Related papers: Complexity of universal access structures
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
We construct general schemes for multi-partite quantum secret sharing using multi-level systems, and find that the consistent conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using the very…
Any secured system can be modeled as a capability-based access control system in which each user is given a set of secret keys of the resources he is granted access to. In some large systems with resource-constrained devices, such as sensor…
In secure summation, $K$ users, each holds an input, wish to compute the sum of the inputs at a server without revealing any information about {\em all the inputs} even if the server may collude with {\em an arbitrary subset of users}. In…
The unconditional security of a quantum key distribution protocol is often defined in terms of the accessible information, that is, the maximum mutual information between the distributed key S and the outcome of an optimal measurement on…
We generalise some well-known graph parameters to operator systems by considering their underlying quantum channels. In particular, we introduce the quantum complexity as the dimension of the smallest co-domain Hilbert space a quantum…
Composite systems are large complex systems con- sisting of interconnected agents (subsystems). Agents in a com- posite system interact with each other towards performing an in- tended goal. Controllability is essential to achieve desired…
We study the reachability problem of a quantum system modelled by a quantum automaton. The reachable sets are chosen to be boolean combinations of (closed) subspaces of the state space of the quantum system. Four different reachability…
This work investigates the existence of complex structures on 2-step nilpotent Lie algebras arising from finite graphs. We introduce the notion of adapted complex structure, namely a complex structure that maps vertices and edges of the…
Given a partition of a graph into connected components, the membership oracle asserts whether any two vertices of the graph lie in the same component or not. We prove that for $n\ge k\ge 2$, learning the components of an $n$-vertex hidden…
Recent decades have seen the discovery of numerous complex materials. At the root of the complexity underlying many of these materials lies a large number of possible contending atomic- and larger-scale configurations and the intricate…
In this work we revisit the fundamental findings by Chen et al. in [5] on general information transfer in linear ramp secret sharing schemes to conclude that their method not only gives a way to establish worst case leakage [5, 25] and best…
It is known that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings x and y is equal to the length of the longest shared secret key that two parties can establish via a probabilistic protocol with…
We study structure of pure morphic and morphic sequences and prove the following result: the subword complexity of arbitrary morphic sequence is either $\Theta(n^{1+1/k})$ for some $k\in\mathbb N$, or is $O(n \log n)$.
Consider a source and multiple users who observe the independent and identically distributed (i.i.d.) copies of correlated Gaussian random variables. The source wishes to compress its observations and store the result in a public database…
This paper shows how maximum possible configuration efficiency of an indefinitely large software system is constrained by chosing a fixed upper limit to the number of program units per subsystem. It is then shown how the configuration…
Projecting fields between different meshes commonly arises in computational physics. This operation requires a supermesh construction and its computational cost is proportional to the number of cells of the supermesh $n$. Given any two…
The fundamental limits of biometric identification systems under a strong secrecy criterion are investigated. In the previous studies of this scenario, the fundamental trade-off among secrecy, template, privacy- and secrecy-leakages has…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
Following a review of related results in rigidity theory, we provide a construction to obtain generically universally rigid frameworks with the minimum number of edges, for any given set of n nodes in two or three dimensions. When a set of…