I am a PhD candidate at the University of Illinois at Urbana-Champaign in the department of Computer Science working with Madhusudan Parthasarathy. My primary area of research touches programming languages, logic, and formal methods. I am also an avid jazz alto saxophone player 🎷. Shoot me an email if you’d like to talk about anything below.

I'm on the faculty job market.

Current Interests

  • Bridges between natural language and formal computer language
  • Language-general techniques for putting symbolic knowledge into machine learning models
  • Data-driven, automated construction of DSLs
  • Data-driven techniques for making conjectures in math and science
  • Computational universality with errors:

    How can finitely-accurate processes perform universal computations?

  • Formal expressivity and algorithmic capabilities of neural architecture classes
  • Open-ended evolution, especially of language, and connections between evolution and learning
  • Human-computer collaborative music improvisation
  • Teaching computer science and music improvisation together:

    Learning to improvise within classes of "regular" riffing patterns, adding a "stack", etc.

  • Rigorous, logical characterizations of creativity:

    What's the difference between creative processes and automatic processes?

Ongoing Projects

  • DSL synthesis: foundational theory and algorithms for automatically synthesizing DSLs that express relevant domain concepts succinctly and irrelevant ones less succinctly or not at all
  • Emergence of symbolic language: developing a computational model in which symbolic language and abstraction are emergent outcomes of computation
  • Example-driven geometry proofs: using small diagrams to guide auxiliary constructions in geometry proofs

Publications

Synthesizing DSLs for Few-shot Learning
Paul Krogmeier and P. Madhusudan
in submission
Languages with Decidable Learning: A Meta-theorem
Paul Krogmeier and P. Madhusudan
★Distinguished Paper Award at OOPSLA 2023
Synthesizing Axiomatizations using Logic Learning
Paul Krogmeier*, Zhengyao Lin*, Adithya Murali*, and P. Madhusudan
OOPSLA 2022
Composing Neural Learning and Symbolic Reasoning with an Application to Visual Discrimination
Adithya Murali, Atharva Sehgal, Paul Krogmeier, and P. Madhusudan
IJCAI 2022
Learning Formulas in Finite Variable Logics
Paul Krogmeier and P. Madhusudan
★Distinguished Paper Award at POPL 2022
Deciding Accuracy of Differential Privacy Schemes
Gilles Barthe, Rohit Chadha, Paul Krogmeier, A. Prasad Sistla, and Mahesh Viswanathan
POPL 2021
Decidable Synthesis of Programs with Uninterpreted Functions
Paul Krogmeier, Umang Mathur, Adithya Murali, P. Madhusudan, and Mahesh Viswanathan
CAV 2020
Deciding Memory Safety for Single-Pass Heap-Manipulating Programs
Umang Mathur, Adithya Murali, Paul Krogmeier, P. Madhusudan, and Mahesh Viswanathan
POPL 2020
Towards Context-Aware Data Refinement
Paul Krogmeier, Steven Kidd, and Benjamin Delaware
Intl. Workshop on Coq for Programming Languages 2018

*equal contribution