PLSE Blog

Getting hardware right is crucial – without correct hardware, there’s no way to guarantee that software will work as intended. To raise the stakes even higher, hardware designers really only have one shot to get it right – once the hardware’s made, you can’t really patch it! To address this importance, there are many tools which use formal methods to give strong guarantees that hardware is correct. In practice, this often entails writing equivalence proofs showing that hardware behaves the same as some high-level model. In this post, we’ll take a look at the challenges I ran into while making Gator, a project I worked on which explored how to make these proofs easier!

In 1931, Kurt Godel stunned the world of mathematics when he published his “Incompleteness Theorem.” To summarize, the theorem stated that, no matter what set of rules we believe to be true about our world, there will always be statements that are… unprovable. This infuriated various mathematicians, who had believed that mathematics would be the key to proving everything! Now, I am not a mathematician, and this blog post is not a discussion of logic. However, this research (which I promise we will discuss momentarily) is often plagued by a strong desire for absolute correctness and proof, much like the mathematicians of the past. This ailment is in direct opposition with the only true rule known about the world of software testing, which is: Software testing is very hard.

Every programmer loves writing tests, but tests can’t say much about the correctness of your program. Wait a minute, what? You mean I’ve been writing tests all this time for absolutely nothing? I’ve been lied to in my undergrad software engineering course? Unfortunately, it seems like we’ve known this fact since at least 1969. A transcript from a conference on software engineering techniques sponsored by the NATO science committee contains the following quote by Edsger W. Dijkstra:

The past few weeks, I’ve been learning more about a few different kinds of weaving. One form of weaving is card weaving (also called tablet weaving), where the loom is instead replaced by square pieces of cardboard with holes punched in each corner. You may be wondering: how does a bunch of pieces of cardboard with holes weave cloth? I wondered the same thing myself! It seemed bonkers to think that you could do something with a bunch of cards that produced anything like fabric.

Ten years since its inception, the Herbie project remains an active source of research and is a marquee project of PLSE. It directly spawned four publications: Herbie at PLDI 2015, Pareto-Herbie (Pherbie) at ARITH 2021, Rival at ARITH 2023, and Odyssey at UIST 2023, and influenced many more papers (see an incomplete list). However, as with any long-standing project, we must question the fundamental idea behind it to inspire new directions of work. Previously, we pitched Herbie as a numerical analyst’s companion, a tool that automatically improves the accuracy of floating-point expressions. Now, we reenvision Herbie as a numerical compiler for programmers, lowering real expressions to floating-point implementations that are optimized for a given platform.

In my own research on Computer Algebra Systems (CAS), I often work some pretty cool data structures 😎. In this post, I want to show off one that’s responsible for simplifying polynomials. But first, I have a little secret…In high-school, I thought polynomials were boring! The hours I spent finding roots dragged on and on. They didn’t make pretty graphs like the trig functions. It’s only at this point in my life that I more fully appreciate them.

Have you ever wondered why hardware security isn’t a solved problem? It’s been six years since Spectre and Meltdown sent tech companies scrambling to fix the vulnerabilities that hardware manufacturers created with their own optimizations. Everyone involved–chip manufacturers, big tech, the security community–seems to agree that hardware security bugs are Bad and To Be Avoided. So if everyone believes that these vulnerabilies shouldn’t happen, why do they keep happening?

Testing cannot ensure correctness, but verification can. The problem with a specify-and-verify approach is the first part: the specification. Programmers are often reluctant to write specifications because it seems like extra work, beyond writing the code.

One of the great joys of being a researcher is observing an interesting phenomenon and deciding that you want to understand it and recreate it. Then there’s the additional joy of being a knitting researcher, and having that phenomenon be a cool object you can also display in your house or wear!