Markovian Testing Equivalence and Exponentially Timed Internal Actions

TL;DR

This paper extends Markovian testing equivalence to include exponentially timed internal actions, ensuring accurate process comparison considering timing, with formal properties and efficient decision procedures.

Contribution

It introduces a new Markovian testing equivalence framework that accounts for timed internal actions, providing a congruence, axiomatization, modal logic, and polynomial-time decision algorithm.

Findings

Behavioral equivalence is a congruence.

A sound and complete axiomatization is provided.

Decidability is achieved in polynomial time.

Abstract

In the theory of testing for Markovian processes developed so far, exponentially timed internal actions are not admitted within processes. When present, these actions cannot be abstracted away, because their execution takes a nonzero amount of time and hence can be observed. On the other hand, they must be carefully taken into account, in order not to equate processes that are distinguishable from a timing viewpoint. In this paper, we recast the definition of Markovian testing equivalence in the framework of a Markovian process calculus including exponentially timed internal actions. Then, we show that the resulting behavioral equivalence is a congruence, has a sound and complete axiomatization, has a modal logic characterization, and can be decided in polynomial time.