spot/doc/org/tut30.org

Converting Rabin (or Other) to Büchi, and simplifying it

• Shell
• Python
• C++

Consider the following Rabin automaton, generated by ltl2dstar:

ltldo ltl2dstar -f 'F(Xp1 xor XXp1)' > tut30.hoa

Our goal is to generate an equivalent Büchi automaton, preserving determinism if possible. However nothing of what we will write is specific to Rabin acceptance: the same code will convert automata with any acceptance to Büchi acceptance.

Shell

We use autfilt with option -B to request Büchi acceptance and state-based output and -D to express a preference for deterministic output. Using option -D/--deterministic (or --small) actually activates the "post-processing" routines of Spot: the acceptance will not only be changed to Büchi, but simplification routines (useless SCCs removal, simulation-based reductions, acceptance sets simplifications, WDBA-minimization, …) will also be applied.

autfilt -B -D tut30.hoa

HOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic very-weak
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--

In the general case transforming an automaton with a complex acceptance condition into a Büchi automaton can make the output bigger. However the post-processing routines may manage to simplify the result further.

Python

The Python version uses the postprocess() routine:

import spot
aut = spot.automaton('tut30.hoa').postprocess('buchi', 'sbacc', 'deterministic')
print(aut.to_str('hoa'))

HOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic terminal
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--

The postprocess() function has an interface similar to the translate() function discussed previously:

import spot
help(spot.postprocess)

Help on function postprocess in module spot:

postprocess(automaton, *args, formula=None, xargs=None)
    Post process an automaton.

    This applies a number of simplification algorithms, depending on
    the options supplied. Keep in mind that 'Deterministic' expresses
    just a preference that may not be satisfied if the input is
    not already 'Deterministic'.

    The optional arguments should be strings among the following:
    - at most one in 'Generic', 'GeneralizedBuchi', 'Buchi', or
      'Monitor', 'parity', 'parity min odd', 'parity min even',
      'parity max odd', 'parity max even', 'coBuchi'
      (type of acceptance condition to build)
    - at most one in 'Small', 'Deterministic', 'Any'
      (preferred characteristics of the produced automaton)
    - at most one in 'Low', 'Medium', 'High'
      (optimization level)
    - any combination of 'Complete', 'StateBasedAcceptance'
      (or 'SBAcc' for short), and 'Colored (only for parity
      acceptance)

    The default corresponds to 'generic', 'small' and 'high'.

    If a formula denoted by this automaton is known, pass it to as the
    optional `formula` argument; it can help some algorithms by
    providing an easy way to complement the automaton.

    Additional options can be supplied using a `spot.option_map`, or a
    string (that will be converted to `spot.option_map`), as the `xargs`
    argument.  This is similar to the `-x` option of command-line tools;
    so check out the spot-x(7) man page for details.

C++

The C++ version of this code is a bit more verbose, because the postprocess() function does not exist. You have to instantiate a postprocessor object, configure it, and then call it for each automaton to process.

  #include <iostream>
  #include <spot/parseaut/public.hh>
  #include <spot/twaalgos/postproc.hh>
  #include <spot/twaalgos/hoa.hh>

  int main()
  {
    spot::parsed_aut_ptr pa = parse_aut("tut30.hoa", spot::make_bdd_dict());
    if (pa->format_errors(std::cerr))
      return 1;
    if (pa->aborted)
      {
        std::cerr << "--ABORT-- read\n";
        return 1;
      }
    spot::postprocessor post;
    post.set_type(spot::postprocessor::Buchi);
    post.set_pref(spot::postprocessor::SBAcc
                  | spot::postprocessor::Deterministic);
    post.set_level(spot::postprocessor::High);
    auto aut = post.run(pa->aut);
    spot::print_hoa(std::cout, aut) << '\n';
    return 0;
  }

HOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic terminal
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--

rm -f tut30.hoa