Post-processing Error Correction Rules

These rely on the programmer anticipating what sort of errors may occur and providing means for dealing with them in advance. For example:

• ``5in'' $\rightarrow$ ``sin'',
• ``c0s'' $\rightarrow$ ``cos'',
• ``/ < i < n'' $\rightarrow$ ``1 < i < n'',
• ``5<sub>2</sub>'' $\rightarrow$ ``S₂''

The limitation of this approach is that it is not possible to automatically generate these rules. However, a stochastic grammar is able to automatically choose likely alternatives when given an unparsable formula. Miller and Viola  give an example, where their system attempted to parse ``0<sup>0<sub>0</sub></sup>''. The system realised that ``0₀'' was not a legal construct and concluded that it was most likely to be ``00''. As the output ``0⁰⁰'' would be illegal, due to a two digit number not being allowed to begin with a ``0'', it considered all the digits to be approximately the same size, and use an alternative recognition of the first digit, giving ``600'' as the best interpretation. While this was not the ``correct'' interpretation of the formula given that the input was ``0^0₀'', it was the most likely interpretation within the constraints of the grammar the system was using.

give an example, where their system attempted to parse ``0<sup>0<sub>0</sub></sup>''. The system realised that ``0₀'' was not a legal construct and concluded that it was most likely to be ``00''. As the output ``0⁰⁰'' would be illegal, due to a two digit number not being allowed to begin with a ``0'', it considered all the digits to be approximately the same size, and use an alternative recognition of the first digit, giving ``600'' as the best interpretation. While this was not the ``correct'' interpretation of the formula given that the input was ``0^0₀'', it was the most likely interpretation within the constraints of the grammar the system was using.