TY - JOUR
T1 - Axiomatization, computability and stability for discrete event time algorithms
AU - Königsberg, Zvi Retchkiman
N1 - Publisher Copyright:
© 2020 Instituto Politecnico Nacional. All rights reserved.
PY - 2020
Y1 - 2020
N2 - This work proposes a formalization of discrete event time algorithms. A Church type thesis, its proof, and the notion of stability for discrete event time algorithms are presented. The Church thesis for discrete algorithms motivates us to consider the Church thesis for the case when we are dealing with discrete event time algorithms. The notions of discrete event time algorithm and discrete event time dynamical system are postulated to be equivalent. The stability concept for discrete event time algorithms is defined. The stability analysis presentation starts concentrating in discrete event time algorithms, i.e., discrete event time dynamical systems, whose Petri net model is described by difference equations, and continues considering Lyapunov energy functions in terms of the logical structures of the vocabulary. A stability analysis based on the reachability tree of the Petri net model is also discussed.
AB - This work proposes a formalization of discrete event time algorithms. A Church type thesis, its proof, and the notion of stability for discrete event time algorithms are presented. The Church thesis for discrete algorithms motivates us to consider the Church thesis for the case when we are dealing with discrete event time algorithms. The notions of discrete event time algorithm and discrete event time dynamical system are postulated to be equivalent. The stability concept for discrete event time algorithms is defined. The stability analysis presentation starts concentrating in discrete event time algorithms, i.e., discrete event time dynamical systems, whose Petri net model is described by difference equations, and continues considering Lyapunov energy functions in terms of the logical structures of the vocabulary. A stability analysis based on the reachability tree of the Petri net model is also discussed.
KW - Church thesis
KW - Discrete event time algorithms
KW - Discrete event time dynamical systems
KW - Petri nets
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85098790722&partnerID=8YFLogxK
U2 - 10.13053/CYS-24-4-3875
DO - 10.13053/CYS-24-4-3875
M3 - Artículo
AN - SCOPUS:85098790722
SN - 1405-5546
VL - 24
SP - 1561
EP - 1569
JO - Computacion y Sistemas
JF - Computacion y Sistemas
IS - 4
ER -