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Hardware accelerators (HAs) are essential building blocks for fast and energy-efficient computing systems. Accelerator Quick Error Detection (A-QED) is a recent formal technique which uses Bounded Model Checking for pre-silicon verification of HAs. A-QED checks an HA for self-consistency, i.e., whether identical inputs within a sequence of operations always produce the same output. Under modest assumptions, A-QED is both sound and complete. However, as is well-known, large design sizes significantly limit the scalability of formal verification, including A-QED. We overcome this scalability challenge through a new decomposition technique for A-QED, called A-QED with Decomposition $(A-Q E D^{2})$. A-QED <sup>2</sup> systematically decomposes an HA into smaller, functional sub-modules, called sub-accelerators, which are then verified independently using A-QED. We prove completeness of $A-QED^{2} $; in particular, if the full HA under verification contains a bug, then $A-QED^{2}$ ensures detection of that bug during A-QED verification of the corresponding subaccelerators. Results on over 100 (buggy) versions of a wide variety of HAs with millions of logic gates demonstrate the effectiveness and practicality of $A-QED^{2}$.

Scaling Up Hardware Accelerator Verification using A-QED with Functional Decomposition