Biblio

We present two novel sound and complete netlist transformations, which substantially improve verification scalability while enabling very efficient trace reconstruction. First, we present a 2QBF variant of input reparameterization, capable of eliminating inputs without introducing new logic and without complete range computation. While weaker in reduction potential, it yields up to 4 orders of magnitude speedup to trace reconstruction when used as a fast-and-lossy preprocess to traditional reparameterization. Second, we present a novel scalable approach to leverage sequential unateness to merge selective inputs, in cases greatly reducing netlist size and verification complexity. Extensive benchmarking demonstrates the utility of these techniques. Connectivity verification particularly benefits from these reductions, up to 99.8%.

Cache coherence protocol bugs can cause multicores to fail. Existing coherence verification approaches incur state explosion at small scales or require considerable human effort. As protocols' complexity and multicores' core counts increase, verification continues to be a challenge. Recently, researchers proposed fractal coherence which achieves scalable verification by enforcing observational equivalence between sub-systems in the coherence protocol. A larger sub-system is verified implicitly if a smaller sub-system has been verified. Unfortunately, fractal protocols suffer from two fundamental limitations: (1) indirect-communication: sub-systems cannot directly communicate and (2) partially-serial-invalidations: cores must be invalidated in a specific, serial order. These limitations disallow common performance optimizations used by conventional directory protocols: reply-forwarding where caches communicate directly and parallel invalidations. Therefore, fractal protocols lack performance scalability while directory protocols lack verification scalability. To enable both performance and verification scalability, we propose Fractal++ which employs a new class of protocol optimizations for verification-constrained architectures: decoupled-replies, contention-hints, and fully-parallel-fractal-invalidations. The first two optimizations allow reply-forwarding-like performance while the third optimization enables parallel invalidations in fractal protocols. Unlike conventional protocols, Fractal++ preserves observational equivalence and hence is scalably verifiable. In 32-core simulations of single- and four-socket systems, Fractal++ performs nearly as well as a directory protocol while providing scalable verifiability whereas the best-performing previous fractal protocol performs 8% on average and up to 26% worse with a single-socket and 12% on average and up to 34% worse with a longer-latency multi-socket system.