Related papers: Threefold Post Correspondence System
We introduce the notion of a {\it mock tridiagonal system}. This is a generalization of a tridiagonal system in which the irreducibility assumption is replaced by a certain non-vanishing condition. We show how mock tridiagonal systems can…
We introduce a new model of spatial random multiple access systems with a non-standard departure policy: all arriving messages are distributed uniformly on a finite sphere in the space, and when a successful transmission of a single message…
Developing conversational systems that can converse in many languages is an interesting challenge for natural language processing. In this paper, we introduce multilingual addressee and response selection. In this task, a conversational…
Post Embedding Problems are a family of decision problems based on the interaction of a rational relation with the subword embedding ordering, and are used in the literature to prove non multiply-recursive complexity lower bounds. We refine…
This paper is an overview and survey of work on the 3x+1 problem, also called the Collatz problem, and generalizations of it. It gives a history of the problem. It addresses two questions: (1) What can mathematics currently say about this…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
We derive three fundamental decompositions on relevant information quantities in feedback systems. The feedback systems considered in this paper are only restricted to be causal in time domain and the channels are allowed to be subject to…
We revisit finite-state communicating systems with round-based communication under mailbox semantics. Mailboxes correspond to one FIFO buffer per process (instead of one buffer per pair of processes in peer-to-peer systems). Round-based…
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…
In tri-partite systems, there are three basic biseparability, $A$-$BC$, $B$-$CA$ and $C$-$AB$ biseparability according to bipartitions of local systems. We begin with three convex sets consisting of these basic biseparable states in the…
Particle systems admit a variety of tensor product structures (TPSs) depending on the complete system of commuting observables chosen for the analysis. Different notions of entanglement are associated with these different TPSs. Global…
In this note, we construct a $3$-dimensional generalisation of the Pascal's triangle that we named Pascal's cube, as it has the construction of a cube with entries given by extended binomial coefficients ${}^cC^{a}_{b}$. The Pascal's cube…
In a variant of communication complexity tasks, two or more separated parties cooperate to compute a function of their local data, using a limited amount of communication. It is known that communication of quantum systems and shared…
We consider the transmission of a common message from a transmitter to three receivers over a broadcast channel, referred to as a multicast channel in this case. All the receivers are allowed to cooperate with each other over full-duplex…
In this paper we revisit the basic variant of the classical secretary problem. We propose a new approach in which we separate between an agent that evaluates the secretary performance and one that has to make the hiring decision. The…
Nowadays, we are to find out solutions to huge computing problems very rapidly. It brings the idea of parallel computing in which several machines or processors work cooperatively for computational tasks. In the past decades, there are a…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
We study the manipulability of social choice correspondences in situations where individuals have incomplete information about others' preferences. We propose a general concept of manipulability that depends on the extension rule used to…
In times of Industry 4.0 and cyber-physical systems (CPS) providing security is one of the biggest challenges. A cyber attack launched at a CPS poses a huge threat, since a security incident may affect both the cyber and the physical world.…
The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general…