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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def _initialize_splittable_dimensions(self, mtf_graph):
 """Initializer for self._splittable_mtf_dimension_names. Args: mtf_graph: an mtf.Graph. Returns: A set(string) of the names of Mesh TensorFlow dimensions that may be assigned in a layout. """

    all_mtf_dimension_names = set()  # set(string)
    for mtf_operation in mtf_graph.operations:
      for mtf_tensor in mtf_operation.outputs:
        for mtf_dimension in mtf_tensor.shape.dims:
          if not re.match(r"_anonymous_\d*", mtf_dimension.name):
            all_mtf_dimension_names.add(mtf_dimension.name)

    unsplittable_mtf_dimension_names = set()  # set(string)
    for mtf_operation in mtf_graph.operations:
      unsplittable_mtf_dimension_names.update(mtf_operation.unsplittable_dims)

    return all_mtf_dimension_names - unsplittable_mtf_dimension_names