Temporal logics like Computation Tree Logic (CTL) have been widely used as expressive formalisms to capture rich behavioural specifications. CTL can express properties such as reachability, termination, invariants and responsiveness, which are difficult to test. This paper suggests a mechanism for the automated repair of infinite-state programs guided by CTL properties. Our produced patches avoid the overfitting issue that occurs in test-suite-guided repair, where the repaired code may not pass tests outside the given test suite. To realise this vision, we propose a novel find-and-fix framework based on Datalog, a widely used domain-specific language for program analysis, which readily supports nested fixed-point semantics of CTL via stratified negation. Specifically, our framework encodes the program and CTL properties into Datalog facts and rules and performs the repair by modifying the facts to pass the analysis rules. In the framework, to achieve both analysis and repair results, we adapt existing techniques – including loop summarisation and Symbolic Execution of Datalog (SEDL) – with key modifications. Our approach achieves analysis accuracy of 56.6% on a CTL verification benchmark and 88.5% on a termination/responsiveness benchmark, surpassing the best baseline performances of 27.7% and 76.9%, respectively. Our approach repairs all detected bugs, which is not achieved by existing tools.

Large language models such as Codex, have shown the capability to produce code for many programming tasks. However, the success rate of existing models is low, especially for complex programming tasks. One of the reasons is that language models lack awareness of program semantics, resulting in incorrect programs, or even programs which do not compile. In this paper, we systematically study whether automated program repair (APR) techniques can fix the incorrect solutions produced by language models in LeetCode contests. The goal is to study whether APR techniques can enhance reliability in the code produced by large language models. Our study revealed that: (1) automatically generated code shares common programming mistakes with human-crafted solutions, indicating APR techniques may have potential to fix auto-generated code; (2) given bug location information provided by a statistical fault localization approach, the newly released Codex edit mode, which supports editing code, is similar to or better than existing Java repair tools TBar and Recoder in fixing incorrect solutions. By analyzing the experimental results generated by these tools, we provide several suggestions: (1) enhancing APR tools to surpass limitations in patch space (e.g., introducing more flexible fault localization) is desirable; (2) as large language models can derive more fix patterns by training on more data, future APR tools could shift focus from adding more fix patterns to synthesis/semantics based approaches, (3) combination of language models with APR to curate patch ingredients, is worth studying.