Memory minimisation in control with stochastic automata

1971 ◽  
Vol 7 (24) ◽  
pp. 710 ◽  
Author(s):  
B.R. Gaines
Keyword(s):  
Stochastic Automata

scholarly journals Multipreconditioned GMRES for simulating stochastic automata networks

2018 ◽  
Vol 16 (1) ◽  
pp. 986-998
Author(s):  
Chun Wen ◽  
Ting-Zhu Huang ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen ◽  
Hong-Fan Zhang ◽  
...  
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Linear Systems ◽  
Iterative Methods ◽  
Communication Systems ◽  
Queueing Systems ◽  
Steady State Probability ◽  
Stochastic Automata ◽  
Automata Networks ◽  
Generator Matrices

AbstractStochastic Automata Networks (SANs) have a large amount of applications in modelling queueing systems and communication systems. To find the steady state probability distribution of the SANs, it often needs to solve linear systems which involve their generator matrices. However, some classical iterative methods such as the Jacobi and the Gauss-Seidel are inefficient due to the huge size of the generator matrices. In this paper, the multipreconditioned GMRES (MPGMRES) is considered by using two or more preconditioners simultaneously. Meanwhile, a selective version of the MPGMRES is presented to overcome the rapid increase of the storage requirements and make it practical. Numerical results on two models of SANs are reported to illustrate the effectiveness of these proposed methods.

On extension of stochastic k-automata

1977 ◽  
Vol 1 (1) ◽  
pp. 231-241
Author(s):  
Sławomir Janicki ◽  
Dominik Szynal
Keyword(s):  
Probability Measure ◽  
Common Generalization ◽  
Stochastic Automata ◽  
Stochastic Automaton ◽  
Chain Type ◽  
Markov’S Chain

There are a great many research works concerning the well-known stochastic automata of Moore, Mealy, Rabin, Turing and others. Recently an automaton of Markov’s chain type has been introduced by Bartoszyński. This automaton is obtained by a generalization of Pawlak’s deterministic machine. The aim of this note is to give a concept of a stochastic automaton of Markov’s generalized chain type. The introduced automaton called a stochastic k-automaton (s.k-a.) is a common generalization of Bartoszyński’s automaton and Grodzki’s deterministic k-machine. By a stochastic k-automaton we mean an ordered triple M k = ⟨ U , a , π ⟩, k ⩾ 1, where U denotes a finite non-empty set, a is a function from Uk to [0, 1] with ∑ v ∈ U k a ( v ) = 1, and π is a function from Uk+1 to [0,1] with ∑ u ∈ U π ( v , u ) = 1 for every v ∈ U k . For all N ⩾ k we can define a probability measure PN on U N = U × U × … × U as follows: P N ( u 1 , u 2 , … , u N ) = a ( u 1 , u 2 , … , u k ) π ( u 1 , u 2 , … , u k + 1 ) π ( u 2 , u 3 , … , u k + 2 ) … π ( u N − k , u N − k + 1 , … , u N ). We deal with the problems of the shrinkage and the extension of a system of s.k-a.’s M k ( i ) = ⟨ U , a ( i ) , π ( i ) ⟩, i = 1 , 2 , … , m , m ⩾ 2. In this note there are given conditions under which an s.k-a. M k = ⟨ U , a , π ⟩ exists and the language of this automaton defined as L M = { ( u 1 , u 2 , u 3 , … ) : ∧ N ⩾ 1 P N ( u l , u 2 , … u N ) > 0 } either contains the languages of all the automata M k ( i ) , i = 1 , 2 , … , m, or this language equals the intersection of all those languages.

scholarly journals The dimension of stability of stochastic automata

1974 ◽  
Vol 24 (3) ◽  
pp. 201-211 ◽  
Author(s):  
Wojciech Rytter
Keyword(s):  
Stochastic Automata

Virulence of Vector-borne Pathogens. A Stochastic Automata Model of Perpetuation

1994 ◽  
Vol 740 (1 Disease in Ev) ◽  
pp. 249-259 ◽  
Author(s):  
ANTHONY E. KISZEWSKI ◽  
ANDREW SPIELMAN
Keyword(s):  
Stochastic Automata ◽  
Vector Borne

scholarly journals Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

2003 ◽  
Vol 53 (1) ◽  
pp. 43-69 ◽  
Author(s):  
Oleg Gusak ◽  
Tuğrul Dayar ◽  
Jean-Michel Fourneau
Keyword(s):  
Discrete Time ◽  
Stochastic Automata ◽  
Automata Networks

Graphs and Stochastic Automata Networks

1995 ◽  
pp. 217-235 ◽  
Author(s):  
Jean-Michel Fourneau ◽  
Franck Quessette
Keyword(s):  
Stochastic Automata ◽  
Automata Networks
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