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spot/doc/org/autfilt.org
Alexandre Duret-Lutz 59e1f6a339 ltlfilt: implement --reject-word and --accept-word 
* bin/common_range.hh: Store the common definition of words.
* bin/autfilt.cc: Use it.
* bin/ltlfilt.cc: Likewise, and implement those two options.
* tests/core/acc_word.test: Test them.
* doc/org/autfilt.org: Augment the last example to point out
that it can now be done with ltlfilt.
* NEWS: Mention the new options.
2016-04-09 10:10:41 +02:00

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# -*- coding: utf-8 -*-
#+TITLE: =autfilt=
#+SETUPFILE: setup.org
#+HTML_LINK_UP: tools.html
The =autfilt= tool can filter, transform, and convert a stream of automata.
The tool operates a loop over 5 phases:
- input one automaton
- optionally preprocess the automaton
- optionally filter the automaton (i.e., decide whether to ignore the
automaton or continue with it)
- optionally postprocess the automaton
- output the automaton
The simplest way to use the tool is simply to use it for input and
output (i.e., format conversion) without any transformation and
filtering.
* Conversion between formats
=autfilt= can read automata written in the [[http://adl.github.io/hoaf/][Hanoi Omega Automata
Format]], as [[http://spinroot.com/spin/Man/never.html][Spin never claims]], using [[http://www.tcs.hut.fi/Software/lbtt/doc/html/Format-for-automata.html][LBTT's format]], or using
[[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]]. Automata in those formats (even a mix of those
formats) can be concatenated in the same stream, =autfilt= will
process them in batch. (The only restriction is that inside a file an
automaton in LBTT's format may not follow an automaton in
=ltl2dstar='s format.)
By default the output uses the HOA format. This can be changed using
[[file:oaut.org][the common output options]] like =--spin=, =--lbtt=, =--dot=,
=--hoaf=...
#+BEGIN_SRC sh :results silent :exports both
cat >example.hoa <<EOF
HOA: v1
States: 1
Start: 0
AP: 1 "p0"
Acceptance: 1 Inf(0)
--BODY--
State: 0
[0] 0 {0}
[!0] 0
--END--
EOF
autfilt example.hoa --dot
#+END_SRC
#+BEGIN_SRC sh :results verbatim :exports results
SPOT_DOTEXTRA= autfilt example.hoa --dot=
#+END_SRC
#+RESULTS:
: digraph G {
: rankdir=LR
: node [shape="circle"]
: I [label="", style=invis, width=0]
: I -> 0
: 0 [label="0"]
: 0 -> 0 [label="p0\n{0}"]
: 0 -> 0 [label="!p0"]
: }
The =--spin= options implicitly requires a degeneralization:
#+BEGIN_SRC sh :results verbatim :exports both
autfilt example.hoa --spin
#+END_SRC
#+RESULTS:
#+begin_example
never {
accept_init:
if
:: ((p0)) -> goto accept_init
:: ((!(p0))) -> goto T0_S2
fi;
T0_S2:
if
:: ((p0)) -> goto accept_init
:: ((!(p0))) -> goto T0_S2
fi;
}
#+end_example
#+BEGIN_SRC sh :results verbatim :exports both
autfilt example.hoa --lbtt
#+END_SRC
#+RESULTS:
: 1 1t
: 0 1
: 0 0 -1 p0
: 0 -1 ! p0
: -1
* Displaying statistics
One special output format of =autfilt= is the statistic output. For
instance the following command calls [[file:randaut.org][=randaut=]] to generate 10 random
automata, and pipe the result into =autfilt= to display various
statistics.
#+BEGIN_SRC sh :results verbatim :exports both
randaut -n 10 -A0..2 -Q10..20 -e0.05 2 |
autfilt --stats='%s states, %e edges, %a acc-sets, %c SCCs, det=%d'
#+END_SRC
#+RESULTS:
#+begin_example
16 states, 30 edges, 1 acc-sets, 3 SCCs, det=0
20 states, 42 edges, 2 acc-sets, 1 SCCs, det=0
15 states, 27 edges, 2 acc-sets, 1 SCCs, det=0
10 states, 17 edges, 1 acc-sets, 1 SCCs, det=1
13 states, 25 edges, 1 acc-sets, 1 SCCs, det=0
11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0
19 states, 41 edges, 2 acc-sets, 1 SCCs, det=0
11 states, 18 edges, 0 acc-sets, 1 SCCs, det=0
12 states, 21 edges, 1 acc-sets, 5 SCCs, det=0
18 states, 37 edges, 1 acc-sets, 5 SCCs, det=0
#+end_example
The following =%= sequences are available:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/^ %%/,/^$/p' | sed '$d'
#+END_SRC
#+RESULTS:
#+begin_example
%% a single %
%A, %a number of acceptance sets
%C, %c number of SCCs
%d 1 if the output is deterministic, 0 otherwise
%E, %e number of edges
%F name of the input file
%G, %g acceptance condition (in HOA syntax)
%L location in the input file
%M, %m name of the automaton
%n number of nondeterministic states in output
%p 1 if the output is complete, 0 otherwise
%r processing time (excluding parsing) in seconds
%S, %s number of states
%T, %t number of transitions
%w one word accepted by the output automaton
#+end_example
When a letter is available both as uppercase and lowercase, the
uppercase version refer to the input automaton, while the lowercase
refer to the output automaton. Of course this distinction makes sense
only if =autfilt= was instructed to perform an operation on the input
automaton.
* Filtering automata
=autfilt= supports multiple ways to filter automata based on different
characteristics of the automaton.
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Filtering options.*:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
--acc-sets=RANGE keep automata whose number of acceptance sets are
in RANGE
--accept-word=WORD keep automata that accept WORD
--ap=RANGE match automata with a number of atomic
propositions in RANGE
--are-isomorphic=FILENAME keep automata that are isomorphic to the
automaton in FILENAME
--edges=RANGE keep automata whose number of edges are in RANGE
--equivalent-to=FILENAME keep automata thare are equivalent
(language-wise) to the automaton in FILENAME
--included-in=FILENAME keep automata whose languages are included in that
of the automaton from FILENAME
--intersect=FILENAME keep automata whose languages have an non-empty
intersection with the automaton from FILENAME
--is-complete keep complete automata
--is-deterministic keep deterministic automata
--is-empty keep automata with an empty language
--is-inherently-weak keep only inherently weak automata
--is-terminal keep only terminal automata
--is-unambiguous keep only unambiguous automata
--is-weak keep only weak automata
--reject-word=WORD keep automata that reject WORD
--states=RANGE keep automata whose number of states are in RANGE
-u, --unique do not output the same automaton twice (same in
the sense that they are isomorphic)
-v, --invert-match select non-matching automata
#+end_example
For instance =--states=2..5 --acc-sets=3= will /keep/ only automata that
use 3 acceptance sets, and that have between 2 and 5 states.
Except for =--unique=, all these filters can be inverted. Using
=--states=2..5 --acc-sets=3 -v= will /drop/ all automata that use 3
acceptance sets and that have between 2 and 5 states, and keep the
others.
* Simplifying automata
The standard set of automata simplification routines (these are often
referred to as the "post-processing" routines, because these are the
procedures performed by [[file:ltl2tgba.org][=ltl2tgba=]] after translating a formula into a
TGBA) are available through the following options.
This set of options controls the desired type of output automaton:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Output automaton type:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: -B, --ba Büchi Automaton (with state-based acceptance)
: -C, --complete output a complete automaton
: -G, --generic any acceptance is allowed (default)
: -M, --monitor Monitor (accepts all finite prefixes of the given
: property)
: -S, --state-based-acceptance, --sbacc
: define the acceptance using states
: --tgba Transition-based Generalized Büchi Automaton
These options specify any simplification goal:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Simplification goal:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: -a, --any no preference, do not bother making it small or
: deterministic
: -D, --deterministic prefer deterministic automata
: --small prefer small automata
Finally, the following switches control the amount of effort applied
toward the desired goal:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Simplification level:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: --high all available optimizations (slow)
: --low minimal optimizations (fast)
: --medium moderate optimizations
By default, =--any --low= is used, which cause all simplifications to
be skipped. However if any goal is given, than the simplification level
defaults to =--high= (unless specified otherwise). If a simplification
level is given without specifying any goal, then the goal default to =--small=.
So if you want to reduce the size of the automaton, try =--small= and
if you want to try to make (or keep) it deterministic use
=--deterministic=.
Note that the =--deterministic= flag has two possible behaviors
depending on the constraints on the acceptance conditions:
- When =autfilt= is configured to work with generic acceptance (the
=--generic= option, which is the default), then the
=--deterministic= flag will do whatever it takes to output a
deterministic automaton, and this includes changing the acceptance
condition if needed (see below).
- If options =--tgba= or =--ba= are used, the =--deterministic= option
is taken as a /preference/: =autfilt= will try to favor determinism
in the output, but it may not always succeed and may output
non-deterministic automata. Note that if =autfilt --deterministic
--tgba= fails to output a deterministic automaton, it does not
necessarily implies that a deterministic TGBA does not exist: it
just implies that =autfilt= could not find it.
** Determinization
Spot has basically two ways to determinize automata, and that it uses
when =--deterministic= is passed.
- Automata that express obligation properties (this can be decided),
can be *determinized and minimized* into weak Büchi automata, as
discussed by [[http://www.daxc.de/eth/paper/atva07.pdf][Dax at al. (ATVA'07)]].
- Büchi automata (preferably with transition-based acceptance) can be
determinized into parity automata using a Safra-like procedure close
to the one presented by [[http://www.romanredz.se/papers/FI2012.pdf][Redziejowski (Fund. Inform. 119)]], with a few
additional tricks. This procedure does not necessarily produce a
minimal automaton.
When =--deterministic= is used, the first of these two procedures is
attempted on any supplied automaton. (It's even attempted for
deterministic automata, because that might reduce them.)
If that first procedure failed, and the input automaton is not
deterministic and =--generic= (the default for =autfilt=) is used,
then the second procedure is used. In this case, automata will be
first converted to transition-based Büchi automata if their condition
is more complex.
* Transformations
The following transformations are available:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Transformations:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
#+begin_example
--cleanup-acceptance remove unused acceptance sets from the automaton
--cnf-acceptance put the acceptance condition in Conjunctive Normal
Form
--complement complement each automaton (currently support only
deterministic automata)
--complement-acceptance complement the acceptance condition (without
touching the automaton)
--decompose-strength=t|w|s extract the (t) terminal, (w) weak, or (s)
strong part of an automaton (letters may be
combined to combine more strengths in the output)
--destut allow less stuttering
--dnf-acceptance put the acceptance condition in Disjunctive Normal
Form
--exclusive-ap=AP,AP,... if any of those APs occur in the automaton,
restrict all edges to ensure two of them may not
be true at the same time. Use this option
multiple times to declare independent groups of
exclusive propositions.
--instut[=1|2] allow more stuttering (two possible algorithms)
--keep-states=NUM[,NUM...] only keep specified states. The first state
will be the new initial state. Implies
--remove-unreachable-states.
--mask-acc=NUM[,NUM...] remove all transitions in specified acceptance
sets
--merge-transitions merge transitions with same destination and
acceptance
--product=FILENAME, --product-and=FILENAME
build the product with the automaton in FILENAME
to intersect languages
--product-or=FILENAME build the product with the automaton in FILENAME
to sum languages
--randomize[=s|t] randomize states and transitions (specify 's' or
't' to randomize only states or transitions)
--remove-ap=AP[=0|=1][,AP...]
remove atomic propositions either by existential
quantification, or by assigning them 0 or 1
--remove-dead-states remove states that are unreachable, or that cannot
belong to an infinite path
--remove-fin rewrite the automaton without using Fin
acceptance
--remove-unreachable-states
remove states that are unreachable from the
initial state
--sat-minimize[=options] minimize the automaton using a SAT solver
(only work for deterministic automata)
--separate-sets if both Inf(x) and Fin(x) appear in the acceptance
condition, replace Fin(x) by a new Fin(y) and
adjust the automaton
--simplify-exclusive-ap if --exclusive-ap is used, assume those AP
groups are actually exclusive in the system to
simplify the expression of transition labels
(implies --merge-transitions)
--strip-acceptance remove the acceptance condition and all acceptance
sets
#+end_example
* Examples
Here is an automaton with transition-based acceptance:
#+BEGIN_SRC sh :results silent :exports both
cat >aut-ex1.hoa<<EOF
HOA: v1
States: 3
Start: 0
AP: 2 "a" "b"
acc-name: Buchi
Acceptance: 4 Inf(0)&Fin(1)&Fin(3) | Inf(2)&Inf(3) | Inf(1)
--BODY--
State: 0 {3}
[t] 0
[0] 1 {1}
[!0] 2 {0}
State: 1 {3}
[1] 0
[0&1] 1 {0}
[!0&1] 2 {2}
State: 2
[!1] 0
[0&!1] 1 {0}
[!0&!1] 2 {0}
--END--
EOF
#+END_SRC
(Note: the '=.=' argument passed to =--dot= below hides default
options discussed [[file:oaut.org::#default-dot][on another page]], while the '=a=' causes the
acceptance condition to be displayed.)
#+NAME: autfilt-ex1
#+BEGIN_SRC sh :results verbatim :exports code
autfilt aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex1
#+begin_example
digraph G {
rankdir=LR
label=<(Fin(<font color="#F17CB0">❶</font>) &amp; Fin(<font color="#B276B2">❸</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>)) | (Inf(<font color="#FAA43A">❷</font>)&amp;Inf(<font color="#B276B2">❸</font>)) | Inf(<font color="#F17CB0">❶</font>)>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#B276B2">❸</font>>]
0 -> 1 [label=<a<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
0 -> 2 [label=<!a<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 [label="1"]
1 -> 0 [label=<b<br/><font color="#B276B2">❸</font>>]
1 -> 1 [label=<a &amp; b<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 -> 2 [label=<!a &amp; b<br/><font color="#FAA43A">❷</font><font color="#B276B2">❸</font>>]
2 [label="2"]
2 -> 0 [label=<!b>]
2 -> 1 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
2 -> 2 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex1.png :cmdline -Tpng :var txt=autfilt-ex1 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex1.png]]
Using =-S= will "push" the acceptance membership of the transitions to the states:
#+NAME: autfilt-ex2
#+BEGIN_SRC sh :results verbatim :exports code
autfilt -S aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex2
#+begin_example
digraph G {
rankdir=LR
label=<(Fin(<font color="#F17CB0">❶</font>) &amp; Fin(<font color="#B276B2">❸</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>)) | (Inf(<font color="#FAA43A">❷</font>)&amp;Inf(<font color="#B276B2">❸</font>)) | Inf(<font color="#F17CB0">❶</font>)>
labelloc="t"
node [shape="circle"]
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label=<0<br/><font color="#B276B2">❸</font>>]
0 -> 0 [label=<1>]
0 -> 1 [label=<a>]
0 -> 2 [label=<!a>]
1 [label=<1<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
1 -> 0 [label=<b>]
1 -> 6 [label=<a &amp; b>]
1 -> 7 [label=<!a &amp; b>]
2 [label=<2<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
2 -> 3 [label=<!b>]
2 -> 4 [label=<a &amp; !b>]
2 -> 5 [label=<!a &amp; !b>]
3 [label=<3>]
3 -> 0 [label=<1>]
3 -> 1 [label=<a>]
3 -> 2 [label=<!a>]
4 [label=<4<br/><font color="#5DA5DA">⓿</font>>]
4 -> 0 [label=<b>]
4 -> 6 [label=<a &amp; b>]
4 -> 7 [label=<!a &amp; b>]
5 [label=<5<br/><font color="#5DA5DA">⓿</font>>]
5 -> 3 [label=<!b>]
5 -> 4 [label=<a &amp; !b>]
5 -> 5 [label=<!a &amp; !b>]
6 [label=<6<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
6 -> 0 [label=<b>]
6 -> 6 [label=<a &amp; b>]
6 -> 7 [label=<!a &amp; b>]
7 [label=<7<br/><font color="#FAA43A">❷</font><font color="#B276B2">❸</font>>]
7 -> 3 [label=<!b>]
7 -> 4 [label=<a &amp; !b>]
7 -> 5 [label=<!a &amp; !b>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex2.png :cmdline -Tpng :var txt=autfilt-ex2 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex2.png]]
Using =--cnf-acceptance= simply rewrites the acceptance condition in Conjunctive Normal Form:
#+NAME: autfilt-ex3
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --cnf-acceptance aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex3
#+begin_example
digraph G {
rankdir=LR
label=<(Inf(<font color="#5DA5DA">⓿</font>) | Inf(<font color="#F17CB0">❶</font>) | Inf(<font color="#B276B2">❸</font>)) &amp; (Fin(<font color="#B276B2">❸</font>) | Inf(<font color="#F17CB0">❶</font>) | Inf(<font color="#FAA43A">❷</font>))>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#B276B2">❸</font>>]
0 -> 1 [label=<a<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
0 -> 2 [label=<!a<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 [label="1"]
1 -> 0 [label=<b<br/><font color="#B276B2">❸</font>>]
1 -> 1 [label=<a &amp; b<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 -> 2 [label=<!a &amp; b<br/><font color="#FAA43A">❷</font><font color="#B276B2">❸</font>>]
2 [label="2"]
2 -> 0 [label=<!b>]
2 -> 1 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
2 -> 2 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex3.png :cmdline -Tpng :var txt=autfilt-ex3 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex3.png]]
Using =--remove-fin= transforms the automaton to remove all traces
of Fin-acceptance: this usually requires adding non-deterministic jumps to
altered copies of strongly-connected components.
#+NAME: autfilt-ex4
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --remove-fin aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex4
#+begin_example
digraph G {
rankdir=LR
label=<Inf(<font color="#5DA5DA">⓿</font>) | Inf(<font color="#F17CB0">❶</font>) | (Inf(<font color="#FAA43A">❷</font>)&amp;Inf(<font color="#B276B2">❸</font>))>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#B276B2">❸</font>>]
0 -> 1 [label=<a<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
0 -> 2 [label=<!a<br/><font color="#B276B2">❸</font>>]
1 [label="1"]
1 -> 0 [label=<b<br/><font color="#B276B2">❸</font>>]
1 -> 1 [label=<a &amp; b<br/><font color="#B276B2">❸</font>>]
1 -> 2 [label=<!a &amp; b<br/><font color="#FAA43A">❷</font><font color="#B276B2">❸</font>>]
2 [label="2"]
2 -> 0 [label=<!b>]
2 -> 1 [label=<a &amp; !b>]
2 -> 2 [label=<!a &amp; !b>]
2 -> 3 [label=<!a &amp; !b>]
3 [label="3"]
3 -> 3 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex4.png :cmdline -Tpng :var txt=autfilt-ex4 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex4.png]]
Use =--mask-acc=NUM= to remove some acceptances sets and all
transitions they contain. The acceptance condition will be updated to
reflect the fact that these sets can never be visited.
#+NAME: autfilt-ex5
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --mask-acc=1,2 aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex5
#+begin_example
digraph G {
rankdir=LR
label=<Fin(<font color="#F17CB0">❶</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>)>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#F17CB0">❶</font>>]
0 -> 1 [label=<!a<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
1 [label="1"]
1 -> 0 [label=<!b>]
1 -> 2 [label=<a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
1 -> 1 [label=<!a &amp; !b<br/><font color="#5DA5DA">⓿</font>>]
2 [label="2"]
2 -> 0 [label=<b<br/><font color="#F17CB0">❶</font>>]
2 -> 2 [label=<a &amp; b<br/><font color="#5DA5DA">⓿</font><font color="#F17CB0">❶</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex5.png :cmdline -Tpng :var txt=autfilt-ex5 :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex5.png]]
Atomic propositions can be removed from an automaton in three ways:
- use ~--remove-ap=a~ to remove =a= by existential quantification, i.e., both =a= and its negation will be replaced by true.
This does not remove any transition.
- use ~--remove-ap=a=0~ to keep only transitions compatible with =!a= (i.e, transitions requiring =a= will be removed).
- use ~--remove-ap=a=1~ to keep only transitions compatible with =a= (i.e, transitions requiring =!a= will be removed).
Here are the results of these three options on our example:
#+NAME: autfilt-ex6a
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --remove-ap=a aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex6a
#+begin_example
digraph G {
rankdir=LR
label=<(Fin(<font color="#F17CB0">❶</font>) &amp; Fin(<font color="#B276B2">❸</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>)) | (Inf(<font color="#FAA43A">❷</font>)&amp;Inf(<font color="#B276B2">❸</font>)) | Inf(<font color="#F17CB0">❶</font>)>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#B276B2">❸</font>>]
0 -> 1 [label=<1<br/><font color="#F17CB0">❶</font><font color="#B276B2">❸</font>>]
0 -> 2 [label=<1<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 [label="1"]
1 -> 0 [label=<b<br/><font color="#B276B2">❸</font>>]
1 -> 1 [label=<b<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 -> 2 [label=<b<br/><font color="#FAA43A">❷</font><font color="#B276B2">❸</font>>]
2 [label="2"]
2 -> 0 [label=<!b>]
2 -> 1 [label=<!b<br/><font color="#5DA5DA">⓿</font>>]
2 -> 2 [label=<!b<br/><font color="#5DA5DA">⓿</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex6a.png :cmdline -Tpng :var txt=autfilt-ex6a :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex6a.png]]
#+NAME: autfilt-ex6b
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --remove-ap=a=0 aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex6b
#+begin_example
digraph G {
rankdir=LR
label=<(Fin(<font color="#F17CB0">❶</font>) &amp; Fin(<font color="#B276B2">❸</font>) &amp; Inf(<font color="#5DA5DA">⓿</font>)) | (Inf(<font color="#FAA43A">❷</font>)&amp;Inf(<font color="#B276B2">❸</font>)) | Inf(<font color="#F17CB0">❶</font>)>
labelloc="t"
fontname="Lato"
node [fontname="Lato"]
edge [fontname="Lato"]
node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
I [label="", style=invis, width=0]
I -> 0
0 [label="0"]
0 -> 0 [label=<1<br/><font color="#B276B2">❸</font>>]
0 -> 1 [label=<1<br/><font color="#5DA5DA">⓿</font><font color="#B276B2">❸</font>>]
1 [label="1"]
1 -> 0 [label=<!b>]
1 -> 1 [label=<!b<br/><font color="#5DA5DA">⓿</font>>]
}
#+end_example
#+BEGIN_SRC dot :file autfilt-ex6b.png :cmdline -Tpng :var txt=autfilt-ex6b :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex6b.png]]
#+NAME: autfilt-ex6c
#+BEGIN_SRC sh :results verbatim :exports code
autfilt --remove-ap=a=1 aut-ex1.hoa --dot=.a
#+END_SRC
#+RESULTS: autfilt-ex6c
#+BEGIN_SRC dot :file autfilt-ex6c.png :cmdline -Tpng :var txt=autfilt-ex6c :exports results
$txt
#+END_SRC
#+RESULTS:
[[file:autfilt-ex6c.png]]
#+BEGIN_SRC sh :results silent :exports results
rm -f example.hoa aut-ex1.hoa
#+END_SRC
The following example checks whether the formula ~a U b U c~ accepts
the word ~b; cycle{c}~.
#+BEGIN_SRC sh :results verbatim :exports both
ltl2tgba 'a U b U c' |
autfilt --accept-word 'b; cycle{c}' -q && echo "word accepted"
#+END_SRC
#+RESULTS:
: word accepted
Here is an example where we generate an infinite stream of random LTL
formulas using [[file:randltl.org][=randltl=]], convert them all to automata using
[[file:ltl2tgba.org][=ltl2tgba=]], filter out the first 10 automata that accept both the
words =a&!b;cycle{!a&!b}= and =!a&!b;cycle{a&b}= yet reject any word
of the form =cycle{b}=, and display the associated formula (which was
stored as the name of the automaton by =ltl2tgba=).
#+BEGIN_SRC sh :results verbatim :exports both
randltl -n -1 a b | ltlfilt --simplify --uniq | ltl2tgba -F- |
autfilt --accept-word='a&!b;cycle{!a&!b}' --accept-word='!a&!b;cycle{a&b}' \
--reject-word='cycle{b}' --stats=%M -n 10
#+END_SRC
#+RESULTS:
#+begin_example
F!b
!b
F(!a & !b)
(!a & (XX!a | (!a W F!b))) R !b
F(Fb R !b)
Fa R F!b
Fa U !b
!b & X(!b W Ga)
Fb R F!b
XF!b U (!b & (!a | G!b))
#+end_example
Note that the above example could be simplified using the
=--accept-word= and =--reject-word= options of =ltlfilt= directly.
However this demonstrates that using =--stats=%M=, it is possible to
filter formulas based on some properties of automata that have been
generated by from them. The translator needs not be =ltl2tgba=: other
tools can be wrapped with [[file:ltldo.org][=ltldo --name=%f=]] to ensure they work well
in a pipeline and preserve the formula name in the HOA output. For
example Here is a list of 5 LTL formulas that =ltl2dstar= converts to
Rabin automata that have exactly 4 states:
#+BEGIN_SRC sh :results verbatim :exports both
randltl -n -1 a b | ltlfilt --simplify --remove-wm |
ltldo ltl2dstar --name=%f | autfilt --states=4 --stats=%M -n 5
#+END_SRC
#+RESULTS:
: Gb | G!b
: b R (a | b)
: (a & !b & (b | (F!a U (!b & F!a)))) | (!a & (b | (!b & (Ga R (b | Ga)))))
: (a & (a U !b)) | (!a & (!a R b))
: a | G((a & GFa) | (!a & FG!a))
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