spot/doc/org/tut10.org

# -*- coding: utf-8 -*-
#+TITLE: Translating an LTL formula into a never claim
#+SETUPFILE: setup.org
#+HTML_LINK_UP: tut.html

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

* Shell

#+BEGIN_SRC sh :results verbatim :exports both
ltl2tgba --spin 'GFa -> GFb'
#+END_SRC

#+RESULTS:
#+begin_example
never { /* F(GFb | G!a) */
T0_init:
  if
  :: ((!(a))) -> goto accept_S0
  :: ((true)) -> goto T0_init
  :: ((b)) -> goto accept_S2
  fi;
accept_S0:
  if
  :: ((!(a))) -> goto accept_S0
  fi;
accept_S2:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
T0_S3:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
}
#+end_example

* 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:

#+BEGIN_SRC python :results output :exports both
import spot
print(spot.formula('GFa -> GFb').translate('BA').to_str('spin'))
#+END_SRC

#+RESULTS:
#+begin_example
never {
T0_init:
  if
  :: ((!(a))) -> goto accept_S0
  :: ((true)) -> goto T0_init
  :: ((b)) -> goto accept_S2
  fi;
accept_S0:
  if
  :: ((!(a))) -> goto accept_S0
  fi;
accept_S2:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
T0_S3:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
}

#+end_example

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:

#+BEGIN_SRC python :results output :exports both
import spot
print(spot.translate('GFa -> GFb', 'BA').to_str('spin'))
#+END_SRC

#+RESULTS:
#+begin_example
never {
T0_init:
  if
  :: ((!(a))) -> goto accept_S0
  :: ((true)) -> goto T0_init
  :: ((b)) -> goto accept_S2
  fi;
accept_S0:
  if
  :: ((!(a))) -> goto accept_S0
  fi;
accept_S2:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
T0_S3:
  if
  :: ((b)) -> goto accept_S2
  :: ((!(b))) -> goto T0_S3
  fi;
}

#+end_example

* C++

All the translation pipeline (this include simplifying the formula,
translating the simplified formula into an automaton, and simplifying
the resulting automaton) is handled by the =spot::translator= object.
This object can configured by calling =set_type()= to chose 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) for the resulting automaton. Finally, the output as a
never claim is done via the =print_never_claim= function.

#+BEGIN_SRC C++ :results verbatim :exports both
  #include <string>
  #include <iostream>
  #include <spot/tl/parse.hh>
  #include <spot/tl/print.hh>
  #include <spot/twaalgos/translate.hh>
  #include <spot/twaalgos/neverclaim.hh>

  int main()
  {
    std::string input = "[]<>p0 || <>[]p1";
    spot::parsed_formula pf = spot::parse_infix_psl(input);
    if (pf.format_errors(std::cerr))
      return 1;
    spot::translator trans;
    trans.set_type(spot::postprocessor::BA);
    spot::twa_graph_ptr aut = trans.run(pf.f);
    print_never_claim(std::cout, aut) << '\n';
    return 0;
  }
#+END_SRC

#+RESULTS:
#+begin_example
never {
T0_init:
  if
  :: (p1) -> goto accept_S0
  :: (true) -> goto T0_init
  :: (p0) -> goto accept_S2
  fi;
accept_S0:
  if
  :: (p1) -> goto accept_S0
  fi;
accept_S2:
  if
  :: (p0) -> goto accept_S2
  :: (!(p0)) -> goto T0_S3
  fi;
T0_S3:
  if
  :: (p0) -> goto accept_S2
  :: (!(p0)) -> goto T0_S3
  fi;
}
#+end_example

* Additional comments

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

#+BEGIN_SRC python :results output :exports both
import spot
help(spot.translate)
#+END_SRC

#+RESULTS:
#+begin_example
Help on function translate in module spot:

translate(formula, *args)
    Translate a formula into an automaton.

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

    The optional arguments should be strings among the following:
    - at most one in 'TGBA', 'BA', or 'Monitor'
      (type of automaton 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', and
      'StateBasedAcceptance' (or 'SBAcc' for short)

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

#+end_example