|THE CHURCH THESIS, ITS PROOF, AND THE NOTION OF STABILITY AND STABILIZATION FOR ANALOG ALGORITHMS
|Year of Publication
|KÖNIGSBERG, ZVIRETCHKIMAN, DERSHOWITZ, NACHUM
|03B05, 03D99, 68Q01, 93D05
This work presents the Church thesis, its proof, and the notion of stability and stabilization for analog algorithms. The Church thesis for discrete algorithms motivates us to consider the Church thesis for the case when we are dealing with analog algorithms. Its presentation and proof follows a similar construction to the one given for discrete algorithms. The notions of analog algorithm and dynamical system are postulated to be equivalent. The stability and stabilization concepts for analog algorithms are defined. The stability and stabilization presentation starts concentrating in continuous and discrete dynamical systems i.e., analog algorithms, described by differential or difference equations and continues considering Lyapunov energy functions.
 Y. Gurevich, Sequential abstract-state machines capture sequential algorithms, ACM Trans. Comput. Log., 1 (2000).