4cf7503fff
Most of those errors were pointed out by the language-check tool. However while fixing those I found a few other issues that I fixed. In particular I updated the bibliographic reference for ltlsynt, added some DOI links for some cited papers that had no link, and fixed the broken introduction of ltlgrind. * doc/org/autcross.org, doc/org/autfilt.org, doc/org/citing.org, doc/org/compile.org, doc/org/concepts.org, doc/org/csv.org, doc/org/dstar2tgba.org, doc/org/genaut.org, doc/org/hierarchy.org, doc/org/install.org, doc/org/ioltl.org, doc/org/ltl2tgba.org, doc/org/ltl2tgta.org, doc/org/ltlcross.org, doc/org/ltldo.org, doc/org/ltlfilt.org, doc/org/ltlgrind.org, doc/org/ltlsynt.org, doc/org/oaut.org, doc/org/randaut.org, doc/org/randltl.org, doc/org/satmin.org, doc/org/tut01.org, doc/org/tut02.org, doc/org/tut03.org, doc/org/tut10.org, doc/org/tut11.org, doc/org/tut12.org, doc/org/tut20.org, doc/org/tut22.org, doc/org/tut24.org, doc/org/tut30.org, doc/org/tut40.org, doc/org/tut50.org, doc/org/tut51.org, doc/org/tut52.org, doc/org/tut90.org, doc/org/upgrade2.org: Fix errors. * bin/autfilt.cc, bin/common_aoutput.cc, bin/genaut.cc: Fix some typos in --help text that appeared in the above org files.
283 lines
9 KiB
Org Mode
283 lines
9 KiB
Org Mode
# -*- coding: utf-8 -*-
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#+TITLE: =randaut=
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#+DESCRIPTION: Spot command-line tool for generating random ω-automata.
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#+INCLUDE: setup.org
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#+HTML_LINK_UP: tools.html
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#+PROPERTY: header-args:sh :results verbatim :exports code
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The =randaut= tool generates random (connected) automata.
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By default, it will generate a random automaton with 10 states, no
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acceptance set, and using a set of atomic propositions you have to
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supply.
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#+NAME: randaut1
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#+BEGIN_SRC sh
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randaut a b --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut1.svg :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.svg]]
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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 =-Q= option. This
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option will accept a range as argument, so for instance =-Q3..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 =-e= (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 $Q$ states and density $e$, the degree of each
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state will follow a normal distribution with mean $1+(Q-1)d$ and
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variance $(Q-1)e(1-e)$.
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In particular =-e0= will cause all states to have 1 successor, and
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=-e1= will cause all states to be interconnected.
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#+NAME: randaut2
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#+BEGIN_SRC sh
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randaut -Q3 -e0 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut2.svg :var txt=randaut2 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut2.svg]]
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#+NAME: randaut3
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#+BEGIN_SRC sh
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randaut -Q3 -e1 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut3.svg :var txt=randaut3 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut3.svg]]
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* Acceptance condition
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The generation of the acceptance condition and acceptance sets is
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controlled with the following four parameters:
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- =-A ACCEPTANCE= (or =--acceptance=ACCEPTANCE=) controls both the
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acceptance condition, and the number of associated acceptance sets.
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The =ACCEPTANCE= argument is documented in =--help= as follows:
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#+BEGIN_SRC sh :exports results
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randaut --help | sed -n '/^ \(ACCEPTANCE\|RANGE\)/,/^$/p'
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#+END_SRC
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#+RESULTS:
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#+begin_example
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RANGE may have one of the following forms: 'INT', 'INT..INT', or '..INT'.
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In the latter case, the missing number is assumed to be 1.
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ACCEPTANCE may be either a RANGE (in which case generalized Büchi is
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assumed), or an arbitrary acceptance formula such as 'Fin(0)|Inf(1)&Fin(2)' in
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the same syntax as in the HOA format, or one of the following patterns:
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none
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all
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Buchi
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co-Buchi
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generalized-Buchi RANGE
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generalized-co-Buchi RANGE
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Rabin RANGE
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Streett RANGE
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generalized-Rabin INT RANGE RANGE ... RANGE
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parity (min|max|rand) (odd|even|rand) RANGE
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random RANGE
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random RANGE PROBABILITY
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The random acceptance condition uses each set only once, unless a probability
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(to reuse the set again every time it is used) is given.
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#+end_example
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When a range of the form $i..j$ is used, the actual value is taken randomly
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between $i$ and $j$ (included).
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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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- =-S= (or =--state-based-acceptance=) requests that the automaton
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use state-based acceptance. In this case, =-a= is the probability
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that a /state/ belong to the acceptance set. (Because Spot only
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deals with transition-based acceptance internally, this options
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force all transitions leaving a state to belong to the same
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acceptance sets. But if the output format allows state-based
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acceptance, it will be used.)
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- =--colored= requests that each transition (of state if combined with =-S=)
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in the generated automaton should belong to exactly one set (in that
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case =-a= is ignored, and =-A= must be used to specify an acceptance
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condition with at least one set).
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In addition, =-B= (or =--ba=) is a shorthand for =-A1 -S=,
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ans =-s= (or =--spin=) implies =-B=.
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#+NAME: randaut4
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#+BEGIN_SRC sh
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randaut -Q3 -e0.5 -A3 -a0.5 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut4.svg :var txt=randaut4 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut4.svg]]
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#+NAME: randaut5
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#+BEGIN_SRC sh
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randaut -Q3 -e0.4 -B -a0.7 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut5.svg :var txt=randaut5 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut5.svg]]
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#+NAME: randaut5b
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#+BEGIN_SRC sh
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randaut -Q6 -e0.4 -S -a.2 -A 'Streett 1..3' 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut5b.svg :var txt=randaut5b :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut5b.svg]]
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For generating random parity automata you should use the option
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=--colored= to make sure each transition (or state in the following
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example) belong to exactly one acceptance set. Note that you can
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specify a precise parity acceptance such as =parity min even 3=, or
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give =randaut= some freedom, as in this example.
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#+NAME: randaut5c
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#+BEGIN_SRC sh
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randaut -Q10 -S --colored -A 'parity rand rand 3..4' 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut5c.svg :var txt=randaut5c :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut5c.svg]]
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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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#+NAME: randaut6
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#+BEGIN_SRC sh
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randaut -D -Q3 -e0.6 -A2 -a0.5 2 --dot
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#+END_SRC
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#+BEGIN_SRC dot :file randaut6.svg :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.svg]]
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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 =-e= and =-Q= 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 [[file:oaut.org][the common output options]]
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like =--hoaf=, =--dot==, =--lbtt=, and =--spin=. Note that =--spin=
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automatically implies =--ba=.
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Automata are sent to standard output by default, by you can use =-o=
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to give a filename, or even a pattern for filenames. For instance the
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following generates 20 automata, but store them in different files
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according to the acceptance condition. The format =%g= represent the
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formula for the acceptance condition and would not make a nice
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filename, but =%[s]g= is a short name for that acceptance condition
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(its is replaced by "other" if Spot does not know better). We use
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=-Hl= to output one automaton per line, so that =wc -l= will count
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automata.
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#+BEGIN_SRC sh :exports both
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randaut -n20 -Q10 -A 'random 3' 2 -Hl -o 'randaut-%[s]g.hoa'
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wc -l randaut-*.hoa
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#+END_SRC
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#+RESULTS:
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: 1 randaut-Fin-less.hoa
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: 4 randaut-Rabin-like.hoa
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: 7 randaut-Streett-like.hoa
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: 2 randaut-generalized-Buchi.hoa
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: 1 randaut-generalized-Rabin.hoa
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: 1 randaut-generalized-Streett.hoa
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: 4 randaut-other.hoa
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: 20 total
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#+BEGIN_SRC sh :results silent :exports results
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rm -f rautaut-*.hoa
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#+END_SRC
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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 useful when piped to another tool
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that can process automata in batches.
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Here is an example were we use [[file:autfilt.org][=autfilt=]] to scan an infinite stream
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(=-n -1=) of random parity automata for the first automaton (=-n 1=)
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that have exactly 5 SCCs of particular natures: we want 1 trivial SCC
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(i.e. an SCC with no cycle), 1 rejecting SCC (an SCC without any
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accepting SCCs), 2 inherently weak SCCs (SCCs contains only rejecting
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cycles) among which one should be weak (all transitions should belong
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to the same sets). This leaves us with one extra SCC that should
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necessarily mix accepting and rejecting cycles.
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(Note: the '=.=' argument passed to =--dot= below hides default
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options discussed [[file:oaut.org::#default-dot][on another page]], while '=s=' causes SCCs to be
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displayed.)
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#+NAME: randaut7
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#+BEGIN_SRC sh
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randaut -n -1 --colored -A'parity min odd 4' a b |
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autfilt --sccs=5 --trivial-sccs=1 --rejecting-sccs=1 \
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--inherently-weak-sccs=2 --weak-sccs=1 -n 1 --dot=.s
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#+END_SRC
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#+BEGIN_SRC dot :file randaut7.svg :var txt=randaut7 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:randaut7.svg]]
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You should be able to find each of the expected type of SCCs in the above picture.
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The green rectangles mark the three SCCs that contain some accepting cycles.
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# LocalWords: utf randaut html args SRC svg txt randltl sed Buchi
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# LocalWords: acc ba rankdir hoaf lbtt Hl wc rautaut SCCs SCC sccs
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# LocalWords: A'parity
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