Joachim asked whether property weak (#22) made sense with universal branching.
The definition of SCC might not be very clear in the context of universal branching.
I believe that if we consider a branching transition as several arcs when defining SCCs, our definition of weak matches the established definition of weak alternating automata.
It might even make sense to add a very-weak property in case all SCCs have size 1.
Note that when defined on words (our case) weak alternating Büchi automata are as expressive as alternating Büchi automata and as Büchi automata. However weak Büchi automata are less expressive. So weak really has to be understood as a structural property of the automaton (and I will have to make efforts not to think obligation whenever I read weak).
Joachim asked whether property
weak(#22) made sense with universal branching.The definition of
SCCmight not be very clear in the context of universal branching.I believe that if we consider a branching transition as several arcs when defining SCCs, our definition of
weakmatches the established definition of weak alternating automata.It might even make sense to add a
very-weakproperty in case all SCCs have size 1.Note that when defined on words (our case) weak alternating Büchi automata are as expressive as alternating Büchi automata and as Büchi automata. However weak Büchi automata are less expressive. So
weakreally has to be understood as a structural property of the automaton (and I will have to make efforts not to think obligation whenever I readweak).