Relabeling Formulas

Table of Contents

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


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-B├╝chi 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))
	:: (p0) -> goto T0_init
	:: (p1) || (p2) -> goto accept_all

Aside: another way to work around syntax limitations of tools is to use ltldo. On the above example, ltldo ltl2ba -f '"Proc@Here" U ("var > 10" | "var < 4")' -s would produce a never clam with the correct atomic proposition, even though ltl2ba cannot parse them.


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
m = spot.relabeling_map()
g = spot.relabel('"Proc@Here" U ("var > 10" | "var < 4")', 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))


The spot::relabeling_map is just implemented as a std::map.

#include <string>
#include <iostream>
#include <spot/tl/parse.hh>
#include <spot/tl/print.hh>
#include <spot/tl/relabel.hh>

int main()
  std::string input = "\"Proc@Here\" U (\"var > 10\" | \"var < 4\")";
  spot::parsed_formula pf = spot::parse_infix_psl(input);
  if (pf.format_errors(std::cerr))
    return 1;
  spot::formula f = pf.f;
  spot::relabeling_map m;
  f = spot::relabel(f, spot::Pnn, &m);
  for (auto& i: m)
      std::cout << "#define " << 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::Pnn), you can actually use --relabel=abc (or spot.Abc, or spot::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.