Translating an LTL formula into a never claim
Table of Contents
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 "tl/parse.hh" #include "tl/print.hh" #include "twaalgos/translate.hh" #include "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'.