Share This Author
Disjointness is Hard in the Multiparty Number-on-the-Forehead Model
- Troy Lee, A. Shraibman
- Computer Science, Mathematics23rd Annual IEEE Conference on Computational…
- 27 December 2007
These results imply subexponential lower bounds on the size of proofs needed to refute certain unsatisfiable CNFs in a broad class of proof systems, including tree-like Lovász–Schrijver proofs.
Quantum Attacks on Bitcoin, and How to Protect Against Them
- Divesh Aggarwal, G. Brennen, Troy Lee, M. Santha, M. Tomamichel
- Computer Science, MathematicsLedger
- 27 October 2017
It is found that the proof-of-work used by Bitcoin is relatively resistant to substantial speedup by quantum computers in the next 10 years, mainly because specialized ASIC miners are extremely fast compared to the estimated clock speed of near-term quantum computers.
Negative weights make adversaries stronger
- P. Høyer, Troy Lee, R. Spalek
- Computer Science, MathematicsSymposium on the Theory of Computing
- 5 November 2006
A stronger version of the adversary method which goes beyond this principle to make explicit use of the stronger condition that the algorithm actually computes the function, and which is a lower bound on bounded-error quantum query complexity.
THE QUANTUM ADVERSARY METHOD AND CLASSICAL FORMULA SIZE LOWER BOUNDS
- Sophie Laplante, Troy Lee, M. Szegedy
- Computer Science, Mathematics20th Annual IEEE Conference on Computational…
- 12 January 2005
Two new complexity measures for Boolean functions are introduced, which are named sumPI and maxPI, and the main result is proven via a combinatorial lemma which relates the square of the spectral norm of a matrix to the squares ofthe spectral norms of its submatrices.
The approximate rank of a matrix and its algorithmic applications: approximate rank
- N. Alon, Troy Lee, A. Shraibman, S. Vempala
- Mathematics, Computer ScienceSymposium on the Theory of Computing
- 1 June 2013
Borders are given on the ε-rank of a real matrix A, defined for any ε > 0 as the minimum rank over matrices that approximate every entry of A to within an additive ε.
A Direct Product Theorem for Discrepancy
- Troy Lee, A. Shraibman, R. Spalek
- Mathematics23rd Annual IEEE Conference on Computational…
- 22 June 2008
This work shows an optimal product theorem for discrepancy, namely that for any two Boolean functions f, g, disc(f odot g)=thetas(disc(f) disc(g)).
Quantum Query Complexity of State Conversion
- Troy Lee, R. Mittal, B. Reichardt, R. Spalek, M. Szegedy
- Computer Science, MathematicsIEEE Annual Symposium on Foundations of Computer…
- 12 November 2010
It is obtained that the general adversary bound characterizes the quantum query complexity of any function whatsoever, implying that discrete and continuous-time query models are equivalent in the bounded-error setting, even for the general state-conversion problem.
A note on the sign degree of formulas
- Troy Lee
- Computer Science, MathematicsArXiv
- 24 September 2009
These results essentially answer in the affirmative a conjecture of O'Donnell and Servedio that the sign degree--the minimal degree of a polynomial that agrees in sign with a function on the Boolean cube--of every formula of size n is O(sqrt(n).
Improved quantum query algorithms for triangle finding and associativity testing
It is shown that the quantum query complexity of detecting if an n-vertex graph contains a triangle is O(n9/7), and the main theorem shows how this high-level language can be compiled as a learning graph and gives the resulting complexity.
A New Rank Technique for Formula Size Lower Bounds
- Troy Lee
- Mathematics, Computer ScienceSymposium on Theoretical Aspects of Computer…
- 22 February 2007
A new technique for proving formula size lower bounds based on matrix rank gives bounds at least as large as those given by the method of Khrapchenko, originally used to prove an n2 lower bound on the parity function.