Axiomatization, Computability and Stability for Discrete Event Time Algorithms

Abstract

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 function sin terms of the logical structures of the vocabulary. A stability analysis based on the reachability tree of the Petri net model is also discussed.