spot/doc/org/tut02.org

Relabeling Formulas

• Shell
• Python
• C++
• Additional comments
  • Two ways to name atomic propositions
  • Relabeling Boolean sub-expressions

The task is to read an LTL formula, relabel all (possibly complex) atomic propositions, and provide #define statements for each of these renamings, writing everything in Spin's syntax.

Shell

ltlfilt -ps --relabel=pnn --define -f '"Proc@Here" U ("var > 10" | "var < 4")'

#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
(p0) U ((p1) || (p2))

When is this output interesting, you may ask? It is useful for instance if you want to call ltl2ba (or any other LTL-to-Büchi translator) using a formula with complex atomic propositions it cannot parse. Then you can pass the rewritten formula to ltl2ba, and prepend all those #define to its output. For instance:

ltlfilt -ps --relabel=pnn --define=tmp.defs -f '"Proc@Here" U ("var > 10" | "var < 4")' >tmp.ltl
cat tmp.defs; ltl2ba -F tmp.ltl
rm tmp.defs tmp.ltl

#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
never { /* (p0) U ((p1) || (p2))
 */
T0_init:
	if
	:: (p0) -> goto T0_init
	:: (p1) || (p2) -> goto accept_all
	fi;
accept_all:
	skip
}

Python

The spot.relabel function takes an optional third parameter that should be a relabeling_map. If supplied, this map is filled with pairs of atomic propositions of the form (new-name, old-name).

import spot
f = spot.formula('"Proc@Here" U ("var > 10" | "var < 4")')
m = spot.relabeling_map()
g = spot.relabel(f, spot.Pnn, m)
for newname, oldname in m.items():
  print("#define {} ({})".format(newname.to_str(), oldname.to_str('spin', True)))
print(g.to_str('spin', True))

#define p0 ((Proc@Here))
#define p1 ((var < 4))
#define p2 ((var > 10))
(p0) U ((p1) || (p2))

C++

The spot::ltl::relabeling_map is just a std::map with a custom destructor.

  #include <string>
  #include <iostream>
  #include "ltlparse/public.hh"
  #include "tl/print.hh"
  #include "tl/relabel.hh"

  int main()
  {
    std::string input = "\"Proc@Here\" U (\"var > 10\" | \"var < 4\")";
    spot::ltl::parse_error_list pel;
    spot::ltl::formula f = spot::ltl::parse_infix_psl(input, pel);
    if (spot::ltl::format_parse_errors(std::cerr, input, pel))
      return 1;
    spot::ltl::relabeling_map m;
    f = spot::ltl::relabel(f, spot::ltl::Pnn, &m);
    for (auto& i: m)
      {
        std::cout << "#define ";
        print_psl(std::cout, i.first) << " (";
        print_spin_ltl(std::cout, i.second, true) << ")\n";
      }
    print_spin_ltl(std::cout, f, true) << '\n';
    return 0;
  }

#define p0 (Proc@Here)
#define p1 (var < 4)
#define p2 (var > 10)
(p0) U ((p1) || (p2))

Additional comments

Two ways to name atomic propositions

Instead of --relabel=pnn (or spot.Pnn, or spot::ltl::Pnn), you can actually use --relabel=abc (or spot.Abc, or spot::ltl::Abc) to have the atomic propositions named a, b, c, etc.

Relabeling Boolean sub-expressions

Instead of relabeling each atomic proposition, you could decide to relabel each Boolean sub-expression:

ltlfilt -ps --relabel-bool=pnn --define -f '"Proc@Here" U ("var > 10" | "var < 4")'

#define p0 (Proc@Here)
#define p1 ((var < 4) || (var > 10))
(p0) U (p1)

The relabeling routine is smart enough to not give different names to Boolean expressions that have some sub-expression in common.

For instance a U (a & b) will not be relabeled into (p0) U (p1) because that would hide the fact that both p0 and p1 check for a. Instead we get this:

ltlfilt -ps --relabel-bool=pnn --define -f 'a U (a & b)'

#define p0 (a)
#define p1 (b)
(p0) U ((p0) && (p1))

This "Boolean sub-expression" relabeling is available in Python and C++ via the relabel_bse function. The interface is identical to relabel.