Testing Probabilistic Processes: Can Random Choices Be Unobservable?

TL;DR

This paper investigates whether internal probabilistic choices in processes can remain unobservable, proposing two semantics that are shown to coincide and be consistent with process operators.

Contribution

It introduces two novel semantics for probabilistic processes that preserve unobservability of internal choices and demonstrates their equivalence and robustness.

Findings

The two semantics coincide and are equivalent.

Both semantics are preserved under standard process operators.

The paper addresses the challenge of unobservable probabilistic choices in process theory.

Abstract

A central paradigm behind process semantics based on observability and testing is that the exact moment of occurring of an internal nondeterministic choice is unobservable. It is natural, therefore, for this property to hold when the internal choice is quantified with probabilities. However, ever since probabilities have been introduced in process semantics, it has been a challenge to preserve the unobservability of the random choice, while not violating the other laws of process theory and probability theory. This paper addresses this problem. It proposes two semantics for processes where the internal nondeterminism has been quantified with probabilities. The first one is based on the notion of testing, i.e. interaction between the process and its environment. The second one, the probabilistic ready trace semantics, is based on the notion of observability. Both are shown to coincide. They are also preserved under the standard operators.