61602a3bba
Suggested in #299. * doc/org/autfilt.org, doc/org/concepts.org, doc/org/dstar2tgba.org, doc/org/genaut.org, doc/org/hierarchy.org, doc/org/hoa.org, doc/org/ltl2tgba.org, doc/org/ltl2tgta.org, doc/org/ltlcross.org, doc/org/oaut.org, doc/org/randaut.org, doc/org/satmin.org, doc/org/tut11.org, doc/org/tut23.org, doc/org/tut24.org, doc/org/tut30.org, doc/org/tut31.org, doc/org/tut50.org, doc/org/tut51.org: Adjust all dot outputs to produce svg. * doc/org/arch.tex, doc/org/hierarchy.tex, doc/org/satmin.tex: Adjust to produce a pdf with 12pt text. * doc/Makefile.am: Adjust the generation of arch.svg, hierarchy.svg, and satmin.svg: From above. * doc/org/.dir-locals.el.in, doc/org/init.el.in: Adjust dot arguments to produce svg with 12pt text (the default was 14pt). * doc/org/spot.css: Use Lato as the main font for consistency with automata. * HACKING: pdf2svg is now required to build the doc.
223 lines
6.7 KiB
Org Mode
223 lines
6.7 KiB
Org Mode
# -*- coding: utf-8 -*-
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#+TITLE: =ltl2tgta=
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#+DESCRIPTION: Spot command-line tool for translating LTL into Transition-based Generalized Testing Automata.
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#+SETUPFILE: setup.org
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#+HTML_LINK_UP: tools.html
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This tool generates various form of Testing Automata, i.e., automata
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that observe the /changes/ of atomic propositions, not their values.
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Three types of automata can be output. The only output format
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supported currently is [[http://www.graphviz.org/][GraphViz]]'s format, with option =-8= to enable
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UTF-8 characters as in other tools.
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The =--ta= option will translate a formula into Testing Automaton, as
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described by [[http://spinroot.com/spin/Workshops/ws06/039.pdf][Geldenhuys and Hansen (Spin'06)]].
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Here is the output on =a U Gb= (we omit the call to =dot=, as shown while
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discussing [[file:ltl2tgba.org][=ltl2tgba=]]).
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#+NAME: augb-ta
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgta --ta --multiple-init 'a U Gb'
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#+END_SRC
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#+RESULTS: augb-ta
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#+begin_example
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digraph G {
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rankdir=LR
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node [style="filled", fillcolor="#ffffa0"]
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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edge[arrowhead=vee, arrowsize=.7]
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-1 [label="", style=invis, height=0]
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-1 -> 1 [label="!a & b"]
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-2 [label="", style=invis, height=0]
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-2 -> 2 [label="a & !b"]
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-3 [label="", style=invis, height=0]
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-3 -> 3 [label="a & b"]
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1 [label="2\n!a & b",shape=box]
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1 -> 4 [label="{a}\n"]
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2 [label="1\na & !b"]
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2 -> 3 [label="{b}\n"]
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2 -> 1 [label="{a, b}\n"]
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3 [label="0\na & b",shape=box]
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3 -> 4 [label="{a}\n"]
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3 -> 1 [label="{a}\n"]
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3 -> 2 [label="{b}\n"]
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4 [label="3",peripheries=2,shape=box]
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4 -> 4 [label="{a}\n{0}"]
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}
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#+end_example
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#+BEGIN_SRC dot :file augb-ta.svg :var txt=augb-ta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:augb-ta.svg]]
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As always, the labels of the states have no influence on the language
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recognized by the automaton. This automaton has three possible
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initial states. The initial state should be chosen depending on the
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initial valuation of =a= and =b= in the system to be synchronized with
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this testing automaton. For instance if =a= is true and =b= false in
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the initial state, the testing automaton should start in the state
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pointed to by the initial arrow labeled =a & !b=. In the rest of the
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testing automaton, the transitions are labeled by the sets of atomic
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propositions that should change in the system for the testing
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automaton to progress. States with a double enclosure are Büchi
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accepting, meaning that any execution that visits one of these states
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is accepting. All states have an implicit self-loop labeled by ={}=:
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if the system progress without changing the value of =a= and =b=, the
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testing automaton remains in the same state. Rectangle states are
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livelock-accepting: any execution of the system that get stuck into
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one of these state is accepting.
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Without the =--multiple-init= option, a fake initial state is added.
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This is the default since it often makes the result more readable.
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#+NAME: augb-ta2
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgta --ta 'a U Gb'
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#+END_SRC
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#+RESULTS:
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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=init]
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1 -> 2 [label="!a & b\n"]
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1 -> 3 [label="a & b\n"]
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1 -> 4 [label="a & !b\n"]
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2 [label="2",shape=box]
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2 -> 5 [label="{a}\n"]
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3 [label="3",shape=box]
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3 -> 5 [label="{a}\n"]
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3 -> 2 [label="{a}\n"]
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3 -> 4 [label="{b}\n"]
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4 [label="1"]
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4 -> 3 [label="{b}\n"]
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4 -> 2 [label="{a, b}\n"]
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5 [label="4",peripheries=2,shape=box]
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5 -> 5 [label="{a}\n{0}"]
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}
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#+end_example
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#+BEGIN_SRC dot :file augb-ta2.svg :var txt=augb-ta2 :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:augb-ta2.svg]]
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The =--gba= option can be used to request a Generalized Testing
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Automaton, i.e., a Testing Automaton with Generalized Büchi
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acceptance. In that case double-enclosures are not used anymore, and
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Büchi accepting transitions are marked with the same ={0,1}=
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notation used in TGBA.
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#+NAME: gfagfb-gta
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgta --gta 'GFa & GFb'
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#+END_SRC
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#+RESULTS:
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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=init]
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1 -> 2 [label="a & b\n"]
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1 -> 3 [label="!a & b\n"]
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1 -> 4 [label="a & !b\n"]
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1 -> 5 [label="!a & !b\n"]
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2 [label="1",shape=box]
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2 -> 3 [label="{a}\n{0,1}"]
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2 -> 4 [label="{b}\n{0,1}"]
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2 -> 5 [label="{a, b}\n{0,1}"]
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3 [label="3"]
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3 -> 2 [label="{a}\n{1}"]
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3 -> 4 [label="{a, b}\n{1}"]
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3 -> 5 [label="{b}\n{1}"]
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4 [label="2"]
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4 -> 2 [label="{b}\n{0}"]
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4 -> 3 [label="{a, b}\n{0}"]
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4 -> 5 [label="{a}\n{0}"]
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5 [label="4"]
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5 -> 2 [label="{a, b}\n"]
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5 -> 3 [label="{b}\n"]
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5 -> 4 [label="{a}\n"]
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}
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#+end_example
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#+BEGIN_SRC dot :file gfagfb-gta.svg :var txt=gfagfb-gta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:gfagfb-gta.svg]]
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The interpretation is similar to that of the TA. Execution that
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stutter in a livelock-accepting (square) state are accepting as well
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as execution that visit the =0= and =1= acceptance sets
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infinitely often. Those acceptance sets are carried by transitions,
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as in TGBAs.
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Finally, the default is to output a Transition-based Generalized
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Testing Automaton [fn:topnoc]. In TGTAs, the stuttering states are
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made explicit with ={}= self-loops. Since these self-loop can be in
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acceptance sets, livelock acceptance states are no longer needed.
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#+NAME: gfagfb-tgta
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#+BEGIN_SRC sh :results verbatim :exports code
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ltl2tgta 'GFa & GFb'
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#+END_SRC
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#+RESULTS:
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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=init]
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1 -> 2 [label="a & b\n"]
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1 -> 3 [label="!a & b\n"]
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1 -> 4 [label="a & !b\n"]
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1 -> 5 [label="!a & !b\n"]
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2 [label="3"]
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2 -> 3 [label="{a}\n{0,1}"]
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2 -> 4 [label="{b}\n{0,1}"]
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2 -> 5 [label="{a, b}\n{0,1}"]
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2 -> 2 [label="{}\n{0,1}"]
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3 [label="2"]
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3 -> 2 [label="{a}\n{1}"]
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3 -> 4 [label="{a, b}\n{1}"]
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3 -> 5 [label="{b}\n{1}"]
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3 -> 3 [label="{}\n"]
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4 [label="4"]
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4 -> 2 [label="{b}\n{0}"]
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4 -> 3 [label="{a, b}\n{0}"]
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4 -> 5 [label="{a}\n{0}"]
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4 -> 4 [label="{}\n"]
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5 [label="1"]
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5 -> 2 [label="{a, b}\n"]
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5 -> 3 [label="{b}\n"]
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5 -> 4 [label="{a}\n"]
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5 -> 5 [label="{}\n"]
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}
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#+end_example
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#+BEGIN_SRC dot :file gfagfb-tgta.svg :var txt=gfagfb-tgta :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:gfagfb-tgta.svg]]
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[fn:topnoc]: This new class of automaton, as well as the
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implementation of the previous testing automata classes, is part of
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Ala Eddine BEN SALEM's PhD work, and should appear in a future edition
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of ToPNoC (LNCS 7400).
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# LocalWords: ltl tgta num toc Automata automata GraphViz UTF Gb na
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# LocalWords: Geldenhuys tgba SRC init invis nb Acc augb sed png fn
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# LocalWords: cmdline Tpng txt Büchi livelock gba gta GFa GFb TGTAs
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# LocalWords: gfagfb topnoc Eddine SALEM's ToPNoC LNCS eval setenv
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# LocalWords: concat getenv setq
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