What is the correct format to convert following diagram into required syntax for teaching tool.

Question

Answer 1

For instance, you can use the following formula:

exists(
    {q0,q1},
    q0&!q1|q0&q1,
    !q0 &!q1 & !a & !next(q0) |
    !q0 & q1 & !a &  next(q0) &  next(q1) |
     q0 & q1 & !a & !next(q0) & !next(q1) |
     q0 & q1 &  a &  next(q0) & !next(q1) |
     q0 &!q1 & !a & !next(q0) & !next(q1) ,
    {},
    F G (!q0&!q1|q1&!q0)
)

or as an alternative this one as well:

exists(
    {q0,q1},
    q0,
    !q0 & q1 & !a &  next(q0) & next(q1) |
     q0 & q1 &  a &  next(q0) & !next(q1) | 
    !q0 &!q1 & !a & !next(q0) |
     q0      & !a & !next(q0) & !next(q1) ,
    {},
    F G !q0
)