# Continuous Reachability for Unordered Data Petri nets is in PTime

## TL;DR

This paper proves that the continuous reachability problem for unordered data Petri nets can be decided in polynomial time, providing a new efficient method for analyzing these complex models.

## Contribution

The authors characterize continuous reachability for UDPN and develop a polynomial time algorithm based on a combinatorial argument.

## Key findings

- Continuous reachability for UDPN is in PTime.
- Existence of runs with only polynomially many data values when reachability holds.
- Provides a polynomial time decision procedure for continuous reachability.

## Abstract

Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability and termination problems are decidable, but with higher complexity than for Petri nets. On the other hand, the problem of reachability for UDPN is surprisingly complex, and its decidability status remains open. In this paper, we consider the continuous reachability problem for UDPN, which can be seen as an over-approximation of the reachability problem. Our main result is a characterization of continuous reachability for UDPN and polynomial time algorithm for solving it. This is a consequence of a combinatorial argument, which shows that if continuous reachability holds then there exists a run using only polynomially many data values.