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. Hereditary history-preserving branching bisimilarity
  
  Hereditary history-preserving bisimilarity is one of the finest semantic equivalence for concurrent systems; one that fully captures causality, branching time and their interplay, and respects the internal structure of processes, while satisfying the law P+P=P. It was originally studied on models of concurrency were causality can be modelled by means of partial orders, and here I continue in this tradition. However, to adequately address abstraction from internal activity, one needs a version of this equivalence based on weak, or branching, bisimilarity.
  A naive definition of hereditary history-preserving branching bisimilarity would be unsatisfactory, as witnessed by the observation that it would not be preserved under refinement of actions. I address this issue by proposing a more satisfactory definition of this notion.
• 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. Hereditary history-preserving branching bisimilarity

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