Research Interests
- Software Reliability and Verification
- Automated Theorem Proving
- Combinatorics, especially Graph Theory
- Computer Security
- Topology
- Group Theory
- Programing Language Design
- Computer Algebra
Current Projects
- Abstracting abstract machines quickly!
I am working with Professor Ben Hardekopf and the UCSB Programing Languages lab on developing abstract analysis for abstract machines that yield tractable analysis. The goal is for thsese analysis to be useful for real-world programs given semantics in terms of an abstract machine. This could help identify bugs or perform optimizations in code.
- Understanding 5-valent semi-symmetric graphs. Semi-symmetric graphs are uncommon, and the goal of this project is to learn more about the 5-valent ones. Little is known on the topic; current goals include finding an infinite family of such graphs and provably identifying the smallest such graph.
Resources
Publications
- Churchill, B. R., and Lamagna, E. A. "Summing symbols in mutual
recurrences." In Computing and Combinatorics, B. Fu and D.-Z. Du, Eds.,
vol. 6842 of Lecture Notes in Computer Science. Springer Berlin / Heidel-
berg, 2011, pp. 531-542.
preprint (pdf).
The original publication is available from www.springerlink.com.
- Churchill, B. R., and Lamagna, E. A. "An Efficient Algorithm for Deriving Summation Identities from Mutual Recurrences" (to appear in Discrete Mathematics, Algorithms and Applications) preprint (pdf).
Slides
- Summing Symbols in Mutual Recurrences. These are slides to accompany my talk that I gave at COCOON 2011. They are based on the paper of the same name, the preprint of which is available above.
- Discovering 5-Valent Semi-Symmetric Graphs. A talk on my work at Northern Arizona University's Research Experience for Undergraduates (REU) program. Describes attempts at enumerating 5-valent semi-symmetric graphs and some results.
- Proposal for my work at the NSF Digital Forensics REU at the University of Rhode Island