Stochastic Automata Networks and Near Complete Decomposability

Stochastic Automata Networks

Complete Simulation of Automata Networks

Let A be a finite set and n ≥ 2. This paper introduces the concept of universal simulation in the context of semigroups of transformations of An, also known as finite state-homogeneous automata networks. For m ≥ n, a transformation of Am is defined as n-universal of size m if it may simulate every transformation of An by updating one coordinate (or register) at a time. Using tools from memoryle...

Preconditioning for Stochastic Automata Networks

LANGVILLE, AMY N. Preconditioning for Stochastic Automata Networks. (Under the direction of William J. Stewart.) Many very large Markov chains can be modeled efficiently as Stochastic Automata Networks (SANs). A SAN is composed of individual automata that, for the most part, act independently, requiring only infrequent interaction. SANs represent the generator matrix Q of the underlying Markov ...

Stochastic Automata Networks ( SAN ) - Modellingand

This article describes the use of Stochastic Automata Networks (SAN) as a modelling tool. A SAN model consists of some individual stochastic automata that act more or less independently of each other. An automata is represented by a number of states and probabilistic rules that govern the manner in which it moves from one state to the next. The state of a SAN is given by the state of each of it...

Graphs and Stochastic Automata Networks 1

We show how some graph theoretical arguments may be used to reduce the complexity of the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from a Stochastic Automata Network (SAN). The structural properties of the automata are used to establish new various results. First, we establish the complexity of the resolutio...