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This paper (https://t.co/0hMgVuPE1A) has now been accepted at #TOPLAS and will appear at #PLDI24 as a journal-first presentation. Proud of @meghana_aparna's excellent work on this, and many thanks to my amazing collaborator Tom Reps!
Let me now summarize why I am excited about this direction.
Graphs have long been used as compressed representations of large sets and functions -- BDDs and e-graphs are two classic examples. These graphs are often just automata in disguise -- for example, BDDs are minimal DFAs that read boolean assignments in a bit-serial order. More recently, e-graphs have also been understood to be a sort of tree automata -- see this beautiful work by Wang et al.
https://t.co/tROkujmBQl
But what if, instead of finite word/tree automata, we used richer (but still well-behaved) classes of automata to define compressed graph representations? Or what if we used tree automata not just to represent sets but functions over complex domains?
Our paper's essential finding is that a class of visibly pushdown automata could be used to implement linear algebra operations over very large matrices and vectors. These results follow up on old (and fascinating!) results on algebraic decision diagrams.
In current work, @meghana_aparna is exploring ways to use tree automata to represent such "exponential-scale" linear algebra. She will be at PLDI; ask her about these results!
Some CS papers are written over a few months -- some others, over a year. Our new Arxiv post, led by Tom Reps and @meghana_aparna, describes ideas developed over ~25 years.
https://t.co/jnpIiPmYQR (1/n)🧵

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