f120dd3206
* NEWS: Mention the change. * src/: Rename as ... * spot/: ... this, adjust all headers to include <spot/...> instead of "...", and adjust all Makefile.am to search headers from the top-level directory. * HACKING: Add conventions about #include. * spot/sanity/style.test: Add a few more grep to catch cases that do not follow these conventions. * .gitignore, Makefile.am, README, bench/stutter/Makefile.am, bench/stutter/stutter_invariance_formulas.cc, bench/stutter/stutter_invariance_randomgraph.cc, configure.ac, debian/rules, doc/Doxyfile.in, doc/Makefile.am, doc/org/.dir-locals.el.in, doc/org/g++wrap.in, doc/org/init.el.in, doc/org/tut01.org, doc/org/tut02.org, doc/org/tut03.org, doc/org/tut10.org, doc/org/tut20.org, doc/org/tut21.org, doc/org/tut22.org, doc/org/tut30.org, iface/ltsmin/Makefile.am, iface/ltsmin/kripke.test, iface/ltsmin/ltsmin.cc, iface/ltsmin/ltsmin.hh, iface/ltsmin/modelcheck.cc, wrap/python/Makefile.am, wrap/python/ajax/spotcgi.in, wrap/python/spot_impl.i, wrap/python/tests/ltl2tgba.py, wrap/python/tests/randgen.py, wrap/python/tests/run.in: Adjust.
287 lines
7.1 KiB
Org Mode
287 lines
7.1 KiB
Org Mode
# -*- coding: utf-8 -*-
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#+TITLE: Converting Rabin (or Other) to Büchi, and simplifying it
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#+SETUPFILE: setup.org
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#+HTML_LINK_UP: tut.html
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Consider the following Rabin automaton, generated by =ltl2dstar=:
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#+BEGIN_SRC sh :results silent :exports both
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ltldo ltl2dstar -f 'F(Xp1 xor XXp1)' -H > tut30.hoa
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#+END_SRC
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#+RESULTS:
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#+NAME: tut30in
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#+BEGIN_SRC sh :results verbatim :exports none
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autfilt tut30.hoa --dot=.a
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#+END_SRC
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#+RESULTS: tut30in
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#+begin_example
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digraph G {
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rankdir=LR
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label=<(Fin(<font color="#5DA5DA">⓿</font>) & Inf(<font color="#F17CB0">❶</font>)) | (Fin(<font color="#FAA43A">❷</font>) & Inf(<font color="#B276B2">❸</font>)) | (Fin(<font color="#60BD68">❹</font>) & Inf(<font color="#F15854">❺</font>))>
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labelloc="t"
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node [shape="circle"]
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
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I [label="", style=invis, width=0]
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I -> 6
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0 [label=<0<br/><font color="#FAA43A">❷</font><font color="#F15854">❺</font>>]
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0 -> 2 [label=<!p1>]
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0 -> 4 [label=<p1>]
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1 [label=<1<br/><font color="#FAA43A">❷</font><font color="#F15854">❺</font>>]
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1 -> 4 [label=<!p1>]
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1 -> 3 [label=<p1>]
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2 [label=<2<br/><font color="#B276B2">❸</font><font color="#60BD68">❹</font>>]
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2 -> 0 [label=<!p1>]
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2 -> 4 [label=<p1>]
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3 [label=<3<br/><font color="#B276B2">❸</font><font color="#60BD68">❹</font>>]
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3 -> 4 [label=<!p1>]
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3 -> 1 [label=<p1>]
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4 [label=<4<br/><font color="#F17CB0">❶</font><font color="#FAA43A">❷</font><font color="#60BD68">❹</font>>]
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4 -> 4 [label=<!p1>]
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4 -> 4 [label=<p1>]
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5 [label=<5<br/><font color="#FAA43A">❷</font><font color="#60BD68">❹</font>>]
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5 -> 2 [label=<!p1>]
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5 -> 3 [label=<p1>]
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6 [label=<6<br/><font color="#FAA43A">❷</font><font color="#60BD68">❹</font>>]
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6 -> 5 [label=<!p1>]
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6 -> 5 [label=<p1>]
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}
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#+end_example
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#+BEGIN_SRC dot :file tut30in.png :cmdline -Tpng :var txt=tut30in :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:tut30in.png]]
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Our goal is to generate an equivalent Büchi automaton, preserving
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determinism if possible. However nothing of what we will write is
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specific to Rabin acceptance: the same code will convert automata with
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any acceptance to Büchi acceptance.
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* Shell
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We use =autfilt= with option =-B= to request Büchi acceptance and
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state-based output, =-D= to express a preference for deterministic
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output, and =-H= for output in the HOA format. Using option
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=-D/--deterministic= (or =--small=) actually activates the
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"postprocessing" routines of Spot: the acceptance will not only be
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changed to Büchi, but simplification routines (useless SCCs removal,
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simulation-based reductions, acceptance sets simplifications,
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WDBA-minimization, ...) will also be applied.
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#+BEGIN_SRC sh :results verbatim :exports both :wrap SRC hoa
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autfilt -B -D -H tut30.hoa
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#+END_SRC
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#+RESULTS:
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#+BEGIN_SRC hoa
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HOA: v1
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States: 5
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Start: 1
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AP: 1 "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic weak
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--BODY--
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State: 0 {0}
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[t] 0
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State: 1
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[t] 2
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State: 2
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[!0] 3
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[0] 4
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State: 3
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[0] 0
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[!0] 3
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State: 4
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[!0] 0
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[0] 4
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--END--
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#+END_SRC
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#+NAME: tut30out
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#+BEGIN_SRC sh :results verbatim :exports none
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autfilt -B -D tut30.hoa
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#+END_SRC
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#+RESULTS: tut30out
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#+begin_example
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digraph G {
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rankdir=LR
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node [shape="circle"]
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fontname="Lato"
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node [fontname="Lato"]
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edge [fontname="Lato"]
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node[style=filled, fillcolor="#ffffa0"] edge[arrowhead=vee, arrowsize=.7]
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I [label="", style=invis, width=0]
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I -> 1
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0 [label="0", peripheries=2]
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0 -> 0 [label=<1>]
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1 [label="1"]
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1 -> 2 [label=<1>]
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2 [label="2"]
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2 -> 3 [label=<!p1>]
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2 -> 4 [label=<p1>]
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3 [label="3"]
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3 -> 0 [label=<p1>]
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3 -> 3 [label=<!p1>]
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4 [label="4"]
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4 -> 0 [label=<!p1>]
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4 -> 4 [label=<p1>]
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}
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#+end_example
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#+BEGIN_SRC dot :file tut30out.png :cmdline -Tpng :var txt=tut30out :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:tut30out.png]]
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In the general case transforming an automaton with a complex
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acceptance condition into a Büchi automaton can make the output
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bigger. However the postprocessing routines may manage to simplify
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the result further.
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* Python
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The Python version uses the =postprocess()= routine:
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#+BEGIN_SRC python :results output :exports both :wrap SRC hoa
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import spot
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aut = spot.automaton('tut30.hoa').postprocess('BA', 'deterministic')
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print(aut.to_str('hoa'))
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#+END_SRC
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#+RESULTS:
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#+BEGIN_SRC hoa
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HOA: v1
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States: 5
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Start: 1
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AP: 1 "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic weak
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--BODY--
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State: 0 {0}
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[t] 0
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State: 1
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[t] 2
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State: 2
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[!0] 3
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[0] 4
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State: 3
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[0] 0
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[!0] 3
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State: 4
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[!0] 0
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[0] 4
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--END--
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#+END_SRC
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The =postprocess()= function has an interface similar to
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[[file:tut10.org][the =translate()= function discussed previously]]:
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#+BEGIN_SRC python :results output :exports both
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import spot
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help(spot.postprocess)
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Help on function postprocess in module spot:
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postprocess(automaton, *args)
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Post process an automaton.
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This applies a number of simlification algorithms, depending on
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the options supplied. Keep in mind that 'Deterministic' expresses
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just a preference that may not be satisfied if the input is
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not already 'Deterministic'.
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The optional arguments should be strings among the following:
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- at most one in 'Generic', 'TGBA', 'BA', or 'Monitor'
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(type of automaton to build)
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- at most one in 'Small', 'Deterministic', 'Any'
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(preferred characteristics of the produced automaton)
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- at most one in 'Low', 'Medium', 'High'
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(optimization level)
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- any combination of 'Complete' and 'StateBasedAcceptance'
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(or 'SBAcc' for short)
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The default corresponds to 'generic', 'small' and 'high'.
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#+end_example
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* C++
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The C++ version of this code is a bit more verbose, because the
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=postprocess()= function does not exist. You have to instantiate a
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=postprocessor= object, configure it, and then call it for each
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automaton to process.
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#+BEGIN_SRC C++ :results verbatim :exports both :wrap SRC hoa
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#include <iostream>
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#include <spot/parseaut/public.hh>
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#include <spot/twaalgos/postproc.hh>
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#include <spot/twaalgos/hoa.hh>
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int main()
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{
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spot::parsed_aut_ptr pa = parse_aut("tut30.hoa", spot::make_bdd_dict());
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if (pa->format_errors(std::cerr))
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return 1;
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if (pa->aborted)
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{
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std::cerr << "--ABORT-- read\n";
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return 1;
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}
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spot::postprocessor post;
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post.set_type(spot::postprocessor::BA);
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post.set_pref(spot::postprocessor::Deterministic);
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post.set_level(spot::postprocessor::High);
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auto aut = post.run(pa->aut);
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spot::print_hoa(std::cout, aut) << '\n';
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return 0;
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}
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#+END_SRC
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#+RESULTS:
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#+BEGIN_SRC hoa
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HOA: v1
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States: 5
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Start: 1
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AP: 1 "p1"
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acc-name: Buchi
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Acceptance: 1 Inf(0)
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properties: trans-labels explicit-labels state-acc complete
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properties: deterministic weak
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--BODY--
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State: 0 {0}
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[t] 0
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State: 1
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[t] 2
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State: 2
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[!0] 3
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[0] 4
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State: 3
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[0] 0
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[!0] 3
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State: 4
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[!0] 0
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[0] 4
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--END--
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#+END_SRC
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#+BEGIN_SRC sh :results silent :exports results
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rm -f tut30.hoa
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#+END_SRC
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