spot/doc/org/tut10.org

Translating an LTL formula into a never claim

• Shell
• Python
• C++
• Additional comments

Here is how to translate an LTL (or PSL) formula into a never claim.

Shell

ltl2tgba --spin 'GFa -> GFb'

never { /* F(GFb | G!a) */
T0_init:
  if
  :: (true) -> goto T0_init
  :: (b) -> goto accept_S1
  :: (!(a)) -> goto accept_S2
  fi;
accept_S1:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
accept_S2:
  if
  :: (!(a)) -> goto accept_S2
  fi;
T0_S3:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
}

Python

The formula function returns a formula object (or raises a parse-error exception). Formula objects have a translate() method that returns an automaton, and the automata objects have a to_str method that can output in one of the supported syntaxes.

So the translation is actually a one-liner in Python:

import spot
print(spot.formula('GFa -> GFb').translate('BA').to_str('spin'))

never {
T0_init:
  if
  :: (true) -> goto T0_init
  :: (b) -> goto accept_S1
  :: (!(a)) -> goto accept_S2
  fi;
accept_S1:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
accept_S2:
  if
  :: (!(a)) -> goto accept_S2
  fi;
T0_S3:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
}

The above line can actually be made a bit shorter, because translate() can also be used as a function (as opposed to a method) that takes a formula (possibly as a string) as first argument:

import spot
print(spot.translate('GFa -> GFb', 'buchi', 'sbacc').to_str('spin'))

never {
T0_init:
  if
  :: (true) -> goto T0_init
  :: (b) -> goto accept_S1
  :: (!(a)) -> goto accept_S2
  fi;
accept_S1:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
accept_S2:
  if
  :: (!(a)) -> goto accept_S2
  fi;
T0_S3:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
}

C++

All the translation pipeline (this includes simplifying the formula, translating the simplified formula into an automaton, and simplifying the resulting automaton) is handled by the spot::translator class. An instance of this class can configured by calling set_type() to choose the type of automaton to output, set_level() to set the level of optimization (it's high by default), and set_pref() to set various preferences (like small or deterministic) or characteristic (complete, unambiguous, state-based acceptance) for the resulting automaton. Finally, the output as a never claim is done via the print_never_claim function.

  #include <iostream>
  #include <spot/tl/parse.hh>
  #include <spot/twaalgos/translate.hh>
  #include <spot/twaalgos/neverclaim.hh>

  int main()
  {
    spot::parsed_formula pf = spot::parse_infix_psl("GFa -> GFb");
    if (pf.format_errors(std::cerr))
      return 1;
    spot::translator trans;
    trans.set_type(spot::postprocessor::Buchi);
    trans.set_pref(spot::postprocessor::SBAcc
                   | spot::postprocessor::Small);
    spot::twa_graph_ptr aut = trans.run(pf.f);
    print_never_claim(std::cout, aut) << '\n';
    return 0;
  }

never {
T0_init:
  if
  :: (true) -> goto T0_init
  :: (b) -> goto accept_S1
  :: (!(a)) -> goto accept_S2
  fi;
accept_S1:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
accept_S2:
  if
  :: (!(a)) -> goto accept_S2
  fi;
T0_S3:
  if
  :: (b) -> goto accept_S1
  :: (!(b)) -> goto T0_S3
  fi;
}

Additional comments

The Python version of translate() is documented as follows:

Help on function translate in module spot:

translate(formula, *args, dict=<spot.impl.bdd_dict; proxy of <Swig Object of type 'std::shared_ptr< spot::bdd_dict > *' at 0x7f42f4cea030> >, xargs=None)
    Translate a formula into an automaton.

    Keep in mind that 'Deterministic' expresses just a preference that
    may not be satisfied.

    The optional arguments should be strings among the following:
    - at most one in 'GeneralizedBuchi', 'Buchi', or 'Monitor',
      'generic', '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', 'Unambiguous',
      'StateBasedAcceptance' (or 'SBAcc' for short), and
      'Colored' (only for parity acceptance)

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

    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.