document autfilt and randaut
* NEWS: Mention these tools. * doc/org/autfilt.org, doc/org/randaut.org: New files. * doc/org/tools.org, doc/Makefile.am: Add them.
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Alexandre Duret-Lutz
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308
doc/org/randaut.org
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308
doc/org/randaut.org
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#+TITLE: =randaut=
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#+EMAIL spot@lrde.epita.fr
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#+OPTIONS: H:2 num:nil toc:t
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#+LINK_UP: tools.html
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The =randaut= tool generates random (connected) automata.
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By default, it will generate a random TGBA with 10 states, no
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acceptance sets, and using a set of atomic proposition you have to
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supply.
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut a b
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#+END_SRC
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#+NAME: randaut1
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut a b | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut1
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0", peripheries=2]
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1 -> 2 [label="!a & !b"]
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1 -> 3 [label="!a & b"]
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2 [label="4", peripheries=2]
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2 -> 4 [label="a & b"]
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2 -> 5 [label="a & b"]
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2 -> 3 [label="a & b"]
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2 -> 6 [label="!a & b"]
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3 [label="2", peripheries=2]
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3 -> 3 [label="a & b"]
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3 -> 7 [label="!a & b"]
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3 -> 2 [label="!a & b"]
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3 -> 6 [label="!a & b"]
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4 [label="6", peripheries=2]
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4 -> 8 [label="!a & !b"]
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4 -> 6 [label="!a & !b"]
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4 -> 7 [label="a & b"]
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4 -> 9 [label="!a & b"]
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5 [label="5", peripheries=2]
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5 -> 2 [label="!a & b"]
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5 -> 10 [label="a & !b"]
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6 [label="3", peripheries=2]
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6 -> 3 [label="!a & !b"]
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6 -> 9 [label="!a & !b"]
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7 [label="7", peripheries=2]
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7 -> 9 [label="!a & b"]
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8 [label="1", peripheries=2]
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8 -> 1 [label="!a & b"]
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8 -> 6 [label="!a & !b"]
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9 [label="8", peripheries=2]
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9 -> 3 [label="a & b"]
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9 -> 10 [label="a & b"]
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9 -> 7 [label="a & !b"]
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9 -> 8 [label="!a & b"]
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10 [label="9", peripheries=2]
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10 -> 10 [label="a & !b"]
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10 -> 5 [label="a & !b"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut1.png :cmdline -Tpng :var txt=randaut1 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut1.png]]
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As for [[file:randltl.org][=randltl=]], you can supply a number of atomic propositions
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instead of giving a list of atomic propositions.
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* States and density
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The numbers of states can be controlled using the =-S= option. This
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option will accept a range as argument, so for instance =-S3..6= will
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generate an automaton with 3 to 6 states.
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The number of edges can be controlled using the =-d= (or
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=--density=) option. The argument should be a number between 0 and 1.
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In an automaton with $S$ states and density $d$, the degree of each
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state will follow a normal distribution with mean $1+(S-1)d$ and
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variance $(S-1)d(1-d)$.
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In particular =-d0= will cause all states to have 1 successors, and
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=-d1= will cause all states to be interconnected.
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut -S3 -d0 2
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#+END_SRC
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#+NAME: randaut2
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut -S3 -d0 2 | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut2
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0", peripheries=2]
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1 -> 2 [label="!p0 & !p1"]
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2 [label="2", peripheries=2]
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2 -> 3 [label="!p0 & p1"]
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3 [label="1", peripheries=2]
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3 -> 2 [label="p0 & p1"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut2.png :cmdline -Tpng :var txt=randaut2 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut2.png]]
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut -S3 -d1 2
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#+END_SRC
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#+NAME: randaut3
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut -S3 -d1 2 | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut3
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0", peripheries=2]
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1 -> 2 [label="!p0 & !p1"]
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1 -> 1 [label="!p0 & !p1"]
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1 -> 3 [label="p0 & p1"]
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2 [label="2", peripheries=2]
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2 -> 2 [label="p0 & !p1"]
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2 -> 3 [label="p0 & !p1"]
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2 -> 1 [label="!p0 & !p1"]
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3 [label="1", peripheries=2]
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3 -> 1 [label="!p0 & !p1"]
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3 -> 3 [label="!p0 & !p1"]
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3 -> 2 [label="p0 & p1"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut3.png :cmdline -Tpng :var txt=randaut3 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut3.png]]
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* Acceptance sets
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The generation of acceptance sets is controlled with the following three parameters:
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- =-A= (or =--acc-sets=) controls the number of acceptance sets.
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This can be given as a range (e.g. =-A1..3=) in case you want this
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number to be picked at random in the range.
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- =-a= (or =--acc-probability=) controls the probability that any
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transition belong to a given acceptance set.
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- =--state-acc= requests that the automaton use state-based
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acceptance. In this case, =-a= is the probability that a /state/
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belong to the acceptance set. (Because Spot only deals with
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transition-based acceptance internally, this options force all
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transitions leaving a state to belong to the same acceptance sets.
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But if the output format allows state-acceptance, it will be used.)
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In addition, =-B= (or =--ba=) is a shorthand for =-A1 --state-acc=.
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut -S3 -d0.5 -A2 -a0.2 2
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#+END_SRC
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#+NAME: randaut4
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut -S3 -d0.5 -A2 -a0.2 2 | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut4
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0"]
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1 -> 2 [label="!p0 & !p1\\n{1}"]
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1 -> 3 [label="!p0 & p1"]
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2 [label="2"]
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2 -> 1 [label="!p0 & !p1\\n{0}"]
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2 -> 2 [label="!p0 & !p1"]
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3 [label="1"]
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3 -> 2 [label="!p0 & p1\\n{1}"]
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3 -> 3 [label="!p0 & p1"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut4.png :cmdline -Tpng :var txt=randaut4 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut4.png]]
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut -S3 -d0.4 -B -a0.5 2
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#+END_SRC
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#+NAME: randaut5
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut -S3 -d0.4 -B -a0.5 2 | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut5
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0", peripheries=2]
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1 -> 2 [label="!p0 & !p1\\n{0}"]
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1 -> 1 [label="!p0 & p1\\n{0}"]
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2 [label="2", peripheries=2]
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2 -> 3 [label="!p0 & p1\\n{0}"]
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2 -> 1 [label="p0 & !p1\\n{0}"]
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3 [label="1"]
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3 -> 3 [label="p0 & !p1"]
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3 -> 1 [label="p0 & !p1"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut5.png :cmdline -Tpng :var txt=randaut5 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut5.png]]
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* Determinism
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The output can only contain a single edge between two given states.
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By default, the label of this edge is a random assignment of all
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atomic propositions. Two edges leaving the same state may therefore
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have the same label.
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If the =-D= (or =--deterministic=) option is supplied, the labels
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are generated differently: once the degree $m$ of a state has been
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decided, the algorithm will compute a set of $m$ disjoint
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Boolean formulas over the given atomic propositions, such that the
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sum of all these formulas is $\top$. The resulting automaton is
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therefore deterministic and complete.
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#+BEGIN_SRC sh :results verbatim :exports code
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randaut -D -S3 -d0.6 -A2 -a0.5 2
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#+END_SRC
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#+NAME: randaut6
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#+BEGIN_SRC sh :results verbatim :exports none
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randaut -D -S3 -d0.6 -A2 -a0.5 2 | sed 's/\\/\\\\/'
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#+END_SRC
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#+RESULTS: randaut6
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#+begin_example
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digraph G {
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0 [label="", style=invis, height=0]
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0 -> 1
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1 [label="0"]
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1 -> 2 [label="p0\\n{1}"]
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1 -> 3 [label="!p0\\n{0,1}"]
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2 [label="1"]
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2 -> 3 [label="!p0 & p1"]
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2 -> 1 [label="!p0 & !p1\\n{0}"]
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2 -> 2 [label="p0\\n{0,1}"]
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3 [label="2"]
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3 -> 3 [label="p0 & p1\\n{1}"]
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3 -> 1 [label="p0 & !p1\\n{0}"]
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3 -> 2 [label="!p0"]
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}
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#+end_example
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#+BEGIN_SRC dot :file randaut6.png :cmdline -Tpng :var txt=randaut6 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut6.png]]
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Note that in a deterministic automaton with $a$ atomic propositions,
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it is not possible to have states with more than $2^a$ successors. If
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the combination of =-d= and =-S= allows the situation where a state
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can have more than $2^a$ successors, the degree will be clipped to
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$2^a$. When working with random deterministic automata over $a$
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atomic propositions, we suggest you always request more than $2^a$
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states.
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* Output formats
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The output format can be controlled using =--hoaf=, =--dot==,
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=--lbtt=, and =--spin=. Note that =--spin= automatically implies
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=--ba=.
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* Generating a stream of automata
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Use option =-n= to specify a number of automata to build. A negative
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value will cause an infinite number of automata to be produced. This
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generation of multiple automata is probably useful only with =--hoaf=,
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when piped to another tool that can read this format and process
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automata in batches.
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