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    # April 20, 2022
    
    iteration: 199
    candidate: ITE(1.0*x_2 + z_1 <= -0.0088842, False, 1.0*x_1 + 1.0*x_2 + z_0 + z_1 > -0.5997313)
    
    
    
    
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    debugging notes: (high level )
    
    Gurobi cannot express < , >  (strickly less than or strickly greater than)
    
    
    Current problem:
    
    >> the teacher is not deterministic(i.e., gurobi) and requires further
    constraint to make it determinic. ---> maybe not sure sure? 
    
    
    a. currently gurobi doesn't minimize the objective function
    
    
    b. Understand winning tree
    
    c. understand what is the region represented by Dtree compared to shape produced by 
    sygus
    
    d.  Test this implementation on all the samples from this partion.
    (roughly 180 positive samples ) instead of just 20.
    
    
    e. how well does currently Dtree on 20 samples generalize to the  187  filtered samples
    and how well does it generalize to the entire region chosen?
    
    f. Chiao asks why did we succeedd on this one case?
    answer: we so good!
    
    For Angello specifically, go over chiaos's code to make sure we on 
    same page at the implementation level?
    
    
    1/24/2020
    
    Teacher starting at iteration 11 begins to return duplicate negative examples.
    
        a. Tree is not correct
        b. The fact that teacher can only express <= and not < is causing problem.
    
    
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    Understanding gurobi
    
    ((1*fvar0_A0) + (1*fvar1_A0)) > -0.04754193
    
    in gurobi
    
    ((1*fvar0_A0) + (1*fvar1_A0)) >= -0.04754193
    
    can you find a negative example(perceived state)
    in this shape?
    
    
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    a negative example is a concrete state and perceived state (xi,zi) 
    such that V(xi) > V(f(xi, g(zi))) where f(xi, g(zi)) == xii which is the next state.
    xi and zi must be in current learn shape. 
    
    trans(xi, zi) check if in tree.
    
    
    
    xi=<var1, va2 ,v3>
    zi=<var4,var5>
    xii = f(xi, g(zi))
    
    
    check V(xi) <= V(xii)
    Equivalent to
    V(xi) <= V(f(xi, g(zi))
    and xi zi are in current learnt shape.
    
    
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