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
  :: ((!(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;
}

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
  :: ((!(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;
}

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', 'BA').to_str('spin'))

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;
}

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.

  #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::parse_error_list pel;
    spot::formula f = spot::parse_infix_psl(input, pel);
    if (spot::format_parse_errors(std::cerr, input, pel))
      return 1;
    spot::translator trans;
    trans.set_type(spot::postprocessor::BA);
    spot::twa_graph_ptr aut = trans.run(f);
    print_never_claim(std::cout, aut) << '\n';
    return 0;
  }

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;
}

Additional comments

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

import spot
help(spot.translate)

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'.