross 'autfilt --complement %H >%O' 'ltl2dstar --complement-input=yes -B %H %O' 2>&1
-:1.1-45.7
Running [A0]: autfilt --complement 'lcr-i0-Nr1xZO' >'lcr-o0-urHakt'
Running [A1]: ltl2dstar -B --complement-input=yes 'lcr-i0-mmkgH7' 'lcr-o1-ABdm4L'
Performing sanity checks and gathering statistics...

-:46.1-92.7
Running [A0]: autfilt --complement 'lcr-i1-5kMYrq' >'lcr-o0-9kvBP4'
Running [A1]: ltl2dstar -B --complement-input=yes 'lcr-i1-lVlGfJ' 'lcr-o1-BexLFn'
Performing sanity checks and gathering statistics...

-:93.1-137.7
Running [A0]: autfilt --complement 'lcr-i2-rjvy61' >'lcr-o0-rKKlxG'
Running [A1]: ltl2dstar -B --complement-input=yes 'lcr-i2-Musr0k' 'lcr-o1-LyAxtZ'
Performing sanity checks and gathering statistics...

No problem detected.

In this example, we generate 3 random Büchi automata (because ltl2dstar expects Büchi automata as input) using randaut, and pipe them to autcross. For each of those automata, autcross display the source location of that automaton (here - indicates that the automaton is read from standard input, and this is followed by beginline.column-endline.colum specifying the position of that automaton in the input. If the automata had names, they would be displayed as well.

Then, each tool is called using temporary files to exchange the automata, and the resulting automata are then compared. The last line specifies that no problem was detected.

To simplify the use of some known tools, a set of predefined shorthands are available. Those can be listed with the --list-shorthands option.

autcross --list-shorthands
If a COMMANDFMT does not use any %-sequence, and starts with one of
the following words, then the string on the right is appended.

  autfilt      %H>%O
  dstar2tgba   %H>%O
  ltl2dstar    -B %H %O
  nba2dpa      <%H>%O
  nba2ldpa     <%H>%O
  seminator    %H>%O

Any {name} and directory component is skipped for the purpose of
matching those prefixes.  So for instance
  '{AF} ~/mytools/autfilt-2.4 --remove-fin'
will be changed into
  '{AF} ~/mytools/autfilt-2.4 --remove-fin %H>%O'

What this implies is our previous example could be shortened to:

randaut -B -n 3 a b |
autcross 'autfilt --complement' 'ltl2dstar --complement-input=yes'

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 option.

CSV output

Let's take our example and modify it in two ways. First we pass a --name option to randaut to give each automaton a name (in randaut, %L denotes the serial number of the automaton); this is mostly a cosmetic change, so that autcross will display names. Second, we pass a --csv option to autcross to save statistics in a file.

randaut -B -n 3 a b --name="automaton %L" |
autcross 'autfilt --complement' 'ltl2dstar --complement-input=yes' --csv=autcross.csv
-:1.1-46.7	automaton 0
Running [A0]: autfilt --complement 'lcr-i0-NBvtAU'>'lcr-o0-Yb1YkK'
Running [A1]: ltl2dstar --complement-input=yes -B 'lcr-i0-HuDp9z' 'lcr-o1-llRQXp'
Performing sanity checks and gathering statistics...

-:47.1-94.7	automaton 1
Running [A0]: autfilt --complement 'lcr-i1-PmGjNf'>'lcr-o0-nmcNC5'
Running [A1]: ltl2dstar --complement-input=yes -B 'lcr-i1-m4NkwV' 'lcr-o1-tt6SpL'
Performing sanity checks and gathering statistics...

-:95.1-140.7	automaton 2
Running [A0]: autfilt --complement 'lcr-i2-G3ntkB'>'lcr-o0-tcu4er'
Running [A1]: ltl2dstar --complement-input=yes -B 'lcr-i2-M5xEdh' 'lcr-o1-EDdfc7'
Performing sanity checks and gathering statistics...

No problem detected.

After this execution, the file autcross.csv contains the following:

"input.source","input.name","input.ap","input.states","input.edges","input.transitions","input.acc_sets","input.scc","input.nondetstates","input.nondeterministic","input.alternating","tool","exit_status","exit_code","time","output.ap","output.states","output.edges","output.transitions","output.acc_sets","output.scc","output.nondetstates","output.nondeterministic","output.alternating"
"-:1.1-46.7","automaton 0",2,10,26,26,1,1,6,1,0,"autfilt --complement","ok",0,0.0282075,2,27,95,108,3,2,0,0,0
"-:1.1-46.7","automaton 0",2,10,26,26,1,1,6,1,0,"ltl2dstar --complement-input=yes","ok",0,0.00569124,2,34,121,136,6,2,0,0,0
"-:47.1-94.7","automaton 1",2,10,28,28,1,1,4,1,0,"autfilt --complement","ok",0,0.0293913,2,58,215,232,3,2,0,0,0
"-:47.1-94.7","automaton 1",2,10,28,28,1,1,4,1,0,"ltl2dstar --complement-input=yes","ok",0,0.0052164,2,74,268,296,6,2,0,0,0
"-:95.1-140.7","automaton 2",2,10,26,26,1,2,6,1,0,"autfilt --complement","ok",0,0.0289153,2,21,66,84,2,4,0,0,0
"-:95.1-140.7","automaton 2",2,10,26,26,1,2,6,1,0,"ltl2dstar --complement-input=yes","ok",0,0.00371466,2,24,74,96,2,4,0,0,0

This file can then be loaded in any spreadsheet or statistical application.

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 autcross's --timeout option to limit run time) will appear with empty columns at the end of the CSV line. Those lines with missing data can be omitted with the --omit-missing option.

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

The column names should be almost self-explanatory. See the man page for a description of the columns.

Changing the name of the translators

By default, the names used in the CSV output to designate the tools are the command specified on the command line. Like with ltlcross, this can be adjusted by using a command specification of the form {short name}actual command.

For instance

randaut -B -n 3 a b --name="automaton %L" |
autcross '{AF}autfilt --complement' '{L2D}ltl2dstar --complement-input=yes' --csv
"input.source","input.name","input.ap","input.states","input.edges","input.transitions","input.acc_sets","input.scc","input.nondetstates","input.nondeterministic","input.alternating","tool","exit_status","exit_code","time","output.ap","output.states","output.edges","output.transitions","output.acc_sets","output.scc","output.nondetstates","output.nondeterministic","output.alternating"
"-:1.1-46.7","automaton 0",2,10,26,26,1,1,6,1,0,"AF","ok",0,0.0249475,2,27,95,108,3,2,0,0,0
"-:1.1-46.7","automaton 0",2,10,26,26,1,1,6,1,0,"L2D","ok",0,0.00409422,2,34,121,136,6,2,0,0,0
"-:47.1-94.7","automaton 1",2,10,28,28,1,1,4,1,0,"AF","ok",0,0.0252846,2,58,215,232,3,2,0,0,0
"-:47.1-94.7","automaton 1",2,10,28,28,1,1,4,1,0,"L2D","ok",0,0.00478925,2,74,268,296,6,2,0,0,0
"-:95.1-140.7","automaton 2",2,10,26,26,1,2,6,1,0,"AF","ok",0,0.0275854,2,21,66,84,2,4,0,0,0
"-:95.1-140.7","automaton 2",2,10,26,26,1,2,6,1,0,"L2D","ok",0,0.0033738,2,24,74,96,2,4,0,0,0

Language preserving transformation

By default autcross assumes that for a given input the automata produced by all tools should be equivalent. However it does not assume that those language should be equivalent to the input (it is clearly not the case in our complementation test above).

If the transformation being tested does preserve the language of an automaton, it is worth to pass the --language-preserved option to autfilt. Doing so a bit like adding cat %H>%O as another tool: it will also ensure that the output is equivalent to the input.

Detecting problems

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

Otherwise autcross performs equivalence checks between each pair of automata. This is done in two steps. First, all produced automata A0, A1, etc. are complemented: the complement automata are named Comp(A0), Comp(A1) etc. Second, autcross ensures that Ai*Comp(Aj) is empty for all i and j.

If the --language-preserved option is passed, the input automaton also participate to these equivalence checks.

To simulate a problem, let's compare pretend we want verify that autfilt --complement preserves the input language (clearly it does not, since it actually complement the language of the automaton).

randaut -B -n 3 a b --name="automaton %L" |
autcross --language-preserved 'autfilt --complement'
randaut -B -n 3 a b --name="automaton %L" |
autcross --language-preserved 'autfilt --complement' 2>&1
-:1.1-46.7	automaton 0
Running [A0]: autfilt --complement 'lcr-i0-3gRqrd'>'lcr-o0-ubUpHb'
Performing sanity checks and gathering statistics...
error: A0*Comp(input) is nonempty; both automata accept the infinite word:
       !a & !b; a & !b; cycle{!a & !b; a & !b; !a & b; !a & b; !a & !b; !a & b; !a & b; !a & !b}
error: input*Comp(A0) is nonempty; both automata accept the infinite word:
       !a & !b; !a & !b; cycle{!a & !b; !a & b; a & b}

-:47.1-94.7	automaton 1
Running [A0]: autfilt --complement 'lcr-i1-JxFi09'>'lcr-o0-oQGbj8'
Performing sanity checks and gathering statistics...
error: A0*Comp(input) is nonempty; both automata accept the infinite word:
       !a & b; cycle{a & !b}
error: input*Comp(A0) is nonempty; both automata accept the infinite word:
       !a & b; a & !b; cycle{!a & b; a & b}

-:95.1-140.7	automaton 2
Running [A0]: autfilt --complement 'lcr-i2-SQT7E6'>'lcr-o0-kWt404'
Performing sanity checks and gathering statistics...
error: A0*Comp(input) is nonempty; both automata accept the infinite word:
       a & !b; !a & !b; cycle{a & !b; !a & b}
error: input*Comp(A0) is nonempty; both automata accept the infinite word:
       cycle{!a & b; !a & b; !a & !b; a & !b; a & !b; !a & !b}

error: some error was detected during the above runs,
       please search for 'error:' messages in the above trace.

Here, for each automaton, we get an example of word that is accepted by the automaton and rejected by the input (i.e., accepted by Comp(input)), as well as an example of word accepted by the input but rejected by the automaton (i.e. accepted by Comp(A0)). Those examples would not exit if the language was really preserved by the tool.

Incoherence between the output of several tools (even with --language-preserved) are reported in a similar way.

Miscellaneous options

--stop-on-error

The --stop-on-error option will cause autcross to abort on the first detected error. This include failure to start some tool, read its output, or failure to passe the sanity checks. Timeouts are allowed unless --fail-on-timeout is also given.

One use for this option is when autcross is used in combination with randaut to check tools on an infinite stream of formulas.

--save-bogus=FILENAME

The --save-bogus=FILENAME will save any automaton for which an error was detected (either some tool 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, unless --fail-on-timeout is given.

The main use for this feature is in conjunction with randaut'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.

--no-check

The --no-check option disables all sanity checks. This makes sense if you only care about the output of --csv.

--verbose

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

randaut -B -n 1 a b --name="automaton %L" |
autcross 'autfilt --complement' 'ltl2dstar --complement-input=yes' --verbose
-:1.1-46.7	automaton 0
info: input	(10 st.,26 ed.,1 sets)
Running [A0]: autfilt --complement 'lcr-i0-DfV4Md'>'lcr-o0-Pj9Qk4'
Running [A1]: ltl2dstar --complement-input=yes -B 'lcr-i0-oI6xWU' 'lcr-o1-2jYfyL'
info: collected automata:
info:   A0	(27 st.,95 ed.,3 sets) deterministic complete
info:   A1	(34 st.,121 ed.,6 sets) deterministic complete
Performing sanity checks and gathering statistics...
info: getting rid of any Fin acceptance...
info:         A0	(27 st.,95 ed.,3 sets) -> (58 st.,203 ed.,2 sets)
info:   Comp(A0)	(27 st.,95 ed.,3 sets) -> (51 st.,188 ed.,1 sets)
info:         A1	(34 st.,121 ed.,6 sets) -> (64 st.,228 ed.,3 sets)
info:   Comp(A1)	(34 st.,121 ed.,6 sets) -> (34 st.,121 ed.,1 sets)
info: check_empty A0*Comp(A1)
info: check_empty A1*Comp(A0)

No problem detected.

Use-cases for %M

If the input automata are named, it is possible to use %M in some tool specification to pass this name to the tool. In particular, this can be used to replace the input automaton by something else.

For instance if the name of the automaton is an actual LTL formula (automata produced by ltl2tgba follow this convention), you can cross-compare some tool that input that formula instead of the automaton. For instance consider the following command-line, where we compare the determinization of autfilt -D (starting from an automaton) to the determinization of ltl2dstar (starting from the LTL formula encoded in the name of the automaton). That LTL formula is not in a syntax supported by ltl2dstar, so we call ltl2dstar via ltldo to arrange that.

genltl --eh-patterns=1..3 | ltl2tgba |
  autcross 'autfilt -P -D' 'ltldo ltl2dstar -f %M >%O'
genltl --eh-patterns=1..3 | ltl2tgba |
  autcross 'autfilt -P -D' 'ltldo ltl2dstar -f %M >%O' 2>&1

This example is a bit contrived, and in this case, an alternative would be to use ltlcross, as in:

genltl --eh-patterns=1..3 |
  ltlcross 'ltl2tgba %f | autfilt -P -D > %O' 'ltl2dstar'
genltl --eh-patterns=1..3 |
  ltlcross 'ltl2tgba %f | autfilt -P -D > %O' 'ltl2dstar' 2>&1

However in practice you could also use the name: field of the input automaton, combined with %M in the tool specification, to designate an alternate filename to load, or some key to look up somewhere.