Error Detection and Correction Codes (ECCs) are often used in digital designs to protect data integrity. Especially in safety-critical systems such as automotive electronics, ECCs are widely used and the verification of such complex logic becomes more critical considering the ISO 26262 safety standards. Exhaustive verification of ECC using formal methods has been a challenge given the high number of data bits to protect. As an example, for an ECC of 128 data bits with a possibility to detect up to four-bit errors, the combination of bit errors is given by 128C1 + 128C2 + 128C3 + 128C4 = 1.1 * 10^7. This vast analysis space often leads to bounded proof results. Moreover, the complexity and state-space increase further if the ECC has sequential encoding and decoding stages. To overcome such problems and sign-off the design with confidence within reasonable proof time, we present a pragmatic formal verification approach of complex ECC cores with several complexity reduction techniques and know-how that were learnt during the course of verification. We discuss using the linearity of the syndrome generator as a helper assertion, using the abstract model as glue logic to compare the RTL with the sequential version of the circuit, k-induction-based model checking and using mathematical relations captured as properties to simplify the verification in order to get an unbounded proof result within 24 hours of proof runtime.

Modern hardware designs have grown increasingly efficient and complex. However, they are often susceptible to Common Weakness Enumerations (CWEs). This paper is focused on the formal verification of CWEs in a dataset of hardware designs written in SystemVerilog from Regenerative Artificial Intelligence (AI) powered by Large Language Models (LLMs). We applied formal verification to categorize each hardware design as vulnerable or CWE-free. This dataset was generated by 4 different LLMs and features a unique set of designs for each of the 10 CWEs we target in our paper. We have associated the identified vulnerabilities with CWE numbers for a dataset of 60,000 generated SystemVerilog Register Transfer Level (RTL) code. It was also found that most LLMs are not aware of any hardware CWEs; hence they are usually not considered when generating the hardware code. Our study reveals that approximately 60% of the hardware designs generated by LLMs are prone to CWEs, posing potential safety and security risks. The dataset could be ideal for training LLMs and Machine Learning (ML) algorithms to abstain from generating CWE-prone hardware designs. With the increasing complexity of project requirements, hardware designs have also evolved in a similar way. Modern System-on-Chip (SoC) designs are very complex and often require smart methodologies to address simple problems.