# How to translate LTL formula to Kripke or Omega using tool

I am solving some satisfiability questions from exam where one LTL formula should satisfy and other shouldn't or vice versa.

I know how I can check the satisfiability using LTL tool (TemporalLogicProver) by using phi -> (S1 & !S2) or vice versa.

Q Is there any possibility using tool so that I can find a Kripke structure corresponding to that LTL formula or LTL formula to Kripke structure (or Omega Automata) to check whether my understanding is correct ?

For e.g. if I want to get the LTL formula for the below Kripke structure:

+1 vote

Do you mean the following formula?

(a&!b) & G( ((a&!b)->X(!a&b)) & ((!a&b)->X(a&!b)) ) ?

For structures with a single cycle that is not that difficult, there is such a pattern. In general, however, there is the problem that LTL is not as powerful as automata are, so there is no algorithm that could translate any automaton to an LTL formula.
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Thank you for the above formula.
Yes like above formula.
So got your point regarding no algorithm for translation of automaton to an LTL.

So I have to do this intuitively and verify it using the LTL tool. Is it right ?
In general, yes, you have to do that intuitively, but in most cases, a simple pattern as the one above will do.
Thanks a lot :)