A constructive proof of the phase-type characterization theorem

TL;DR

This paper provides a simpler, constructive proof of the phase-type characterization theorem, including a procedure to explicitly create phase type representations when conditions are met.

Contribution

It introduces a new, simpler proof that is constructive, offering a practical method to obtain phase type representations based on the theorem's conditions.

Findings

The new proof is significantly simpler than the original.

A procedure is provided that constructs phase type representations.

The procedure is proven to succeed under the theorem's conditions.

Abstract

The paper presents a new proof of O'Cinneide's characterization theorem. It is much simpler than the original one and constructive in the sense that we not only show the existence of a phase type representation, but present a procedure which creates a phase type representation. We prove that the procedure succeeds when the conditions of the characterization theorem hold.