# Reward Testing Equivalences for Processes

## TL;DR

This paper introduces reward testing to process semantics, providing a finer equivalence that captures conditional liveness properties beyond traditional safety and liveness properties.

## Contribution

It proposes reward testing as a new semantic equivalence that refines existing testing equivalences and captures conditional liveness properties.

## Key findings

- Reward testing is strictly finer than may- and must-testing equivalences.
- Reward testing captures conditional liveness properties.
- It extends the semantic framework for process equivalences.

## Abstract

May and must testing were introduced by De Nicola and Hennessy to define semantic equivalences on processes. May-testing equivalence exactly captures safety properties, and must-testing equivalence liveness properties. This paper proposes reward testing and shows that the resulting semantic equivalence also captures conditional liveness properties. It is strictly finer than both the may- and must-testing equivalence.