# Converting Rabin (or Other) to Büchi, and simplifying it

Consider the following Rabin automaton, generated by `ltl2dstar`:

```ltldo ltl2dstar -f 'F(Xp1 xor XXp1)' > 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 and `-D` to express a preference for deterministic output. 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 tut30.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 very-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 very-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, formula=None, xargs=None)
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

The optional arguments should be strings among the following:
- at most one in 'Generic', 'TGBA', 'BA', or 'Monitor',
'parity', 'parity min odd', 'parity min even',
'parity max odd', 'parity max even' (type of automaton to
build), 'coBuchi'
- 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', 'StateBasedAcceptance'
(or 'SBAcc' for short), and 'Colored (only for parity
acceptance)

The default corresponds to 'generic', 'small' and 'high'.

If a formula denoted by this automaton is known, pass it to as the
optional `formula` argument; it can help some algorithms by
providing an easy way to complement the automaton.

Additional options can be supplied using a `spot.option_map`, or a
string (that will be converted to `spot.option_map`), as the `xargs`
argument.  This is similar to the `-x` option of command-line tools;
so check out the spot-x(7) man page for details.

```

## 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 <spot/parseaut/public.hh>
#include <spot/twaalgos/postproc.hh>
#include <spot/twaalgos/hoa.hh>

int main()
{
spot::parsed_aut_ptr pa = parse_aut("tut30.hoa", spot::make_bdd_dict());
if (pa->format_errors(std::cerr))
return 1;
if (pa->aborted)
{
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 very-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--
```
```rm -f tut30.hoa
```