8. A processing device for recognizing a plurality of atoms of structured handwritten input, the processing device comprising: at least one processor; and a memory connected to the at least one processor, the memory further comprising: instructions for receiving an input indicating a second plurality of atoms of the plurality of atoms corresponding to a portion of the structured handwritten input, at least some of the second plurality of atoms having been misrecognized as a symbol not being under a root structure, instructions for displaying a menu of possible recognition results based on the second plurality of atoms, instructions for receiving a selection of one of the possible recognition results as a correction hint, instructions for determining whether a first part of the second plurality of atoms, corresponding to the correction hint, is under the root structure and whether a second part of the second plurality of atoms, corresponding to the correction hint, is not under the root structure; and instructions for recognizing the plurality of atoms, in conformance with the second correction hint, as including at least one symbol under the root structure, corresponding to the first part of the second plurality of atoms and the second part of the second plurality of atoms, when the first part of the second plurality of atoms is determined to be under the root structure and the second part of the second plurality of atoms is determined to be not under the root structure.
8. A processing device for recognizing a plurality of atoms of structured handwritten input, the processing device comprising: at least one processor; and a memory connected to the at least one processor, the memory further comprising: instructions for receiving an input indicating a second plurality of atoms of the plurality of atoms corresponding to a portion of the structured handwritten input, at least some of the second plurality of atoms having been misrecognized as a symbol not being under a root structure, instructions for displaying a menu of possible recognition results based on the second plurality of atoms, instructions for receiving a selection of one of the possible recognition results as a correction hint, instructions for determining whether a first part of the second plurality of atoms, corresponding to the correction hint, is under the root structure and whether a second part of the second plurality of atoms, corresponding to the correction hint, is not under the root structure; and instructions for recognizing the plurality of atoms, in conformance with the second correction hint, as including at least one symbol under the root structure, corresponding to the first part of the second plurality of atoms and the second part of the second plurality of atoms, when the first part of the second plurality of atoms is determined to be under the root structure and the second part of the second plurality of atoms is determined to be not under the root structure. 9. The processing device of claim 8 , wherein: the instructions for recognizing the plurality of atoms, in conformance with the second correction hint, further comprise: instructions for producing a second plurality of possible recognition results by summing scores corresponding to ones of a plurality of rewriting rules applied when producing each of the ones of the second plurality of possible recognition results from the plurality of atoms, instructions for determining whether applying any of the ones of the plurality of rewriting rules to the plurality of atoms to produce the ones of the second plurality of possible recognition results conforms with the correction hint, instructions for adding a penalty score to ones of the sums of the scores having a corresponding rewriting rule not conforming to the correction hint, and instruction for selecting a best recognition result from the second plurality of possible recognition results, the best recognition result having a highest score among the summed scores of each of the ones of the second possible recognition results.