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Alexandre Duret-Lutz 4e025ecd2b org: Really fix example generation 
* doc/org/autfilt.org, doc/org/dstar2tgba.org, doc/org/hoa.org,
doc/org/ltlcross.org: Fix several typos.  In particular ":results" and
":exports" both end with s.
2015-07-17 23:43:01 +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]], or using [[http://www.tcs.hut.fi/Software/lbtt/doc/html/Format-for-automata.html][LBTT'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 output format can be controlled 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
: 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 --hoa -n 10 -A0..2 -Q10..20 -d0.05 2 |
autfilt --stats='%s states, %e edges, %a acc-sets, %c SCCs, det=%d'
#+END_SRC
#+RESULTS:
#+begin_example
16 states, 28 edges, 1 acc-sets, 1 SCCs, det=0
19 states, 37 edges, 0 acc-sets, 1 SCCs, det=0
16 states, 24 edges, 1 acc-sets, 1 SCCs, det=0
12 states, 16 edges, 0 acc-sets, 5 SCCs, det=0
12 states, 17 edges, 2 acc-sets, 3 SCCs, det=0
15 states, 21 edges, 2 acc-sets, 5 SCCs, det=0
10 states, 12 edges, 0 acc-sets, 4 SCCs, det=1
10 states, 14 edges, 1 acc-sets, 1 SCCs, det=0
19 states, 27 edges, 1 acc-sets, 1 SCCs, det=0
11 states, 12 edges, 1 acc-sets, 9 SCCs, det=1
#+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 pairs or 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
%n number of nondeterministic states in output
%p 1 if the output is complete, 0 otherwise
%r conversion time (including post-processings, but
not parsing) in seconds
%S, %s number of states
%T, %t number of transitions
#+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
--are-isomorphic=FILENAME keep automata that are isomorphic to the
automaton in FILENAME
--edges=RANGE keep automata whose number of edges are in RANGE
--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
--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
: --generic Any acceptance is allowed (default)
: -M, --monitor Monitor (accepts all finite prefixes of the given
: property)
: --tgba Transition-based Generalized Büchi Automaton
These options specifies desired properties:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Translation intent:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: -a, --any no preference, do not bother making it small or
: deterministic (default)
: -C, --complete output a complete automaton (combine with other
: intents)
: -D, --deterministic prefer deterministic automata
: --small prefer small automata
: -S, --state-based-acceptance, --sbacc
: define the acceptance using states
Finally, the following switches control the amount of effort applied
to reach the desired properties:
#+BEGIN_SRC sh :results verbatim :exports results
autfilt --help | sed -n '/Optimization level:/,/^$/p' | sed '1d;$d'
#+END_SRC
#+RESULTS:
: --high all available optimizations (slow)
: --low minimal optimizations (fast, default)
: --medium moderate optimizations
By default, =--any --low= is used, which cause all simplifications to
be skipped. If you want to reduce the size of the automaton, try
=--small --high= and if you want to try to make it deterministic
(their is to guaranty of result, this is only a preference), try
=--deterministic --high=.
* 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-acceptance complement the acceptance condition (without
touching the automaton)
--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 build the product with the automaton in FILENAME
--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
--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_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>>]
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>>]
}
#+end_example
#+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
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