ltlcross: replace %H,%T,%N by %O

Also get rid of the lbt_parser, and fix the LBT support of the HOA
parser.

* doc/org/ltlcross.org, doc/org/ltldo.org: Update.
* src/bin/common_trans.cc, src/bin/common_trans.hh: Add support for
%O, and keep %T,%N,%H as hidden aliases without disabling them.
* src/bin/ltlcross.cc, src/bin/ltldo.cc, src/tgbatest/ltl2tgba.cc:
Call hoa_parse instead of lbt_parse.
* src/hoaparse/hoaparse.yy: Improve error reporting from LBT.
* src/hoaparse/hoascan.ll: Fix typos preventing parsing of
LBT files with more than 10 states.
* src/tgbaalgos/lbtt.cc, src/tgbaalgos/lbtt.hh: Delete the lbt
parser.
* src/tgbatest/lbttparse.test: Adjust the expected error message.
* NEWS: Update.
This commit is contained in:
Alexandre Duret-Lutz 2015-02-01 01:54:39 +01:00
parent dbd824c539
commit 847270b480
13 changed files with 264 additions and 540 deletions

View file

@ -60,54 +60,57 @@ ltlcross --help | sed -n '/character sequences:/,/^$/p' | sed '1d;$d'
: LBT, or Wring's syntax
: %F,%S,%L,%W the formula as a file in Spot, Spin, LBT, or
: Wring's syntax
: %N,%T,%D the output automaton as a Never claim, in LBTT's
: or in LTL2DSTAR's format
: %O,%D the automaton is output as either (%O) HOA/never
: claim/LBTT, or (%D) in LTL2DSTAR'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'
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%O' 'spin -f %s >%O'
#+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
by the formula in Spin's syntax, and =%O= 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
ltlcross -f 'GFa' -f 'X(a U b)' 'ltl2tgba -s %s >%O' 'spin -f %s >%O' 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'
Running [P0]: ltl2tgba -s '([](<>(a)))' >'lcr-o0-hvzgTC'
Running [P1]: spin -f '([](<>(a)))' >'lcr-o1-iYh45L'
Running [N0]: ltl2tgba -s '(!([](<>(a))))' >'lcr-o0-z6nzjV'
Running [N1]: spin -f '(!([](<>(a))))' >'lcr-o1-8JB5F4'
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'
Running [P0]: ltl2tgba -s '(X((a) U (b)))' >'lcr-o0-rqfB6d'
Running [P1]: spin -f '(X((a) U (b)))' >'lcr-o1-OUNHEn'
Running [N0]: ltl2tgba -s '(!(X((a) U (b))))' >'lcr-o0-qzVvdx'
Running [N1]: spin -f '(!(X((a) U (b))))' >'lcr-o1-eUfHTG'
Performing sanity checks and gathering statistics...
no problem detected
No problem detected.
#+end_example
=ltlcross= can only read three kinds of output:
=ltlcross= can only read four 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=. The newer syntax introduced by
should be indicated using =%O=. The newer syntax introduced by
Spin 6.24, using =do= instead of =if=, is also supported.
- [[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=.
--lbtt=. These should also be indicated using =%O=.
- Non-alaternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]] with an acceptance
condition that is is generalized-Büchi or inferior. These
should also be indicated using =%O=.
- [[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
@ -124,24 +127,24 @@ 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='
- '=ltl3ba -M0 -f %s >%N=' (less deterministic output, can be smaller)
- '=ltl3ba -M1 -f %s >%N=' (more deterministic output)
- '=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
- '=spin -f %s >%O='
- '=ltl2ba -f %s >%O='
- '=ltl3ba -M0 -f %s >%O=' (less deterministic output, can be smaller)
- '=ltl3ba -M1 -f %s >%O=' (more deterministic output)
- '=modella -r12 -g -e %L %O='
- '=/path/to/script4lbtt.py %L %O=' (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='
- '=ltl2tgba -s %s >%O=' (smaller output, Büchi automaton)
- '=ltl2tgba -s -D %s >%O=' (more deterministic output, Büchi automaton)
- '=ltl2tgba --lbtt %s >%O=' (smaller output, TGBA)
- '=ltl2tgba --lbtt -D %s >%O=' (more deterministic output, TGBA)
- '=lbt <%L >%O='
- '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %L %D='
(deterministic Rabin output)
- '=ltl2dstar --automata=streett --ltl2nba=spin:path/to/ltl2tgba@-sD
%L %D=' (deterministic Streett output)
- '=ltl2dstar --ltl2nba=spin:path/to/ltl2tgba@-sD %L - | dstar2tgba
-s >%N=' (external conversion from Rabin to Büchi done by
-s >%O=' (external conversion from Rabin to Büchi done by
=dstar2tgba= for more reduction of the Büchi automaton than
what =ltlcross= would provide)
- '=java -jar Rabinizer.jar -ltl2dstar %F %D; mv %D.dst %D=' (Rabinizer
@ -161,22 +164,22 @@ ltlcross --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.
lbt <%L>%T
ltl2ba -f %s>%N
lbt <%L>%O
ltl2ba -f %s>%O
ltl2dstar %L %D
ltl2tgba -H %f>%H
ltl3ba -f %s>%N
ltl2tgba -H %f>%O
ltl3ba -f %s>%O
ltl3dra -f %f>%D
modella %L %T
spin -f %s>%N
modella %L %O
spin -f %s>%O
#+end_example
What this implies is that running =ltlcross ltl2ba ltl3ba ...= is
the same as running =ltlcross 'ltl2ba -f %s>%N' 'ltl3ba -f %s>%N' ...=
the same as running =ltlcross 'ltl2ba -f %s>%O' 'ltl3ba -f %s>%O' ...=
Because only the prefix of the actual command is checked, you can
still specify some options. For instance =ltlcross 'ltl2tgba -D' ...=
is short for =ltlcross 'ltl2tgba -D -H %F>%H' ...=
is short for =ltlcross 'ltl2tgba -D -H %F>%O' ...=
* Getting statistics
@ -194,37 +197,37 @@ they are not supported by =spin= and =lbt=).
randltl -n 2 a b |
ltlfilt --remove-wm |
ltlcross --csv=results.csv \
'ltl2tgba -s %f >%N' \
'spin -f %s >%N' \
'lbt < %L >%T'
'ltl2tgba -s %f >%O' \
'spin -f %s >%O' \
'lbt < %L >%O'
#+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
'ltl2tgba -s %f >%O' \
'spin -f %s >%O' \
'lbt < %L >%O' --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)))))))' >'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'
-:1: (1)
Running [P0]: ltl2tgba -s '(1)' >'lcr-o0-zO7jLB'
Running [P1]: spin -f '(true)' >'lcr-o1-r7P86U'
Running [P2]: lbt < 'lcr-i0-idYSPi' >'lcr-o2-l220te'
Running [N0]: ltl2tgba -s '(0)' >'lcr-o0-ylbgfR'
Running [N1]: spin -f '(false)' >'lcr-o1-HwVbKa'
Running [N2]: lbt < 'lcr-i0-uVICRx' >'lcr-o2-MSsIfu'
Performing sanity checks and gathering statistics...
-: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'
-:2: (!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))
Running [P0]: ltl2tgba -s '(!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))' >'lcr-o0-sPvik7'
Running [P1]: spin -f '(!((!(((p0) U ([](p1))) U (p1))) U ([](<>(p0)))))' >'lcr-o1-yQ8BZq'
Running [P2]: lbt < 'lcr-i1-uob0MN' >'lcr-o2-0IrdjL'
Running [N0]: ltl2tgba -s '(!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))' >'lcr-o0-tSN3Xp'
Running [N1]: spin -f '(!(((p0) U ([](p1))) U (p1))) U ([](<>(p0)))' >'lcr-o1-DsLkqK'
Running [N2]: lbt < 'lcr-i1-WmkDD5' >'lcr-o2-D77Ai7'
Performing sanity checks and gathering statistics...
No problem detected.
@ -237,19 +240,19 @@ cat results.csv
#+END_SRC
#+RESULTS:
#+begin_example
"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
"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"
"(1)","ltl2tgba -s %f >%O","ok",0,0.137237,1,1,1,1,1,0,1,0,0,0,0,1,0,0,200,4142,1
"(1)","spin -f %s >%O","ok",0,0.00531029,2,2,2,1,2,1,1,0,0,0,0,1,0,0,201,4161,2
"(1)","lbt < %L >%O","ok",0,0.00358417,3,3,3,0,3,2,1,0,0,0,0,1,0,0,220,4550,21
"(0)","ltl2tgba -s %f >%O","ok",0,0.0377477,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0,1
"(0)","spin -f %s >%O","ok",0,0.00286865,2,2,1,1,2,1,1,0,0,0,0,1,0,0,1,0,1
"(0)","lbt < %L >%O","ok",0,0.00280551,1,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1
"(!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))","ltl2tgba -s %f >%O","ok",0,0.0415092,2,3,4,1,2,1,0,1,0,1,1,0,1,0,400,8567,2
"(!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))","spin -f %s >%O","ok",0,0.209455,23,86,127,1,17,10,0,2,5,21,1,0,0,1,4392,116876,24
"(!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))","lbt < %L >%O","ok",0,0.00363823,37,109,164,3,35,28,0,7,0,28,1,0,1,0,7182,155216,4006
"(!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))","ltl2tgba -s %f >%O","ok",0,0.0406385,2,4,4,1,1,0,0,0,1,0,0,0,0,1,400,8522,1
"(!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))","spin -f %s >%O","ok",0,0.781573,22,152,257,1,9,4,0,0,5,21,1,0,0,1,4400,282361,208
"(!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))","lbt < %L >%O","ok",0,0.00471071,72,551,914,3,52,47,0,0,5,72,1,0,0,1,14201,983174,8808
#+end_example
This file can be loaded in any spreadsheet or statistical application.
@ -269,33 +272,33 @@ cat results.json
#+begin_example
{
"tool": [
"ltl2tgba -s %f >%N",
"spin -f %s >%N",
"lbt < %L >%T"
"ltl2tgba -s %f >%O",
"spin -f %s >%O",
"lbt < %L >%O"
],
"formula": [
"(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))"
"(1)",
"(0)",
"(!((!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))))",
"(!(((p0) U (G(p1))) U (p1))) U (G(F(p0)))"
],
"fields": [
"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"
],
"inputs": [ 0, 1 ],
"results": [
[ 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 ]
[ 0,0,"ok",0,0.137237,1,1,1,1,1,0,1,0,0,0,0,1,0,0,200,4142,1 ],
[ 0,1,"ok",0,0.00531029,2,2,2,1,2,1,1,0,0,0,0,1,0,0,201,4161,2 ],
[ 0,2,"ok",0,0.00358417,3,3,3,0,3,2,1,0,0,0,0,1,0,0,220,4550,21 ],
[ 1,0,"ok",0,0.0377477,1,1,0,1,1,1,0,0,0,0,0,1,0,0,1,0,1 ],
[ 1,1,"ok",0,0.00286865,2,2,1,1,2,1,1,0,0,0,0,1,0,0,1,0,1 ],
[ 1,2,"ok",0,0.00280551,1,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,1 ],
[ 2,0,"ok",0,0.0415092,2,3,4,1,2,1,0,1,0,1,1,0,1,0,400,8567,2 ],
[ 2,1,"ok",0,0.209455,23,86,127,1,17,10,0,2,5,21,1,0,0,1,4392,116876,24 ],
[ 2,2,"ok",0,0.00363823,37,109,164,3,35,28,0,7,0,28,1,0,1,0,7182,155216,4006 ],
[ 3,0,"ok",0,0.0406385,2,4,4,1,1,0,0,0,1,0,0,0,0,1,400,8522,1 ],
[ 3,1,"ok",0,0.781573,22,152,257,1,9,4,0,0,5,21,1,0,0,1,4400,282361,208 ],
[ 3,2,"ok",0,0.00471071,72,551,914,3,52,47,0,0,5,72,1,0,0,1,14201,983174,8808 ]
]
}
#+end_example
@ -335,9 +338,9 @@ for i in range(0, len(data["tool"])):
#+END_SRC
#+RESULTS:
: 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 \\
: ltl2tgba -s %f >%O & 4 & 0.1 & 1.5 & 2.2 & 2.2 & 1.0 & 1.2 & 0.5 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.5 & 0.2 & 0.2 & 250.2 & 5307.8 & 1.2 \\
: spin -f %s >%O & 4 & 0.2 & 12.2 & 60.5 & 96.8 & 1.0 & 7.5 & 4.0 & 0.5 & 0.5 & 2.5 & 10.5 & 0.5 & 0.5 & 0.0 & 0.5 & 2248.5 & 100849.5 & 58.8 \\
: lbt < %L >%O & 4 & 0.0 & 28.2 & 165.8 & 270.2 & 1.5 & 22.8 & 19.5 & 0.2 & 1.8 & 1.2 & 25.0 & 0.5 & 0.5 & 0.2 & 0.2 & 5401.0 & 285735.0 & 3209.0 \\
The script =bench/ltl2tgba/sum.py= is a more evolved version of the
above script that generates two kinds of LaTeX tables.
@ -499,22 +502,22 @@ 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:
configurations, and the strings =ltl2tgba -s --small %f >%O= and
=ltl2tgba -s --deter %f >%O= 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
ltlcross -f a -f Ga 'ltl2tgba -s --small %f >%O' 'ltl2tgba -s --deter %f >%O' --csv
#+END_SRC
#+RESULTS:
: "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
: "formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","product_states","product_transitions","product_scc"
: "(a)","ltl2tgba -s --small %f >%O","ok",0,0.043876,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(a)","ltl2tgba -s --deter %f >%O","ok",0,0.0432137,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(!(a))","ltl2tgba -s --small %f >%O","ok",0,0.0400653,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(!(a))","ltl2tgba -s --deter %f >%O","ok",0,0.0450417,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(G(a))","ltl2tgba -s --small %f >%O","ok",0,0.0429628,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(G(a))","ltl2tgba -s --deter %f >%O","ok",0,0.0478663,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(!(G(a)))","ltl2tgba -s --small %f >%O","ok",0,0.0436822,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
: "(!(G(a)))","ltl2tgba -s --deter %f >%O","ok",0,0.039919,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
To present these results graphically, or even when analyzing these
data, it might be convenient to give each configured tool a shorter
@ -524,18 +527,18 @@ 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
ltlcross -f a -f Ga '{small} ltl2tgba -s --small %f >%O' '{deter} ltl2tgba -s --deter %f >%O' --csv
#+END_SRC
#+RESULTS:
: "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
: "formula","tool","exit_status","exit_code","time","states","edges","transitions","acc","scc","nonacc_scc","terminal_scc","weak_scc","strong_scc","nondet_states","nondet_aut","terminal_aut","weak_aut","strong_aut","product_states","product_transitions","product_scc"
: "(a)","small","ok",0,0.0433468,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(a)","deter","ok",0,0.0429179,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4208,2
: "(!(a))","small","ok",0,0.0400513,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(!(a))","deter","ok",0,0.040167,2,2,3,1,2,1,1,0,0,0,0,1,0,0,201,4205,2
: "(G(a))","small","ok",0,0.0447826,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(G(a))","deter","ok",0,0.0439892,1,1,1,1,1,0,0,1,0,0,0,0,1,0,200,2077,1
: "(!(G(a)))","small","ok",0,0.0444007,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
: "(!(G(a)))","deter","ok",0,0.0396312,2,3,4,1,2,1,1,0,0,0,0,1,0,0,400,8442,2
* Detecting problems
@ -591,7 +594,7 @@ positive and negative formulas by the ith translator).
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
coverage. Using '=ltl2tgba -lD %f >%O=' 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
@ -653,7 +656,7 @@ 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'
randltl -n -1 --tree-size 10..25 a b c | ltlcross --stop-on-error 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
#+END_SRC
** =--save-bogus=FILENAME=
@ -670,14 +673,14 @@ 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'
randltl -n -1 --tree-size 10..25 a b c | ltlcross --save-bogus=bugs.ltl 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
#+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'
ltlcross -F bugs.ltl 'ltl2tgba --lbtt %f >%O' 'ltl3ba -f %s >%O'
#+END_SRC
** =--grind=FILENAME=
@ -699,167 +702,144 @@ during the process will be saved in =OTHERFILENAME=.
Example:
#+BEGIN_SRC sh :exports code :results verbatim
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %T" \
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %O" \
--save-bogus=bogus \
--grind=bogus-grind
#+END_SRC
#+BEGIN_SRC sh :exports results :results verbatim
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %T" \
ltlcross -f '(G!b & (!c | F!a)) | (c & Ga & Fb)' "modella %L %O" \
--save-bogus=bogus --grind=bogus-grind 2>&1
true
#+END_SRC
#+RESULTS:
#+begin_example
| & G ! p0 | ! p1 F ! p2 & & p1 G p2 F p0
Running [P0]: modella 'lcr-i0-YBdcX8' 'lcr-o0-VWBBUF'
Running [N0]: modella 'lcr-i0-wteTSc' 'lcr-o0-pqlbRJ'
Running [P0]: modella 'lcr-i0-1XJw2X' 'lcr-o0-p2nbUW'
Running [N0]: modella 'lcr-i0-lSPMMV' 'lcr-o0-3xEoFU'
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
cycle{!p0 & !p1}
Trying to find a bogus mutation of "(G!b & (!c | F!a)) | (c & Ga & Fb)"
Mutation [1/22]
& & p0 G p1 F p2
Running [P0]: modella 'lcr-i1-Ursu0g' 'lcr-o0-Lm3N9N'
Running [N0]: modella 'lcr-i1-AkNujl' 'lcr-o0-VYRbtS'
Trying to find a bogus mutation of (G!b & (!c | F!a)) | (c & Ga & Fb)...
Mutation 1/22: & & p0 G p1 F p2
Running [P0]: modella 'lcr-i1-3PI0CT' 'lcr-o0-GxBDAS'
Running [N0]: modella 'lcr-i1-eOijzR' 'lcr-o0-wkIZxQ'
Performing sanity checks and gathering statistics...
Mutation [2/22]
& G ! p0 | ! p1 F ! p2
Running [P0]: modella 'lcr-i2-uuBGGp' 'lcr-o0-eZLbUW'
Running [N0]: modella 'lcr-i2-qO717t' 'lcr-o0-evKSl1'
Mutation 2/22: & G ! p0 | ! p1 F ! p2
Running [P0]: modella 'lcr-i2-6cYUzP' 'lcr-o0-3ihRBO'
Running [N0]: modella 'lcr-i2-6u8pEN' 'lcr-o0-phxZGM'
Performing sanity checks and gathering statistics...
Mutation [3/22]
| G ! p0 & & p1 G p2 F p0
Running [P0]: modella 'lcr-i3-hQAiDy' 'lcr-o0-PoKIU5'
Running [N0]: modella 'lcr-i3-Jl5vcD' 'lcr-o0-RtIjua'
Mutation 3/22: | G ! p0 & & p1 G p2 F p0
Running [P0]: modella 'lcr-i3-iwZZML' 'lcr-o0-LMB2SK'
Running [N0]: modella 'lcr-i3-r2g9ZJ' 'lcr-o0-HEfh7I'
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
cycle{!p0 & !p1}
Trying to find a bogus mutation of "G!b | (c & Ga & Fb)"
Mutation [1/16]
t
Running [P0]: modella 'lcr-i4-HUTvSH' 'lcr-o0-XXrIgf'
Running [N0]: modella 'lcr-i4-MoZ9EM' 'lcr-o0-w2MB3j'
Trying to find a bogus mutation of G!b | (c & Ga & Fb)...
Mutation 1/16: t
Running [P0]: modella 'lcr-i4-R8PbkI' 'lcr-o0-6ts7wH'
Running [N0]: modella 'lcr-i4-cv7EKG' 'lcr-o0-vVmdYF'
Performing sanity checks and gathering statistics...
Mutation [2/16]
G ! p0
Running [P0]: modella 'lcr-i5-ZjeLsR' 'lcr-o0-lT2URo'
Running [N0]: modella 'lcr-i5-ELzihW' 'lcr-o0-tljGGt'
Mutation 2/16: G ! p0
Running [P0]: modella 'lcr-i5-ZO3HcF' 'lcr-o0-UiydrE'
Running [N0]: modella 'lcr-i5-gOseGD' 'lcr-o0-CL4fVC'
Performing sanity checks and gathering statistics...
Mutation [3/16]
& & p0 G p1 F p2
Mutation 3/16: & & p0 G p1 F p2
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [4/16]
| G ! p0 & p1 F p0
Running [P0]: modella 'lcr-i6-VUy2yy' 'lcr-o0-44be05'
Running [N0]: modella 'lcr-i6-SBBHrD' 'lcr-o0-VAcbTa'
Mutation 4/16: | G ! p0 & p1 F p0
Running [P0]: modella 'lcr-i6-QTDjtB' 'lcr-o0-tFpmKA'
Running [N0]: modella 'lcr-i6-1lnX1z' 'lcr-o0-TWWyjz'
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
cycle{!p0 & !p1}
Trying to find a bogus mutation of "G!b | (c & Fb)"
Mutation [1/10]
t
Trying to find a bogus mutation of G!b | (c & Fb)...
Mutation 1/10: t
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [2/10]
G ! p0
Mutation 2/10: G ! p0
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [3/10]
& p0 F p1
Running [P0]: modella 'lcr-i7-gBs0mN' 'lcr-o0-bgNCRk'
Running [N0]: modella 'lcr-i7-oAYtmS' 'lcr-o0-VvmlRp'
Mutation 3/10: & p0 F p1
Running [P0]: modella 'lcr-i7-CJTWjx' 'lcr-o0-DKbNEw'
Running [N0]: modella 'lcr-i7-tSts1v' 'lcr-o0-CGbWov'
Performing sanity checks and gathering statistics...
Mutation [4/10]
| p0 G ! p1
Running [P0]: modella 'lcr-i8-wLstoX' 'lcr-o0-jZOBVu'
Running [N0]: modella 'lcr-i8-4hBZs2' 'lcr-o0-3Ezn0z'
Mutation 4/10: | p0 G ! p1
Running [P0]: modella 'lcr-i8-6dtbPu' 'lcr-o0-gLnsfu'
Running [N0]: modella 'lcr-i8-Xn6gGt' 'lcr-o0-U7966s'
Performing sanity checks and gathering statistics...
Mutation [5/10]
| G ! p0 F p0
Running [P0]: modella 'lcr-i9-mqY0z7' 'lcr-o0-hcDE9E'
Running [N0]: modella 'lcr-i9-MtDCJc' 'lcr-o0-5fRAjK'
Mutation 5/10: | G ! p0 F p0
Running [P0]: modella 'lcr-i9-Vh7hAs' 'lcr-o0-eYZt3r'
Running [N0]: modella 'lcr-i9-I6dfxr' 'lcr-o0-DoY00q'
Performing sanity checks and gathering statistics...
Mutation [6/10]
| ! p0 & p1 F p0
Running [P0]: modella 'lcr-i10-s5ZlUh' 'lcr-o0-fvp7uP'
Running [N0]: modella 'lcr-i10-4GWe6m' 'lcr-o0-LKFmHU'
Mutation 6/10: | ! p0 & p1 F p0
Running [P0]: modella 'lcr-i10-j7fVvq' 'lcr-o0-aChQ0p'
Running [N0]: modella 'lcr-i10-bnpgwp' 'lcr-o0-KV3G1o'
Performing sanity checks and gathering statistics...
Mutation [7/10]
| G p1 & p0 F p1
Running [P0]: modella 'lcr-i11-wZJKjs' 'lcr-o0-D948VZ'
Running [N0]: modella 'lcr-i11-yVpOyx' 'lcr-o0-rjXtb5'
Mutation 7/10: | G p1 & p0 F p1
Running [P0]: modella 'lcr-i11-uUhFyo' 'lcr-o0-OlrF5n'
Running [N0]: modella 'lcr-i11-XHjeDn' 'lcr-o0-0CINan'
Performing sanity checks and gathering statistics...
Mutation [8/10]
| & p0 p1 G ! p0
Running [P0]: modella 'lcr-i12-g9bpRC' 'lcr-o0-RhIkxa'
Running [N0]: modella 'lcr-i12-rvWBdI' 'lcr-o0-DauTTf'
Mutation 8/10: | & p0 p1 G ! p0
Running [P0]: modella 'lcr-i12-a7eJLm' 'lcr-o0-RUZFmm'
Running [N0]: modella 'lcr-i12-dobiYl' 'lcr-o0-LuVUzl'
Performing sanity checks and gathering statistics...
Mutation [9/10]
| G ! p0 & p0 F p0
Running [P0]: modella 'lcr-i13-sXVtCN' 'lcr-o0-9WE4kl'
Running [N0]: modella 'lcr-i13-49803S' 'lcr-o0-BNXXMq'
Mutation 9/10: | G ! p0 & p0 F p0
Running [P0]: modella 'lcr-i13-nFQYdl' 'lcr-o0-Mq84Rk'
Running [N0]: modella 'lcr-i13-CnPRwk' 'lcr-o0-7f4Fbk'
Performing sanity checks and gathering statistics...
error: P0*N0 is nonempty; both automata accept the infinite word
cycle{!p0}
Trying to find a bogus mutation of "G!c | (c & Fc)"
Mutation [1/7]
t
Trying to find a bogus mutation of G!c | (c & Fc)...
Mutation 1/7: t
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [2/7]
G ! p0
Mutation 2/7: G ! p0
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [3/7]
& p0 F p0
Running [P0]: modella 'lcr-i14-Ohct43' 'lcr-o0-vKfEPB'
Running [N0]: modella 'lcr-i14-aKk2A9' 'lcr-o0-RiFqmH'
Mutation 3/7: & p0 F p0
Running [P0]: modella 'lcr-i14-KsKPgj' 'lcr-o0-Qo3UXi'
Running [N0]: modella 'lcr-i14-FVPvFi' 'lcr-o0-Zh06mi'
Performing sanity checks and gathering statistics...
Mutation [4/7]
| p0 G ! p0
Running [P0]: modella 'lcr-i15-Oht38e' 'lcr-o0-bhxGVM'
Running [N0]: modella 'lcr-i15-iyrAIk' 'lcr-o0-nMFuvS'
Mutation 4/7: | p0 G ! p0
Running [P0]: modella 'lcr-i15-JB045h' 'lcr-o0-EIL4Oh'
Running [N0]: modella 'lcr-i15-sYY8yh' 'lcr-o0-KVOdjh'
Performing sanity checks and gathering statistics...
Mutation [5/7]
| G ! p0 F p0
Mutation 5/7: | G ! p0 F p0
warning: This formula or its negation has already been checked.
Use --allow-dups if it should not be ignored.
Mutation [6/7]
| ! p0 & p0 F p0
Running [P0]: modella 'lcr-i16-nZMD9X' 'lcr-o0-epKIYv'
Running [N0]: modella 'lcr-i16-DSW2N3' 'lcr-o0-6ElnDB'
Mutation 6/7: | ! p0 & p0 F p0
Running [P0]: modella 'lcr-i16-hoqdSg' 'lcr-o0-xghJEg'
Running [N0]: modella 'lcr-i16-5JvOrg' 'lcr-o0-SUdVeg'
Performing sanity checks and gathering statistics...
Mutation [7/7]
| & p0 F p0 G p0
Running [P0]: modella 'lcr-i17-Z6avt9' 'lcr-o0-QJhDjH'
Running [N0]: modella 'lcr-i17-hEo69e' 'lcr-o0-OBHz0M'
Mutation 7/7: | & p0 F p0 G p0
Running [P0]: modella 'lcr-i17-BNo92f' 'lcr-o0-0T8nRf'
Running [N0]: modella 'lcr-i17-J5v5Ff' 'lcr-o0-MOyNuf'
Performing sanity checks and gathering statistics...
The smallest bogus mutation found for (G!b & (!c | F!a)) | (c & Ga & Fb) was G!c | (c & Fc)
Smallest bogus mutation found for (G!b & (!c | F!a)) | (c & Ga & Fb) is G!c | (c & Fc).
error: some error was detected during the above runs.
Check file bogus for problematic formulas.