  The development of correct and efficient software can be hindered by
compilation errors, which must be fixed to ensure the code's syntactic
correctness and program language constraints. Neural network-based approaches
have been used to tackle this problem, but they lack guarantees of output
correctness and can require an unlimited number of modifications. Fixing
compilation errors within a given number of modifications is a challenging
task. We demonstrate that finding the minimum number of modifications to fix a
compilation error is NP-hard. To address compilation error fixing problem, we
propose OrdinalFix, a complete algorithm based on shortest-path CFL
(context-free language) reachability with attribute checking that is guaranteed
to output a program with the minimum number of modifications required.
Specifically, OrdinalFix searches possible fixes from the smallest to the
largest number of modifications. By incorporating merged attribute checking to
enhance efficiency, the time complexity of OrdinalFix is acceptable for
application. We evaluate OrdinalFix on two datasets and demonstrate its ability
to fix compilation errors within reasonable time limit. Comparing with existing
approaches, OrdinalFix achieves a success rate of 83.5%, surpassing all
existing approaches (71.7%).
