System software is often complex and hides exploitable security vulnerabilities. Formal verification promises bug-free software but comes with a prohibitive proof cost. We present Spoq2, the first verification framework to highly automate security verification of unmodified system software. Spoq2 is based on the observation that many security properties, such as noninterference, can be reduced to establishing inductive invariants on individual transitions of a transition system that models system software. However, directly verifying such invariants for real system code overwhelms existing SMT solvers. Spoq2 makes this possible by automatically reducing verification complexity. It decomposes transitions into individual execution paths, extends cone-of-influence analysis to the individual transition level, and eliminates irrelevant machine states, clauses, and control-flow paths before invoking the SMT solver. Spoq2 further optimizes how pointer operations are modeled and verified through pointer abstractions that eliminate expensive bit-wise operations from SMT queries. We demonstrate the effectiveness of Spoq2 by verifying security properties of four unmodified, real-world system codebases with minimal manual effort.

Optimizing a quantum circuit is hard because it requires exploring a vast space of functionally equivalent circuits, produced by applying local circuit rewrites such as gate cancellation and commutation. Each additional rewrite can exponentially expand the space of equivalent circuits, so existing optimizers can only explore a tiny fraction of this space and often produce suboptimal results. We present Quasar, a new quantum circuit optimizer that can generate a step-limited optimal circuit: given a bound on rewrite iterations, it returns the lowest-cost circuit reachable within that bound. To achieve this, Quasar constructs two complementary e-graphs for the quantum circuit’s graph and sequence representations. Quasar then infers an atomic rewrite set for application on both e-graphs, which improves optimization performance by orders of magnitude. Finally, Quasar employs a series of new optimization techniques to ensure both soundness and scalability of equality saturation on quantum circuits. Across standard benchmarks, Quasar achieves geometric-mean reductions of 20.2% in 2-qubit gate count, 33.5% in total gate count, and 24.2% in circuit depth, and a 21.4% fidelity improvement over unoptimized circuits, outperforming or matching state-of-the-art rewrite-based optimizers on 75%, 92%, 62%, and 80% of circuits, respectively.