Lectures & Presentations

Most optimization problems face the challenge of computing an optimum solution requiring superpolynomial time. In particular, they are classified as NP-hard problems that have no polynomial-time algorithm to date. Instead, computer scientists turn to find an approximate solution and create numerous elegant algorithms. However, in the modern era, computational environments have changed drastically, and we […]

   Simulation is a coinductive proof technique to assert the behavioral equivalence of computing systems that has seen fruitful application in distributed systems, concurrent process calculi, and programming languages, since the 1970’s. We have also utilized simulation in our prior work, where we formalized and proved a folklore claim that the state-based and operation-based approaches to […]

In this work, we develop numerical methods for conservation laws that explore statistical, structure-preserving, and machine-learning-based approaches, each built on top of traditional numerical solvers. First, we develop a general Gaussian-process-based “recipe’’ for constructing high-order linear operators such as interpolation, reconstruction, and derivative approximations. Building on this recipe, we derive a kernel-agnostic convergence theory for […]

Hardware design flows have become increasingly complex as modern chips integrate billions of transistors and rely on aggressive synthesis optimizations to meet performance, area, and power targets. While these transformations improve circuit efficiency, they also erase the correspondence between gate-level netlists and their originating HDL source lines. The loss of traceability makes post-synthesis debugging, timing […]