STP Approach to Model Controlled Automata with Application to Reachability Analysis of DEDS

Abstract

This paper introduces semi-tensor product of matrices (STP), a new matrix analysis tool, into the field of discrete event dynamic system (DEDS). Using STP, the dynamics of controlled automaton are modelled as an algebraic expression of the states, events and control specification. Based on this algebraic description, a sufficient and necessary condition is proposed to check whether any two states of a DEDS are reachable or not. The condition suggests an algorithm which can discover all the event strings by which a controlled automaton can move to one state from another one if they are reachable. All the results can be used to analyze corresponding problems of finite automata after simple modification. Finally, illustrative examples examine the correctness of the presented results/algorithm and demonstrate the modification after which the results are suitable for finite automata. The approach of this paper provides a new angle and means to understand and analyze the dynamics of DEDS.

Modeling and analysis of colored petri net based on the semi-tensor product of matrices

“…[1] 1 → 2 Take chopsticks p = ph(2), [2] 1 → 3 Take chopsticks p = ph(5), [27] 10 → 4 Put down chopsticks p = ph(1), [28] 10 → 6 Put down chopsticks p = ph(4), [29] 11 → 5 Put down chopsticks p = ph(1), [30] 11 → 6 Put down chopsticks p = ph(3). Denote take chopsticks ∼ δ 1 2 , put down chopsticks…”

Identification of predictors of Boolean networks from observed attractor states

“…Section details the definition and some special properties that the ordinary product of matrices does not possess. STP has been successfully applied to many fields such as neurosciences and neurology, automation control systems, mathematics and systems science, computer science, and physics . These applications may indicate that STP is a strong mathematical tool for formulating the dynamics of logical systems.…”

Matrix approach to simplification of finite state machines using semi‐tensor product of matrices

“…Thus STP can theoretically replace the classical matrix product in most engineering and science areas. In practice, STP is gaining more and more attentions and has been successfully applied to many fields such as neurosciences and neurology [7][8][9], automation control systems [10,11], mathematics and systems science [9], computer science [12]. These applications may indicate that STP is a strong mathematical tool for formulating the dynamics of logical systems.…”

“…The matrix E in (52) is called the sum matrix ofx i ∈ Δ k (i = 1, • • •, n). Define vector Q = JE(J =[10]) as the sum vector of x i . Let x i ∈ Δ 2 (i = 1 ∼ n) be 2-valued logical variables, Q be the sum vector of x i ; then col (Q) ⩽ n.(54)…”