7.2 KiB
Converting Rabin (or Other) to Büchi, and simplifying it
Consider the following Rabin automaton, generated by ltl2dstar:
ltldo ltl2dstar -f 'F(Xp1 xor XXp1)' -H > tut30.hoa
Our goal is to generate an equivalent Büchi automaton, preserving determinism if possible. However nothing of what we will write is specific to Rabin acceptance: the same code will convert automata with any acceptance to Büchi acceptance.
Shell
We use autfilt with option -B to request Büchi acceptance and
state-based output, -D to express a preference for deterministic
output, and -H for output in the HOA format. Using option
-D/--deterministic (or --small) actually activates the
"postprocessing" routines of Spot: the acceptance will not only be
changed to Büchi, but simplification routines (useless SCCs removal,
simulation-based reductions, acceptance sets simplifications,
WDBA-minimization, …) will also be applied.
autfilt -B -D -H tut30.hoaHOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic inherently-weak
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--
In the general case transforming an automaton with a complex acceptance condition into a Büchi automaton can make the output bigger. However the postprocessing routines may manage to simplify the result further.
Python
The Python version uses the postprocess() routine:
import spot
aut = spot.automaton('tut30.hoa').postprocess('BA', 'deterministic')
print(aut.to_str('hoa'))HOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic inherently-weak
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--
The postprocess() function has an interface similar to
the translate() function discussed previously:
import spot
help(spot.postprocess)Help on function postprocess in module spot:
postprocess(automaton, *args)
Post process an automaton.
This applies a number of simlification algorithms, depending on
the options supplied. Keep in mind that 'Deterministic' expresses
just a preference that may not be satisfied if the input is
not already 'Deterministic'.
The optional arguments should be strings among the following:
- at most one in 'Generic', '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' and 'StateBasedAcceptance'
(or 'SBAcc' for short)
The default corresponds to 'generic', 'small' and 'high'.
C++
The C++ version of this code is a bit more verbose, because the
postprocess() function does not exist. You have to instantiate a
postprocessor object, configure it, and then call it for each
automaton to process.
#include <iostream>
#include "parseaut/public.hh"
#include "twaalgos/postproc.hh"
#include "twaalgos/hoa.hh"
int main()
{
std::string input = "tut30.hoa";
spot::parse_aut_error_list pel;
spot::bdd_dict_ptr dict = spot::make_bdd_dict();
spot::parsed_aut_ptr pa = parse_aut(input, pel, dict);
if (spot::format_parse_aut_errors(std::cerr, input, pel))
return 1;
if (pa->aborted)
{
std::cerr << "--ABORT-- read\n";
return 1;
}
spot::postprocessor post;
post.set_type(spot::postprocessor::BA);
post.set_pref(spot::postprocessor::Deterministic);
post.set_level(spot::postprocessor::High);
auto aut = post.run(pa->aut);
spot::print_hoa(std::cout, aut) << '\n';
return 0;
}HOA: v1
States: 5
Start: 1
AP: 1 "p1"
acc-name: Buchi
Acceptance: 1 Inf(0)
properties: trans-labels explicit-labels state-acc complete
properties: deterministic inherently-weak
--BODY--
State: 0 {0}
[t] 0
State: 1
[t] 2
State: 2
[!0] 3
[0] 4
State: 3
[0] 0
[!0] 3
State: 4
[!0] 0
[0] 4
--END--