Due to the ever-increasing toll of soft errors in memories, Error Correction Codes (ECCs) like Hamming and Reed-Solomon Codes have been used to protect data in memories, in applications ranging from space to terresterial work stations. In past seven decades, most of the research has focused on providing better ECC strategies for data integrity in memories, but the same pace research efforts have not been made to develop better verification methodologies for the newer ECCs. As the memory sizes keep increasing, exhaustive simulation-based testing of ECCs is no longer practical. Hence, formal verification, particularly theorem proving, provides an efficient, yet scarcely explored, alternative for ECC verification. We propose a framework, with extensible libraries, for the formal verification of ECCs using the ACL2 theorem prover. The framework is easy to use and particularly targets the needs of formally verified ECCs in memories. We also demonstrate the usefulness of the proposed framework by verifying two of the most commonly used ECCs, i.e., Hamming and Convolutional codes. To illustrate that the ECCs verified using our formal framework are practically reliable, we utilized a formal record-based memory model to formally verify that the inherent properties of the ECCs like hamming distance, codeword decoding, and error detection/correction remain consistent even when the ECC is implemented on the memory.

中文翻译：

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使用 ACL2 对内存的 ECC 进行正式验证

由于存储器中软错误的数量不断增加，诸如汉明码和里德-所罗门码之类的纠错码 (ECC) 已被用于保护存储器中的数据，应用范围从太空到地面工作站。在过去的七年里，大部分研究都集中在为存储器中的数据完整性提供更好的 ECC 策略上，但并没有以同样的速度为较新的 ECC 开发更好的验证方法。随着内存大小的不断增加，对 ECC 进行详尽的基于仿真的测试已不再实用。因此，形式验证，尤其是定理证明，为 ECC 验证提供了一种有效但很少被探索的替代方法。我们提出了一个带有可扩展库的框架，用于使用 ACL2 定理证明器对 ECC 进行形式验证。该框架易于使用，特别针对内存中经过正式验证的 ECC 的需求。我们还通过验证两个最常用的 ECC，即汉明和卷积码来证明所提出框架的有用性。为了说明使用我们的正式框架验证的 ECC 实际上可靠，我们使用正式的基于记录的内存模型来正式验证 ECC 的固有属性，如汉明距离、码字解码和错误检测/纠正，即使在ECC 是在内存上实现的。