In this paper we prove a theorem about regression, in that the shortest description of a function consistent with a finite sample of data is less than the combined conditional Kolmogorov complexities over the data in the sample.
Verifiable delay functions (VDF) are functions that take a specified number of sequential steps to be evaluated but can be verified efficiently. In this paper, we show that every VDF is provable in PSPACE but every language in PSPACE does not admit to a VDF.
This work analyses the so-called "Relativization Barrier" with respect to the Baker-Gill-Solovay oracle Turing machine. We show that the {\em diagonalization} technique is a valid mathematical proof technique, but it has some prerequisites when referring to the "relativization barrier."
A relational bipartite communication problem is presented that has an efficient quantum simultaneous-messages protocol, but no efficient classical two-way protocol.
In this paper, we show that there exists a balanced linear threshold function (LTF) which is unique games hard to approximate, refuting a conjecture of Austrin, Benabbas, and Magen. We also show that the almost monarchy predicate on k variables is approximable for sufficiently large k.
Settling a conjecture of Shi and Zhang, we determine the unbounded-error communication complexity of the symmetric XOR functions up to a poly-logarithmic factor. Our proof is by a simple reduction to an earlier result of Sherstov.
We define nondeterministic communication complexity in the model of communication complexity with help of Babai, Hayes and Kimmel. We use it to prove logarithmic lower bounds on the NOF communication complexity of explicit graph functions, which are complementary to the bounds proved by Beame, David, Pitassi and Woelfel.
We prove that the sensitivity of any non-trivial graph property on $n$ vertices is at least $\lfloor \frac{1}{2}n \rfloor$ , provided $n$ is sufficiently large.
This paper introduces a new inequality in algorithmic information theory that can be seen as an extended coding theorem. This inequality has applications in new bounds between quantum complexity measures.
We give a $O^*(k^{O(k)})$ time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by $k$ which improves on the previous best running time bound of $O^*(2^{O(k^2/\log k)})$.
We develop a pseudo-random generator to fool degree-$d$ polynomial threshold functions with respect to the Gaussian distribution. For $c>0$ any constant, we construct a pseudo-random generator that fools such functions to within $ε$ and has seed length $\log(n) 2^{O(d)} ε^{-4-c}$.
A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of Doctor of Philosophy (PhD) in the Faculty of Engineering, Department of Computer Science, July 2009.
Sujogya Banerjee, Shahrzad Shirazipourazad, Pavel Ghosh
et al.
Computational complexity of the design problem for a network with a target value of Region-Based Component Decomposition Number (RBCDN) has been proven to be NP-complete.
We motivate and prove a strong pumping lemma for regular tree languages. The new lemma can be seen as the natural correspondent of Ogden's lemma for context-free string languages.