The reverse engineering problem with probabilities and sequential behavior: Probabilistic Sequential Networks

TL;DR

This paper introduces Probabilistic Sequential Networks (PSN), a new model for reverse engineering probabilistic sequential behavior, establishing their algebraic structure and properties, including homomorphisms and equilibrium states.

Contribution

The paper defines Probabilistic Sequential Networks, explores their algebraic properties, and demonstrates their categorical structure and relation to existing sequential dynamical systems.

Findings

Homomorphic PSNs share the same steady state probabilities.

PSN form a category with SDS as a full subcategory.

Examples of morphisms, subsystems, and simulations are provided.

Abstract

The reverse engineering problem with probabilities and sequential behavior is introducing here, using the expression of an algorithm. The solution is partially founded, because we solve the problem only if we have a Probabilistic Sequential Network. Therefore the probabilistic structure on sequential dynamical systems is introduced here, the new model will be called Probabilistic Sequential Network, PSN. The morphisms of Probabilistic Sequential Networks are defined using two algebraic conditions, whose imply that the distribution of probabilities in the systems are close. It is proved here that two homomorphic Probabilistic Sequential Networks have the same equilibrium or steady state probabilities. Additionally, the proof of the set of PSN with its morphisms form the category PSN, having the category of sequential dynamical systems SDS, as a full subcategory is given. Several examples of morphisms, subsystems and simulations are given.