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%).

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