org: examples with alternating automata
* doc/org/tut23.org, doc/org/tut24.org, doc/org/tut31.org: New files. * doc/Makefile.am, doc/org/tut.org: Add them. * doc/org/hoa.org, doc/org/concepts.org: Adjust for alternation support. * NEWS: Add links.
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Alexandre Duret-Lutz
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doc/org/tut24.org
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doc/org/tut24.org
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# -*- coding: utf-8 -*-
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#+TITLE: Iterating over alternating automata
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#+DESCRIPTION: Code example for iterating of alternating ω-automata in Spot
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#+SETUPFILE: setup.org
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#+HTML_LINK_UP: tut.html
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Alternating automata can be explored in a very similar way as
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non-alternating automata. Most of the code from our [[file:tut21.org][custom automaton
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printer]] will still work; the only problem is with universal edges.
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We will use the following example automaton as input (it is just a
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slight variation over an [[file:tut23.org][alternating automaton created previously]] to
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demonstrate a universal initial state).
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#+NAME: tut24in
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#+BEGIN_SRC hoa
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HOA: v1
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States: 3
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Start: 0&1
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AP: 1 "a"
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acc-name: co-Buchi
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Acceptance: 1 Fin(0)
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--BODY--
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State: 0
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[0] 0
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[!0] 0&1
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State: 1
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[!0] 1 {0}
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[0] 2
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State: 2
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[t] 2
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--END--
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#+END_SRC
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#+NAME: tut24dot
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#+BEGIN_SRC sh :results verbatim :exports none :noweb strip-export
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cat >tut24.hoa <<EOF
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<<tut24in>>
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EOF
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autfilt --dot=.a tut24.hoa
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#+END_SRC
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#+BEGIN_SRC dot :file tut24in.png :cmdline -Tpng :var txt=tut24dot :exports results
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$txt
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#+END_SRC
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#+RESULTS:
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[[file:tut24in.png]]
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Let us assume that this automaton has been loaded in variable =aut=,
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and that we run the following code, similar to what we did in the
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[[file:tut21.org][custom automaton printer]].
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#+NAME: nonalt-body
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#+BEGIN_SRC C++ :exports code :noweb strip-export
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std::cout << "Initial state: " << aut->get_init_state_number() << '\n';
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const spot::bdd_dict_ptr& dict = aut->get_dict();
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unsigned n = aut->num_states();
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for (unsigned s = 0; s < n; ++s)
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{
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std::cout << "State " << s << ":\n";
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for (auto& t: aut->out(s))
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{
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std::cout << " edge(" << t.src << " -> " << t.dst << ")\n label = ";
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spot::bdd_print_formula(std::cout, dict, t.cond);
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std::cout << "\n acc sets = " << t.acc << '\n';
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}
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}
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#+END_SRC
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#+NAME: nonalt-main
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#+BEGIN_SRC C++ :exports none :noweb strip-export
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#include <string>
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#include <iostream>
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#include <spot/parseaut/public.hh>
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#include <spot/twaalgos/hoa.hh>
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#include <spot/twa/bddprint.hh>
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void custom_print(spot::twa_graph_ptr& aut);
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int main()
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{
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spot::parsed_aut_ptr pa = parse_aut("tut24.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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// This cannot occur when reading a never claim, but
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// it could while reading a HOA file.
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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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custom_print(pa->aut);
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}
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#+END_SRC
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#+NAME: nonalt-one
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#+BEGIN_SRC C++ :exports results :noweb strip-export :results verbatim
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<<nonalt-main>>
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void custom_print(spot::twa_graph_ptr& aut)
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{
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<<nonalt-body>>
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}
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#+END_SRC
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#+RESULTS: nonalt-one
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#+begin_example
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Initial state: 4294967292
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State 0:
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edge(0 -> 0)
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label = a
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acc sets = {}
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edge(0 -> 4294967295)
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label = !a
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acc sets = {}
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State 1:
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edge(1 -> 1)
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label = !a
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acc sets = {0}
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edge(1 -> 2)
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label = a
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acc sets = {}
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State 2:
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edge(2 -> 2)
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label = 1
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acc sets = {}
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#+end_example
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This output seems correct only for non-universal edges. The reason is
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that Spot always store all edges as a tuple (src,dst,label,acc sets),
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but universal edges are indicated by setting the most significant bit
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of the destination (or of the initial state).
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The "universality" of an edge can be tested using the
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=twa_graph::is_univ_dest()= method: it takes a destination state as
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input, as in =aut->is_univ_dest(t.dst)= or
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=aut->is_univ_dest(aut->get_init_state_number())=. For convenience
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this method can also be called on a edge, as in =aut->is_univ_dest(t)=.
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The set of destination states of a universal edge can be iterated over
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via the =twa_graph::univ_dests()= method. This takes either a
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destination state (=twa_graph::univ_dests(t.dst)=) or more simply an
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edge (=twa_graph::univ_dests(t)=). The =univ_dests()= method will
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also work on non-universal edges, but in this case it will simply
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iterate on the given state.
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Therefor in order to print the universal destinations of any universal
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edge in an alternating automaton, we can use =univ_dests()=
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unconditionally. In this example, we simply call =is_univ_dest()= to
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decide whether to enclose the destinations in braces.
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#+NAME: nonalt-body2
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#+BEGIN_SRC C++ :exports code :noweb strip-export
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unsigned init = aut->get_init_state_number();
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std::cout << "Initial state:";
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if (aut->is_univ_dest(init))
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std::cout << " {";
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for (unsigned i: aut->univ_dests(init))
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std::cout << ' ' << i;
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if (aut->is_univ_dest(init))
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std::cout << " }";
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std::cout << '\n';
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const spot::bdd_dict_ptr& dict = aut->get_dict();
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unsigned n = aut->num_states();
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for (unsigned s = 0; s < n; ++s)
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{
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std::cout << "State " << s << ":\n";
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for (auto& t: aut->out(s))
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{
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std::cout << " edge(" << t.src << " ->";
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if (aut->is_univ_dest(t))
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std::cout << " {";
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for (unsigned dst: aut->univ_dests(t))
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std::cout << ' ' << dst;
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if (aut->is_univ_dest(t))
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std::cout << " }";
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std::cout << ")\n label = ";
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spot::bdd_print_formula(std::cout, dict, t.cond);
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std::cout << "\n acc sets = " << t.acc << '\n';
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}
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}
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#+END_SRC
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#+NAME: nonalt-two
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#+BEGIN_SRC C++ :exports results :noweb strip-export :results verbatim
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<<nonalt-main>>
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void custom_print(spot::twa_graph_ptr& aut)
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{
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<<nonalt-body2>>
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}
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#+END_SRC
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#+RESULTS: nonalt-two
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#+begin_example
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Initial state: { 0 1 }
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State 0:
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edge(0 -> 0)
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label = a
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acc sets = {}
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edge(0 -> { 0 1 })
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label = !a
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acc sets = {}
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State 1:
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edge(1 -> 1)
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label = !a
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acc sets = {0}
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edge(1 -> 2)
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label = a
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acc sets = {}
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State 2:
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edge(2 -> 2)
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label = 1
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acc sets = {}
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#+end_example
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* Python
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Here is the Python version of this code:
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#+BEGIN_SRC python :results output :exports both
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import spot
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aut = spot.automaton("tut24.hoa")
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bdict = aut.get_dict()
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init = aut.get_init_state_number()
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ui = aut.is_univ_dest(init)
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print("Initial states: {}{}{}".format("{ " if ui else "",
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" ".join(map(str, aut.univ_dests(init))),
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" }" if ui else ""))
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for s in range(0, aut.num_states()):
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print("State {}:".format(s))
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for t in aut.out(s):
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ud = aut.is_univ_dest(t)
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print(" edge({} -> {}{}{})".format(t.src,
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"{ " if ud else "",
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" ".join(map(str, aut.univ_dests(t))),
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" }" if ud else ""))
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print(" label =", spot.bdd_format_formula(bdict, t.cond))
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print(" acc sets =", t.acc)
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#+END_SRC
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#+RESULTS:
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#+begin_example
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Initial states: { 0 1 }
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State 0:
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edge(0 -> 0)
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label = a
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acc sets = {}
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edge(0 -> { 0 1 })
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label = !a
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acc sets = {}
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State 1:
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edge(1 -> 1)
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label = !a
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acc sets = {0}
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edge(1 -> 2)
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label = a
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acc sets = {}
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State 2:
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edge(2 -> 2)
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label = 1
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acc sets = {}
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#+end_example
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#+BEGIN_SRC sh :results silent :exports results
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rm -f tut24.hoa
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#+END_SRC
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