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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 To translate a formula into a Testing Automaton
Start by building a Buchi automaton
Step1:  Then, gather all the atomic proposition in the formula, and create an automaton with changesets
Step2:  Then, remove dead states, and remove stuttering transitions (i.e., transitions labeled by {}), marking as livelock accepting (rectangles) any states from which there exists a an accepting path labeled by {}.
Step3:  Finally, use bisimulation to minimize the number of states.
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Python Code:
f = spot.formula('a U Gb')
a = f.translate('ba')
a
Explanation: To translate a formula into a Testing Automaton
Start by building a Buchi automaton
End of explanation
propset = spot.atomic_prop_collect_as_bdd(f, a)
ta = spot.tgba_to_ta(a, propset, True, True, False, False, True)
ta.show('.A')
Explanation: Then, gather all the atomic proposition in the formula, and create an automaton with changesets
End of explanation
ta = spot.tgba_to_ta(a, propset, True, True, False, False, False)
ta.show('.A')
Explanation: Then, remove dead states, and remove stuttering transitions (i.e., transitions labeled by {}), marking as livelock accepting (rectangles) any states from which there exists a an accepting path labeled by {}.
End of explanation
spot.minimize_ta(ta).show('.A')
Explanation: Finally, use bisimulation to minimize the number of states.
End of explanation
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