Formal Verification of ECCs for Memories Using ACL2

Naseer, Mahum; Ahmad, Waqar; Hasan, Osman

doi:10.1007/s10836-020-05904-2

Cited by 1 publication

(1 citation statement)

References 44 publications

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“…In Lean, a coding theory library called Cotoleta was developed and used to prove results about Levenshtein distance [14] and Hamming (7,4) codes [11]. Separately, Hamming(7,4) and 1 2 -rate convolutional codes were verified in the ACL2 theorem prover [20] with a particular focus on correcting memory errors; these codes were verified against a particular memory model. Both of these projects focused on verifying concrete-sized codes; thus they did not require the same level of abstraction or general mathematical reasoning as our work.…”

Section: Related Workmentioning

confidence: 99%

Verified Erasure Correction in Coq with MathComp and VST

Cohen

Wang

Appel

2022

Computer Aided Verification

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Most methods of data transmission and storage are prone to errors, leading to data loss. Forward erasure correction (FEC) is a method to allow data to be recovered in the presence of errors by encoding the data with redundant parity information determined by an error-correcting code. There are dozens of classes of such codes, many based on sophisticated mathematics, making them difficult to verify using automated tools. In this paper, we present a formal, machine-checked proof of a C implementation of FEC based on Reed-Solomon coding. The C code has been actively used in network defenses for over 25 years, but the algorithm it implements was partially unpublished, and it uses certain optimizations whose correctness was unknown even to the code’s authors. We use Coq’s Mathematical Components library to prove the algorithm’s correctness and the Verified Software Toolchain to prove that the C program correctly implements this algorithm, connecting both using a modular, well-encapsulated structure that could easily be used to verify a high-speed, hardware version of this FEC. This is the first end-to-end, formal proof of a real-world FEC implementation; we verified all previously unknown optimizations and found a latent bug in the code.

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