Related papers: Abelian networks II. Halting on all inputs

An abelian network is a collection of communicating automata whose state transitions and message passing each satisfy a local commutativity condition. This paper is a continuation of the abelian networks series of Bond and Levine (2016),…

In Deepak Dhar's model of abelian distributed processors, automata occupy the vertices of a graph and communicate via the edges. We show that two simple axioms ensure that the final output does not depend on the order in which the automata…

An abelian processor is an automaton whose output is independent of the order of its inputs. Bond and Levine have proved that a network of abelian processors performs the same computation regardless of processing order (subject only to a…

The critical group of an abelian network is a finite abelian group that governs the behavior of the network on large inputs. It generalizes the sandpile group of a graph. We show that the critical group of an irreducible abelian network…

The immediate past has witnessed an increased amount of interest in local algorithms, i.e., constant time distributed algorithms. In a recent survey of the topic (Suomela, ACM Computing Surveys, 2013), it is argued that local algorithms…

We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…

It is proved that, in certain subgroups of direct products of countable groups, the property of being an unconditionally closed set coincides with that of being an algebraic set. In particular, these properties coincide in all Abelian…

Automata networks are mappings of the form f : Q Z $\rightarrow$ Q Z , where Q is a finite alphabet and Z is a set of entities; they generalise Cellular Automata and Boolean networks. An update schedule dictates when each entity updates its…

Systems of deterministic finite automata communicating by sending their states upon request are investigated, when the amount of communication is restricted. The computational power and decidability properties are studied for the case of…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

We adapt the bialgebra and Hopf relations to expose internal structure in the ground state of a Hamiltonian with $Z_2$ topological order. Its tensor network description allows for exact contraction through simple diagrammatic rewrite rules.…

A quantum network is an open system consisting of several component Markovian input-output subsystems interconnected by boson field channels carrying quantum stochastic signals. Generalizing the work of Chebotarev and Gregoratti, we…

We investigate dynamical systems characterized by a time series of distinct semi-stable activity patterns, as they are observed in cortical neural activity patterns. We propose and discuss a general mechanism allowing for an adiabatic…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable and the set of admissible switching signals obeys pre-specified restrictions on switches between the subsystems and dwell times on…

Distributed automata are finite-state machines that operate on finite directed graphs. Acting as synchronous distributed algorithms, they use their input graph as a network in which identical processors communicate for a possibly infinite…

Automata networks, and in particular Boolean networks, are used to model diverse networks of interacting entities. The interaction graph of an automata network is its most important parameter, as it represents the overall architecture of…

Finitely many two-way automata work independently and synchronously on a unary input. Some of their states are broadcasting, i.e., dispatched to all other automata. At each step of the computation, each automaton changes state and moves…

We consider directed acyclic networks with multiple sources and multiple terminals where each source generates one i.i.d. random process over an abelian group and all the terminals want to recover the sum of these random processes. The…

Networks in nature do not act in isolation but instead exchange information, and depend on each other to function properly. An incipient theory of Networks of Networks have shown that connected random networks may very easily result in…

We consider networks of infinite-dimensional port-Hamiltonian systems $\mathfrak{S}_i$ on one-dimensional spatial domains. These subsystems of port-Hamiltonian type are interconnected via boundary control and observation and are allowed to…