---
abstract: |
    A timed network consists of an arbitrary number of initially identical 1-clock timed automata, interacting via hand-shake communication. In this setting there is no unique central controller, since all automata are initially identical. We consider the universal safety problem for such controller-less timed networks, i.e., verifying that a bad event (enabling some given transition) is impossible regardless of the size of the network.

    This universal safety problem is dual to the existential coverability problem for timed-arc Petri nets, i.e., does there exist a number $m$ of tokens, such that starting with $m$ tokens in a given place, and none in the other places, some given transition is eventually enabled.

    We show that these problems are PSPACE-complete.
author:
- Parosh Aziz Abdulla
- Mohamed Faouzi Atig
- Radu Ciobanu
- Richard Mayr
- Patrick Totzke
bibliography:
- 'main.bib'
title: 'Universal Safety for Timed Petri Nets is PSPACE-complete'
---

Introduction {#sec:intro}
============

##### Background.

Timed-arc Petri nets (TPN) [@AA2001; @S2005; @AMM07; @BHR2006; @JJMS2011] are an extension of Petri nets where each token carries one real-valued clock and transitions are guarded by inequality constraints where the clock values are compared to integer bounds (via strict or non-strict inequalities). The known 