bin: new ltlmix tool
Fixes #400. * spot/tl/randomltl.cc, spot/tl/randomltl.hh: Adjust to accept a set of formula to replace the atomic propositions. * bin/ltlmix.cc: New file. * bin/Makefile.am: Add it. * bin/man/ltlmix.x: New file. * bin/man/Makefile.am: Add it. * doc/org/ltlmix.org: New file. * doc/Makefile.am: Add it. * bin/man/genltl.x, bin/man/randltl.x, bin/man/spot.x, bin/spot.cc, doc/org/arch.tex, doc/org/concepts.org, doc/org/tools.org, NEWS: Mention ltlmix. * tests/core/ltlmix.test: New file. * tests/Makefile.am: Add it.
This commit is contained in:
Alexandre Duret-Lutz
parent
baf2778c9a
commit
c8b8ac60be
18 changed files with 995 additions and 87 deletions
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@ -22,18 +22,19 @@
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usedby/.style={->,ultra thick,>={Stealth[length=5mm,round]},gray!50!black}}
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\node[cppbox=14.12cm] (libspot) {\texttt{libspot\strut}};
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\node[shbox=3cm,above right=2mm and 0mm of libspot.north west,align=center] (shcmd) {
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\href{https://spot.lrde.epita.fr/randltl.html}{\texttt{randltl}}\\
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\href{https://spot.lrde.epita.fr/ltlfilt.html}{\texttt{ltlfilt}}\\
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\href{https://spot.lrde.epita.fr/randaut.html}{\texttt{randaut}}\\
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\href{https://spot.lrde.epita.fr/autfilt.html}{\texttt{autfilt}}\\
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\href{https://spot.lrde.epita.fr/ltl2tgba.html}{\texttt{ltl2tgba}}\\
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\href{https://spot.lrde.epita.fr/ltl2tgta.html}{\texttt{ltl2tgta}}\\
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\href{https://spot.lrde.epita.fr/dstar2tgba.html}{\texttt{dstar2tgba}}\\
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\href{https://spot.lrde.epita.fr/ltlcross.html}{\texttt{ltlcross}}\\
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\href{https://spot.lrde.epita.fr/ltlgrind.html}{\texttt{ltlgrind}}\\
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\href{https://spot.lrde.epita.fr/ltlsynt.html}{\texttt{ltlsynt}}\\
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\href{https://spot.lrde.epita.fr/ltldo.html}{\texttt{ltldo}}\\
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\href{https://spot.lrde.epita.fr/autcross.html}{\texttt{autcross}}
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\href{https://spot.lre.epita.fr/randltl.html}{\texttt{randltl}}\\
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\href{https://spot.lre.epita.fr/ltlmix.html}{\texttt{ltlmix}}\\
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\href{https://spot.lre.epita.fr/ltlfilt.html}{\texttt{ltlfilt}}\\
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\href{https://spot.lre.epita.fr/randaut.html}{\texttt{randaut}}\\
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\href{https://spot.lre.epita.fr/autfilt.html}{\texttt{autfilt}}\\
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\href{https://spot.lre.epita.fr/ltl2tgba.html}{\texttt{ltl2tgba}}\\
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\href{https://spot.lre.epita.fr/ltl2tgta.html}{\texttt{ltl2tgta}}\\
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\href{https://spot.lre.epita.fr/dstar2tgba.html}{\texttt{dstar2tgba}}\\
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\href{https://spot.lre.epita.fr/ltlcross.html}{\texttt{ltlcross}}\\
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\href{https://spot.lre.epita.fr/ltlgrind.html}{\texttt{ltlgrind}}\\
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\href{https://spot.lre.epita.fr/ltlsynt.html}{\texttt{ltlsynt}}\\
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\href{https://spot.lre.epita.fr/ltldo.html}{\texttt{ltldo}}\\
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\href{https://spot.lre.epita.fr/autcross.html}{\texttt{autcross}}
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};
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\node[cppbox=4.7cm,above right=0mm and 2mm of shcmd.south east] (libgen) {\texttt{libspotgen\strut}};
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\node[cppbox=2.5cm,above right=0mm and 2mm of libgen.south east] (buddy) {\texttt{libbddx\strut}};
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@ -41,8 +42,8 @@
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\node[cppbox=4cm,above right=0mm and 2mm of pyspot.south east] (libltsmin) {\texttt{libspotltsmin\strut}};
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\node[shbox=1.5cm,above right=2mm and 0mm of libgen.north west,align=center] (genaut) {
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\href{https://www.lrde.epita.fr/genaut.html}{\texttt{genaut\strut}}\\
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\href{https://www.lrde.epita.fr/genltl.html}{\texttt{genltl}}
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\href{https://www.lre.epita.fr/genaut.html}{\texttt{genaut\strut}}\\
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\href{https://www.lre.epita.fr/genltl.html}{\texttt{genltl}}
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};
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\node[pybox=3cm,above left=2mm and 0mm of libgen.north east] (pygen) {\texttt{import spot.gen\strut}};
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@ -158,7 +158,7 @@ $txt
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#+END_SRC
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#+RESULTS:
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[[file:concept-buchi.svg]]
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[[file:concept-buchi2.svg]]
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The =1= displayed on the edge that loops on state =1= should be
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read as /true/, i.e., the Boolean formula that accepts
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365
doc/org/ltlmix.org
Normal file
365
doc/org/ltlmix.org
Normal file
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@ -0,0 +1,365 @@
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# -*- coding: utf-8 -*-
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#+TITLE: =ltlgrind=
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#+DESCRIPTION: Spot command-line tool for combining LTL formulas randomly
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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 both
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This tool creates new formulas by combining formulas randomly selected
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from an input set of formulas. Some authors have argued that for some
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tasks, like [[https://www.cs.rice.edu/~vardi/papers/time13.pdf][LTL satisfiability]], working with randomly generated
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formulas is often easy, because random formulas tend to simplify
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trivially. =ltlmix= allows you to take a set of formulas, usually
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some handwritten, meaningful formulas, and combine those formulas to
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build larger sets that are possibly more challenging.
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Here is a very simple example that builds five formulas that are
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Boolean combination of formulas from taken in the set
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$\{\mathsf{GF}a,\mathsf{FG}b,\mathsf{X}c\}$:
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#+BEGIN_SRC sh :exports both
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ltlmix -f GFa -f FGb -f Xc -n 5
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#+END_SRC
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#+RESULTS:
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: !FGb xor !Xc
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: !GFa -> !FGb
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: FGb | (FGb -> Xc)
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: FGb
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: GFa & (FGb | Xc)
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* Shape of the generated formulas
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** Size of the syntax tree
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For each formula that it generates, =ltlmix= constructs a random
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syntax-tree of a certain size (5 by default) in which internal nodes
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represent operators selected randomly from a list of operator, and
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leaves are subformulas selected randomly from the set of input
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formulas. As an example, the syntax tree of =!φ₁ xor !φ₂= has size 5,
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and its leaves =φ₁= and =φ₂= will be taken randomly from the set of
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input formulas.
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The algorithm is actually the same as for =randltl=, except
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that =randltl= use random atomic propositions as leaves when =ltlmix=
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uses random formulas.
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The same input formula can be picked several times to be used on
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multiple leaves of the tree. Note that because Spot implements some
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trivial rewritings directly during the construction of any formula,
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formulas like =FGb | !!FGb= (which correspond to a tree of size 5 in
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the above example) cannot be represented: they are automatically
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simplified to =FGb=. Similarly, something like =φ xor φ= will be
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output as =0=.
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The size of the tree can be changed using the =--tree-size= option.
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#+BEGIN_SRC sh :exports both
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for i in 1 2 3 4 5 6 7 8 9 10 11 12; do
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ltlmix -fXa -fGb -fFc -fXd -fGe --tree-size=$i
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done
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Fc
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!Xd
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0
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Ge xor !Fc
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!Xd xor !Ge
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!Xd xor (Fc | Xd)
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!Ge
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Ge xor (!Ge -> Gb)
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Ge xor (!Xa -> !Fc)
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(Ge & !Fc) xor (!Gb xor !Ge)
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(Ge & !Fc) xor (!Gb xor (Gb | Fc))
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(Ge & (Gb xor Xd)) xor (!Fc -> (Gb | Fc))
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#+end_example
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The above shows that while the size of the syntax tree generally grows
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along with =--tree-size= there are several cases where it reduces
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trivially.
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** Operator priorities
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It is possible to control the set of operators used in the generation.
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The first step is to obtain that list of operators with =--dump-priorities=.
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For instance:
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#+BEGIN_SRC sh :exports both
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ltlmix -fXa -fGb -fFc -fXd -fGe --dump-priorities
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Use --boolean-priorities to set the following Boolean formula priorities:
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sub 5
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false 0
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true 0
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not 1
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equiv 1
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implies 1
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xor 1
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and 1
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or 1
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#+end_example
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In the above list, =false= and =true= represent the Boolean constants
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(which are usually undesirable when building random Boolean formulas),
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and =sub= represent a random formula drawn from the list of input
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formulas.
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The above command shows that each operator has a weight, called
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/priority/. When the priority is 0, the operator is never used. When
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=ltlmix= generates a syntax tree of size N, it looks among all
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operators that can be used at the root of such a tree, and performs a
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weighted random selection. In other words, an operator with priority
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=2= will be twice more likely to be selected than an operator with
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priority =1=.
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Those priorities can be changed with =--boolean-priorities= as in the
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following example, which disables =xor= and makes =<->= thrice more
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likely to appear.
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#+BEGIN_SRC sh :exports both
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for i in 1 2 3 4 5 6 7 8 9 10 11 12; do
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ltlmix -fXa -fGb -fFc -fXd -fGe --tree-size=$i --boolean-prio='xor=0,equiv=3'
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done
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Fc
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!Xd
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1
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Ge <-> !Fc
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!Xd <-> !Ge
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!Xd <-> (Fc | Xd)
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Ge
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Ge <-> (Gb <-> !Ge)
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Ge <-> (!Fc <-> !Xa)
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(Ge & !Fc) <-> (!Ge -> !Gb)
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(Ge & !Fc) <-> ((Gb | Fc) -> !Gb)
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(Ge & (Gb <-> Xd)) <-> ((Gb | Fc) <-> !Fc)
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#+end_example
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** Boolean or LTL syntax tree
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By default, the syntax tree generated on top of the randomly selected
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input formula uses only Boolean operators.
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Using option =-L= will use LTL operators instead.
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#+BEGIN_SRC sh :exports both
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ltlmix -fXa -fGb -fFc --tree-size=10 -L -n10
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Gb R (XFc W 0)
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!(Gb | !Xa)
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1 U !X(0)
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(Xa xor Gb) -> (GXa M Fc)
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GFc M 1
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(Fc U Gb) -> (0 R Xa)
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!Gb <-> (Gb | GFc)
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1
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GFc | (1 U Xa)
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!(Xa | GFc)
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#+end_example
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The following operators are used:
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#+BEGIN_SRC sh :exports both
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ltlmix -fXa -fGb -fFc -fXd -fGe -L --dump-priorities
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Use --ltl-priorities to set the following LTL priorities:
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sub 5
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false 1
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true 1
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not 1
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F 1
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G 1
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X 1
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equiv 1
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implies 1
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xor 1
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R 1
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U 1
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W 1
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M 1
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and 1
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or 1
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#+end_example
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Note that in the LTL case, =false= and =true= can be generated by default.
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* Randomizing atomic propositions with =-A= or =-P=
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Options =-A= or =-P= can be used to change the atomic propositions
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used in the input formulas. This works as follows: if =-A N= was
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given, every time an input formula φ is selected, its atomic
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propositions are replaced by atomic propositions randomly selected in
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a set of size $N$. If φ uses $i$ atomic propositions and $i\ge N$,
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then those $i$ atomic proposition will be remapped to $i$ distinct
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atomic propositions chosen randomly in that set. if $i>N$, some of
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the new atomic propositions may replace several of the original atomic
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propositions.
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Option =-P N= is similar to =-A N= except that the selected atomic
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propositions can possibly be negated.
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These options solve two problems:
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- They lessen the issue that a formula selected several times can lead
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to syntax tree such as =φ | φ | φ= that reduces to =φ=. Now, each
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occurrence of =φ= as a chance to use different atomic propositions.
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(the larger =N= is, the more likely it is that these copies of φ
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will be different).
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- They allow combining formulas that had completely different sets of
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atomic propositions, in such a way that they are now interdependent
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(the smaller N is the more likely it is that subformulas will share
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atomic propositions).
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Here is an example with a single formula, =GFa=, whose atomic proposition
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will be randomly replaced by one of $\{p_0,p_1,p_2,p_3,p_4\}$.
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#+BEGIN_SRC sh :exports both
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ltlmix -fGFa -A5 --tree-size=8 -n10
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#+END_SRC
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#+RESULTS:
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#+begin_example
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(GFp2 & GFp3) xor (!GFp0 xor GFp1)
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(GFp4 -> GFp1) -> !GFp2
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!GFp4 | ((GFp2 & GFp3) -> GFp2)
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!GFp2 | (GFp3 <-> (GFp2 & GFp1))
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!GFp0 | GFp4
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!(GFp2 & GFp1) <-> (GFp3 xor GFp0)
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(GFp2 xor GFp0) | (GFp4 -> !GFp0)
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(GFp4 | !GFp3) -> GFp4
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!GFp0 -> (GFp2 | GFp1)
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!GFp1 <-> (!GFp2 xor !GFp1)
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#+end_example
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Here is a similar example, with polarized atomic propositions instead:
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#+BEGIN_SRC sh :exports both
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ltlmix -fGFa -P5 --tree-size=8 -n10
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#+END_SRC
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#+RESULTS:
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#+begin_example
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(GFp2 & GF!p3) xor (GFp4 -> !GF!p1)
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(GFp4 | !GFp2) -> (GFp1 -> GF!p1)
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!GF!p2 & (GF!p0 xor (GF!p0 -> GF!p3))
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GFp1 <-> (GF!p3 | !GFp0)
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GF!p1 & GFp0 & (GF!p3 xor !GF!p4)
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(GF!p1 xor GF!p2) | (GF!p3 & !GF!p4)
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!(GFp4 xor (!GF!p2 | !GF!p3))
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GFp0 | (!GFp1 -> (GFp1 -> GF!p4))
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GF!p1 xor (!GF!p2 | (GF!p1 <-> GFp0))
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!((GF!p2 <-> GF!p4) & (GFp1 xor GF!p2))
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#+end_example
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* More serious examples
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** Mixing the DAC patterns
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The command [[file:genltl.org][=genltl --dac-pattern=]] will print a list of 55 LTL
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formulas representing various specification patterns listed by Dwyer
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et al. (FMSP'98). Using =--stat=%x= to count the atomic propositions
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in each formula, and some standard unix tools, we can compute that
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they use at most 6 atomic propositions.
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#+BEGIN_SRC sh :exports both
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genltl --dac-pattern --stat=%x | sort -n | tail -n 1
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#+END_SRC
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#+RESULTS:
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: 6
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Based on this, we could decide to generate Boolean combination of
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those formulas while replacing atomic propositions by literals built
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out of a set of 10 atomic propositions (chosen larger than 6 to ensure
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that each individual formula will still make sense after the change of
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atomic propositions).
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#+BEGIN_SRC sh :exports both
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genltl --dac-pattern | ltlmix -n8 -P10
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#+END_SRC
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#+RESULTS:
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: !G((p8 & F!p7) -> (!p4 U (!p7 | (!p2 & !p4 & X(!p4 U p1))))) xor !G(!p3 -> ((p4 & !p7) U (!p4 | ((p4 & p7) U (!p4 | ((p4 & !p7) U (!p4 | ((p4 & p7) U (!p4 | (!p7 W !p4) | Gp7)))))))))
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: !G(!p3 -> Gp5) xor !G(!p7 -> G(p9 -> (!p5 & !p8 & X(!p5 U p2))))
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: G(p6 -> ((!(!p1 & p7 & X(!p1 U (!p1 & !p3))) U (p1 | !p2)) | G!(p7 & XF!p3))) & (G((!p4 & XF!p5) -> XF(!p5 & F!p0)) <-> G((p5 & !p6) -> (p5 W (p5 & p7))))
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: !G((p0 & p9) -> (!p7 W (!p0 | p4))) & !G((p1 & !p2) -> (!p8 W p2))
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: ((Fp2 -> ((!p1 -> (!p2 U (p0 & !p2))) U p2)) -> G(p1 -> G(p9 -> (!p4 & p8 & X(!p4 U !p7))))) xor G(p1 -> Gp9)
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: !G((p5 & !p9 & F!p5) -> ((!p8 -> (p5 U (!p0 & p5))) U !p5)) -> !G((p6 & p9) -> (!p7 W !p9))
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: G((!p1 & !p2) -> (p9 W p1)) <-> (G(p5 -> G(p0 -> F!p4)) -> (Fp6 -> ((!p5 & !p6) U (p6 | ((p5 & !p6) U (p6 | ((!p5 & !p6) U (p6 | ((p5 & !p6) U (p6 | (!p5 U p6)))))))))))
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: ((Fp1 -> ((p6 -> (!p1 U (!p1 & !p2 & X(!p1 U !p9)))) U p1)) <-> (F!p0 -> (p0 U (p0 & !p7 & X(p0 U !p9))))) | (Fp2 -> (p6 U (p2 | (p6 & !p7 & X(p6 U p1)))))
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Now we might want to clean this list a bit by relabeling each formula
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so is uses atomic propositions $\{p_0,p_1,...\}$ starting at 0 and without gap.
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#+BEGIN_SRC sh :exports both
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genltl --dac-pattern | ltlmix -n8 -P10 | ltlfilt --relabel=pnn
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#+END_SRC
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#+RESULTS:
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: !G((p0 & F!p1) -> (!p2 U (!p1 | (!p2 & !p3 & X(!p2 U p4))))) xor !G(!p5 -> ((!p1 & p2) U (!p2 | ((p1 & p2) U (!p2 | ((!p1 & p2) U (!p2 | ((p1 & p2) U (!p2 | (!p1 W !p2) | Gp1)))))))))
|
||||
: !G(!p0 -> Gp1) xor !G(!p2 -> G(p3 -> (!p1 & !p4 & X(!p1 U p5))))
|
||||
: G(p0 -> ((!(!p1 & p2 & X(!p1 U (!p1 & !p3))) U (p1 | !p4)) | G!(p2 & XF!p3))) & (G((!p5 & XF!p6) -> XF(!p6 & F!p7)) <-> G((!p0 & p6) -> (p6 W (p2 & p6))))
|
||||
: !G((p0 & p1) -> (!p2 W (!p0 | p3))) & !G((p4 & !p5) -> (!p6 W p5))
|
||||
: ((Fp0 -> ((!p1 -> (!p0 U (!p0 & p2))) U p0)) -> G(p1 -> G(p3 -> (!p4 & p5 & X(!p4 U !p6))))) xor G(p1 -> Gp3)
|
||||
: !G((p0 & !p1 & F!p0) -> ((!p2 -> (p0 U (p0 & !p3))) U !p0)) -> !G((p1 & p4) -> (!p5 W !p1))
|
||||
: G((!p0 & !p1) -> (p2 W p0)) <-> (G(p3 -> G(p4 -> F!p5)) -> (Fp6 -> ((!p3 & !p6) U (p6 | ((p3 & !p6) U (p6 | ((!p3 & !p6) U (p6 | ((p3 & !p6) U (p6 | (!p3 U p6)))))))))))
|
||||
: ((Fp0 -> ((p1 -> (!p0 U (!p0 & !p2 & X(!p0 U !p3)))) U p0)) <-> (F!p4 -> (p4 U (p4 & !p5 & X(p4 U !p3))))) | (Fp2 -> (p1 U (p2 | (p1 & !p5 & X(p1 U p0)))))
|
||||
|
||||
** Random conjunctions
|
||||
|
||||
Some benchmark (e.g., [[https://www.cs.rice.edu/~vardi/papers/time13.pdf][for LTL satisfiability]]) are built by conjunction
|
||||
of $L$ random formulas picked from a set of basic formulas. Each
|
||||
picked formula has its atomic proposition mapped to random literals
|
||||
built from a subset of $m$ atomic variables.
|
||||
|
||||
Given a value for $m$, option =-P m= will achieve the second part of
|
||||
the above description. To build a conjunction of $L$ formulas, we
|
||||
need to ask for a tree of size $2L-1$ in which only the =and= operator
|
||||
is allowed.
|
||||
|
||||
Here is an example with $L=10$ (hence =--tree-size=19=) and $m=50$.
|
||||
The example use a small set of three basic formulas
|
||||
$\{\mathsf{G}a,\mathsf{F}a,\mathsf{X}a\}$ for illustration, but in
|
||||
practice you should replace these =-f= options by =-F FILENAME=
|
||||
pointing to a file containing all the input formulas to select from.
|
||||
|
||||
#+BEGIN_SRC sh :exports both
|
||||
ltlmix -fGa -fFa -fXa -n10 -P50 \
|
||||
--tree-size=19 --boolean-prio=not=0,or=0,xor=0,equiv=0,implies=0
|
||||
#+END_SRC
|
||||
|
||||
#+RESULTS:
|
||||
#+begin_example
|
||||
Xp27 & F!p21 & G!p19 & X!p26 & Fp4 & Gp43 & Fp39 & Fp7
|
||||
G!p28 & G!p30 & X!p34 & Fp21 & Gp3 & Fp6 & F!p18 & Xp5 & Fp8 & F!p12
|
||||
X!p32 & Xp9 & Gp4 & Xp48 & F!p48 & X!p6 & Fp5 & Xp20 & Fp28 & Fp26
|
||||
G!p46 & X!p14 & Fp29 & X!p36 & Fp12 & Xp47 & Fp42 & Gp14 & Fp19
|
||||
G!p28 & Fp21 & Fp36 & F!p0 & G!p14 & Xp21 & F!p28 & G!p21 & Gp21 & Gp40
|
||||
Gp3 & F!p48 & F!p28 & Xp7 & Gp8 & Xp42 & Gp0 & Xp36 & F!p2 & G!p0
|
||||
Xp36 & Xp46 & F!p31 & Xp11 & Xp26 & G!p9 & F!p36 & X!p12 & Fp15 & Xp18
|
||||
Xp9 & X!p33 & Fp44 & X!p13 & Gp37 & Xp19 & G!p43 & F!p34 & Gp36 & Gp10
|
||||
Xp27 & Xp5 & Fp28 & Xp18 & G!p13 & Gp35 & Gp38 & G!p45 & G!p48 & Gp12
|
||||
Xp7 & G!p48 & Xp14 & Fp24 & Xp43 & Fp47 & Fp14 & Gp30 & Xp23 & G!p31
|
||||
#+end_example
|
||||
|
||||
Selecting 10 random conjuncts out of 3×50×2=300 possibilities has a
|
||||
13.7% chance that at least 2 conjuncts will be identical (see [[https://en.wikipedia.org/wiki/Birthday_problem][Birthday
|
||||
paradox]]), so because of Spot's trivial rewritings, some hove the above
|
||||
formulas may have fewer than 10 conjuncts.
|
||||
|
|
@ -41,6 +41,7 @@ corresponding commands are hidden.
|
|||
* Command-line tools
|
||||
|
||||
- [[file:randltl.org][=randltl=]] Generate random LTL/PSL formulas.
|
||||
- [[file:ltlmix.org][=ltlmix=]] Combine LTL/PSL formulas taken randomly from some input set.
|
||||
- [[file:ltlfilt.org][=ltlfilt=]] Filter, convert, and transform LTL/PSL formulas.
|
||||
- [[file:genltl.org][=genltl=]] Generate LTL formulas from scalable patterns.
|
||||
- [[file:ltl2tgba.org][=ltl2tgba=]] Translate LTL/PSL formulas into various types of automata.
|
||||
|
|
@ -77,6 +78,7 @@ convenience, you can browse their HTML versions:
|
|||
[[./man/ltldo.1.html][=ltldo=]](1),
|
||||
[[./man/ltlfilt.1.html][=ltlfilt=]](1),
|
||||
[[./man/ltlgrind.1.html][=ltlgrind=]](1),
|
||||
[[./man/ltlmix.1.html][=ltlmix=]](1),
|
||||
[[./man/ltlsynt.1.html][=ltlsynt=]](1),
|
||||
[[./man/randaut.1.html][=randaut=]](1),
|
||||
[[./man/randltl.1.html][=randltl=]](1),
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue