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Kolmogorov complexity is the length of the ultimately compressed version of a file (that is, anything which can be put in a computer). Formally, it is the length of a shortest program from which the file can be reconstructed. We discuss the incomputabilty of Kolmogorov complexity, which formal loopholes this leaves us, recent approaches to compute or approximate Kolmogorov complexity, which approaches are problematic and which approaches are viable.
There is a parallelism between Shannon information theory and algorithmic information theory. In particular, the same linear inequalities are true for Shannon entropies of tuples of random variables and Kolmogorov complexities of tuples of strings (H
The quantum complexity of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational co
We investigate the relationship between Orthogonal Time Frequency Space (OTFS) modulation and Orthogonal Short Time Fourier (OSTF) signaling. OTFS was recently proposed as a new scheme for high Doppler scenarios and builds on OSTF. We first show that
Suppose a Boolean function $f$ is symmetric under a group action $G$ acting on the $n$ bits of the input. For which $G$ does this mean $f$ does not have an exponential quantum speedup? Is there a characterization of how rich $G$ must be before the fu
We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density $> 1$ and also to quantum sampling subset sum solutions. We examine a decision versio