International Workshop on
Petri Nets, Higher-Dimensional Automata, Partial Orders, and Concurrency
PHOCON
Associated with PETRI NETS 2026
23 June 2026

PHOCON is a workshop on concurrency theory, in particular Petri nets and non-interleaving concurrency. It concerns itself with models for concurrency, partial-order semantics, their relation to Petri nets, and their applications. Topics of interest include, but are not limited to

• event structures,
• configuration structures,
• negotiations,
• higher-dimensional automata and variants,
• partial-order semantics,
• unfoldings,
• partial-order reduction,
• category theory,
• history-preserving bisimulation and variants,
• real-time concurrency.

Invited talks

• Rob van Glabbeek, University of Edinburgh, UK. TBA
• Stefan Haar, Inria Paris-Saclay, France. Beyond atomic firing
  
  Atomicity of actions in discrete event systems has traditionally been viewed as a crucial desideratum for executability, and efforts have been made to either enforce it (e.g. by semantical restrictions) or to mitigate its effects (e.g. by ensuring rollback options). However, embracing non-atomicity in contextual Petri nets [1] has opened the path to new, more relaxed semantics without losing formal correctness criteria and verification algorithms. In the setting of Boolean networks (BNs), a pivotal construction is the most permissive (MP) semantics [2], using directional intermediate values and allowing new discoveries in the analysis of biological networks. A variety of extended or more restricted semantic constructs has been springing out of these works, see [3,4,5]. After a general survey of these developments, the talk will focus on the recently established link [6,7] between MP semantics for BNs and continuous Petri nets, showing the first contours of a novel passageway between discrete and continuous dynamics.
  [1] Thomas Chatain, Stefan Haar, Maciej Koutny, Stefan Schwoon. Non-Atomic Transition Firing in Contextual Nets. 36th International Conference on Applications and Theory of Petri Nets (ICATPN), 2015, Brussels, Belgium. ⟨hal-01241129⟩
  [2] Paulevé, L., Kolčák, J., Chatain, T. et al. Reconciling qualitative, abstract, and scalable modeling of biological networks. Nat Commun 11, 4256 (2020). https://doi.org/10.1038/s41467-020-18112-5
  [3] Thomas Chatain, Stefan Haar, Loïc Paulevé. Boolean Networks: Beyond Generalized Asynchronicity. AUTOMATA 2018 - 24th IFIP WG 1.5 International Workshop on Cellular Automata and Discrete Complex Systems, Jun 2018, Ghent, Belgium. pp.29-42, ⟨10.1007/978-3-319-92675-9_3⟩. ⟨hal-01768359v2⟩
  [4] Maximilien Gadouleau, Loïc Paulevé, Sara Riva. Bringing memory to Boolean networks: a unifying framework. Journal of Computer and System Sciences, 2025, pp.103729. ⟨10.1016/j.jcss.2025.103729⟩. ⟨hal-05342924⟩
  [5] Philippe Dague. A semantics for Boolean networks consistent with regulatory threshold constraints. Journal of Theoretical Biology, vol. 624, mai 2026
  [6] Stefan Haar, Serge Haddad: On the Expressive Power of Transfinite Sequences for Continuous Petri Nets. Petri Nets 2024: 109-131
  [7] Stefan Haar, J. Kolcák: Continuous Petri Nets Faithfully Fluidify Most Permissive Boolean Networks. CMSB 2025: 89-105

Program

8:30

Welcome / Opening

9:00

Invited talk Stefan Haar. Beyond atomic firing

10:00

Maciej Koutny and Łukasz Mikulski. Structured Concurrency Semantics for Series-Parallel Orders

10:20

Luca Bernardinello, Carlo Ferigato and Lucia Pomello. Orthomodular Lattices in Combinatorial Posets Modelling Concurrent Processes

10:40

Break

11:10

Adwitee Roy, B. Srivathsan and Madhavan Mukund. A Local-Time Semantics for Negotiations

11:30

Serge Lechenne and Hugo Paquet. Universal Properties of Petri Net Unfoldings

11:50

Federica Adobbati, Luca Bernardinello and Lucia Pomello. Solving a Safety Game on a Finite Prefix of the Unfolding of Safe Petri Nets

12:10

Amazigh Amrane, Dylan Bellier and Philipp Schlehuber-Caissier. Polytope representation for space efficient Petri net analysis

12:30

Lunch

14:00

Invited talk Rob van Glabbeek. TBA

Venue and local organization

PHOCON will take place in Hamburg, associated with PETRI NETS 2026. Please see their web site for instructions.

PHOCON sponsors

Contact

phocon@sympa.lmf.cnrs.fr