# Parametric Verification: An Introduction

## TL;DR

This paper introduces the field of parametric verification for concurrent systems, covering formal concepts, models, approaches, and practical tools for analyzing systems with unknown or variable parameters.

## Contribution

It provides a comprehensive overview of parametric verification methods, models, and tools, along with references for further research in the area.

## Key findings

- Coverage of various models like Parametric Timed Automata and Petri Nets
- Introduction of Action Synthesis for property enforcement
- Availability of practical tools and tutorials online

## Abstract

This paper constitutes a short introduction to parametric verification of concurrent systems. It originates from two 1-day tutorial sessions held at the Petri nets conferences in Toru\'n (2016) and Zaragoza (2017). The paper presents not only the basic formal concepts tackled in the video version, but also an extensive literature to provide the reader with further references covering the area. We first introduce motivation behind parametric verification in general, and then focus on different models and approaches, for verifying several kinds of systems. They include Parametric Timed Automata, for modelling real-time systems, where the timing constraints are not necessarily known a priori. Similarly, Parametric Interval Markov Chains allow for modelling systems where probabilities of events occurrences are intervals with parametric bounds. Parametric Petri Nets allow for compact representation of systems, and cope with different types of parameters. Finally, Action Synthesis aims at enabling or disabling actions in a concurrent system to guarantee some of its properties. Some tools implementing these approaches were used during hands-on sessions at the tutorial. The corresponding practicals are freely available on the Web.