# Frederic Green, Ph.D.

Professor

Department of Mathematics and Computer Science

Clark University

Worcester, MA 01610-1477

**Phone: **(508) 793-7410

**Email: **fgreen@black.clarku.edu

Professor Green received a B.S. from Renssalaer Polytechnic Institute in 1973, an M.S. from Worcester Polytechnic Institute and a Ph.D. from Yale University in 1986. He has been with Clark since 1986.

## Current Research and Teaching

Professor Green's research interests include theory of computation, circuit complexity, computational complexity, quantum computation, and theoretical and computational physics.

## Selected Publications

S. Fenner, F. Green, R. Gurjar, and S. Homer, "Some properties of sets in the plane closed under linear extrapolation by a fixed parameter," in arXiv:1212.2889v1 (submitted 12/12/12, 12:12:12 EST).

F. Green, D. Kreymer, and E. Viola, "Block-Symmetric Polynomials Correlate with Parity Better Than Symmetric," in Electronic Colloquium on Computational Complexity, report 160 (2012); PDF available here.

F. Green, D. Kreymer, and E. Viola, "In Brute-Force Search of Correlation Bounds for Polynomials," in Electronic Colloquium on Computational Complexity, report 39 (2011); PDF available here.

D. Bera, S. Fenner, F. Green and S. Homer, Universal Quantum Circuits, in arXiv:0804.2429 (2008). Appeared under the title "Efficient Universal Quantum Circuits", in COCOON 2009, pp. 418-428, LNCS 5609 (Springer-Verlag), and in *Quantum Information and Computation* **10** (2010) 16-27.

F. Green and A. Roy, Uniqueness of optimal mod 3 circuits for parity, in Dagstuhl Seminar Proceedings 07411 "Algebraic Methods in Computational Complexity" (2008). Also available: powerpoint and keynote slides. Updated & corrected version appeared under the title Uniqueness of optimal mod 3 polynomials for parity in *Journal of Number Theory* **130** (2010), pp. 961 - 975, full text available on-line here. (Okay, you read the paper, you glanced at the slides. Now you can see the movie!)

F. Green, Mathematics of Physics and Engineering by E. K. Blum and S. V. Lototsky (book review), SIGACT News **38**, pp. 25 - 30 (2007). PDF.

D. Bera, F. Green and S. Homer, Small-depth quantum circuits (survey article), SIGACT News **35**, pp. 35 - 50 (2007). PDF.

M. Fang, S. Fenner, F. Green, S. Homer, and Y. Zhang, Quantum lower bounds for fanout, arXiv preprint quant-ph/0312208. In *Quantum Information and Computation* **6** (2006), pp. 46-57.

F. Green, A. Roy, and H. Straubing, Bounds on an exponential sum arising in Boolean circuit complexity, in *Comptes Rendus* **341(5)** (2005), pp. 279-282.

S. Fenner, F. Green, S. Homer, and Y. Zhang, Bounds on the power of constant-depth quantum circuits, arXiv preprint quant-ph/0312209. Appeared in *Proceedings of Fundamentals of Computation Theory: 15th International Symposium*, Lecture Notes in Computer Science 3623 (2005), pp. 44-55.