Related papers: Measuring communication complexity using instance …
Humans communicate using systems of interconnected stimuli or concepts -- from language and music to literature and science -- yet it remains unclear how, if at all, the structure of these networks supports the communication of information.…
For any $n$-bit boolean function $f$, we show that the randomized communication complexity of the composed function $f\circ g^n$, where $g$ is an index gadget, is characterized by the randomized decision tree complexity of $f$. In…
We suggest two new methodologies for the design of efficient secure protocols, that differ with respect to their underlying computational models. In one methodology we utilize the communication complexity tree (or branching for f and…
Deterministic and probabilistic communication protocols are introduced in which parties can exchange the values of polynomials (rather than bits in the usual setting). It is established a sharp lower bound $2n$ on the communication…
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 study which outcomes are implementable by disclosing coarse statistics of a data-generating process rather than its full distribution. Players observe data whose joint distribution is only partially known: they know the expectations of…
The theoretical limits of 'lossy' data compression algorithms are considered. The complexity of an object as seen by a macroscopic observer is the size of the perceptual code which discards all information that can be lost without altering…
Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
We define correlational (von Neumann) entropy for an individual quantum state of a system whose time-independent hamiltonian contains random parameters and is treated as a member of a statistical ensemble. This entropy is representation…
Fisher information, Shannon information entropy and Statistical Complexity are calculated for the interface of a normal metal and a superconductor, as a function of the temperature for several materials. The order parameter $\Psi({\bf r})$…
The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
We define a notion of complexity, which quantifies the nonlinearity of the computation of a neural network, as well as a complementary measure of the effective dimension of feature representations. We investigate these observables both for…
Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not…
Communication complexity problems (CCPs) are tasks in which separated parties attempt to compute a function whose inputs are distributed among the parties. Their communication is limited so that not all inputs can be sent. We show that…
The uncertainty principle can be expressed in entropic terms, also taking into account the role of entanglement in reducing uncertainty. The information exclusion principle bounds instead the correlations that can exist between the outcomes…
This paper presents a new language called APSL for formally describing protocols to facilitate automated testing. Many real world communication protocols exchange messages whose structures are not trivial, e.g. they may consist of multiple…
Human communication is commonly represented as a temporal social network, and evaluated in terms of its uniqueness. We propose a set of new entropy-based measures for human communication dynamics represented within the temporal social…
Predictive inference requires balancing statistical accuracy against informational complexity, yet the choice of complexity measure is usually imposed rather than derived. We treat econometric objects as predictive rules, mappings from…