Related papers: Three problems for the clairvoyant demon
We use three kinds of computations: simulation, numeric, and symbolic, to guide risk-averse gamblers in general, and offer particular advice on how to resolve the famous St. Petersburg paradox.
We show that solving delay games with winning conditions given by deterministic and nondeterministic weak Muller automata is 2EXPTIME-complete respectively 3EXPTIME-complete. Furthermore, doubly and triply exponential lookahead is necessary…
It is shown that under reasonable assumptions a Drake-style equation can be obtained for the probability that our universe is the result of a deliberate simulation. Evaluating loose bounds for certain terms in the equation shows that the…
We propose a new approach to solve the classical Monty Hall problem in its general form. The solution is based on basic tools of probability theory, by defining three elementary events which decompose the sample space into a partition. The…
We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can…
We consider the possibility problem of determining if a document is a possible world of a probabilistic document, in the setting of probabilistic XML. This basic question is a special case of query answering or tree automata evaluation, but…
We study quantum Maxwell's demon in a discrete space-time setup. We consider a collection of particles hopping on a one-dimensional chain and a semipermeable barrier that allows the particles to hop in only one direction. Our main result is…
We investigate several varying-mass dark-matter particle models in the framework of phantom cosmology. We examine whether there exist late-time cosmological solutions, corresponding to an accelerating universe and possessing dark energy and…
The notion of convolution of two probability vectors, corresponding to a coincidence experiment can be extended for a family of binary operations determined by (tri)stochastic tensors, to describe Markov chains of a higher order. The…
The problem of pattern selection arises when the evolution equations have many solutions, whereas observed patterns constitute a much more restricted set. An approach is advanced for treating the problem of pattern selection by defining the…
Tiling planar regions with dominoes is a classical problem in which the decision and counting problems are polynomial. We prove a variety of hardness results (both NP- and #P-completeness) for different generalizations of dominoes in three…
This is perhaps a philosophical question rather than a mathematical one, we do not expect to give a full answer, even though we hope to clarify some ideas. In addition, we would like to provide a new perspective on the subject. We will find…
A common approach is present concerning the problem of Dirichlet, both for bounded 3D domains and their (unbounded) complements, regarding the fractional (3D) Poisson equation.
We describe some three-dozen curious phenomena manifested by parabolas inscribed or circumscribed about certain Poncelet triangle families. Despite their pirouetting motion, parabolas' focus, vertex, directrix, etc., will often sweep or…
We give optimal solutions to all versions of the popular counterfeit coin problem obtained by varying whether (i) we know if the counterfeit coin is heavier or lighter than the genuine ones, (ii) we know if the counterfeit coin exists,…
The fact that real dissipative (entropy producing) processes may be detected by non-comoving observers (tilted), in systems that appear to be isentropic for comoving observers, in general relativity, is explained in terms of the information…
Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the…
We give an introduction to some of the recent ideas that go under the name "geometric complexity theory". We first sketch the proof of the known upper and lower bounds for the determinantal complexity of the permanent. We then introduce the…
In the present paper, several issues concerning the second law of thermodynamics, Maxwell's demon and Landauer's principle are dealt with. I argue that if the demon and the system on which it operates without dissipation of external energy…
Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman topology and…