I know of two translators LTL -> deterministic Rabin automaton:

They produce deterministic automata, which can be much larger than their possible non-deterministic variants. Is there a translator LTL -> non deterministic Rabin?

(my synthesis tool could handle small non-det Rabin automata but not large though det ones)


1 Answer 1


You can easily translate LTL to non-deterministic Buchi automata, which can be thought of as a simple fragment of Rabin automata (although they are equally expressive). I don't think any tool would actually output the acceptance condition described as a Rabin condition, but this is very easy to deduce from the Buchi states.

An example of an online tool to do this conversion is: http://www.lsv.ens-cachan.fr/~gastin/ltl2ba/

But I'm sure there are many others, as the construction is relatively simple.

  • $\begingroup$ yes, we can.. But do you mean that there is no "size" benefit in using non-det Rabin automata over non-det Buchi automata for LTL formulas? (i.e., for any LTL formula, the size of minimal non-det Rabin automaton equals to the size of minimal non-det Buchi?) (where size is the number of states) $\endgroup$
    – Ayrat
    Jan 12, 2017 at 19:30
  • 1
    $\begingroup$ It is true that Rabin automata may be more succinct than Buchi automata, even for nondeterministic ones. However, the lower bound in the blowup is the same. In addition, I don't think there is a translation from LTL to non-det Rabin that will give you significantly smaller automata (no more than a polynomial factor, I think). $\endgroup$
    – Shaull
    Jan 12, 2017 at 22:42
  • $\begingroup$ @Ayrat I am not sure whether the tool called GOAL satisfies the OP's requirement. (Personally, I think it is a very wonderful tool with a long-term goal "to handle all the common variants of omega-automata and the logics that are expressively equivalent to these automata". ) $\endgroup$
    – hengxin
    Apr 12, 2017 at 3:27

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