arxiv: 2603.08134 · v2 · submitted 2026-03-09 · 💻 cs.FL

Recognition: no theorem link

Forgetting Event Order in Higher-Dimensional Automata

Safa Zouari

Authors on Pith no claims yet

Pith reviewed 2026-05-15 14:20 UTC · model grok-4.3

classification 💻 cs.FL

keywords higher-dimensional automatainterval ipomsetsST tracesbisimulationtrue concurrencyorder-free semanticssymmetric HDAspresheaf presentation

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The pith

Higher-dimensional automata gain order-independent semantics by matching ST traces to interval ipomsets that track only precedence and concurrency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Higher-dimensional automata traditionally impose an artificial total order on events that does not reflect observable concurrent behavior. The paper replaces this with interval ipomsets, which record only precedence and concurrency relations between events along with interfaces. It proves that every traditional ST trace of an execution path equals the interval ipomset of that path. The authors further show that the presheaf presentation using an unordered base is categorically the same as the combinatorial presentation of symmetric HDAs. They characterize both ST and hereditary history preserving bisimulation directly by isomorphism of these ipomsets, producing a unified semantics free of ordering artifacts.

Core claim

For any higher-dimensional automaton the traditional ST trace of an execution path corresponds precisely to its associated interval ipomset. The presheaf-theoretic presentation with an unordered base is categorically isomorphic to the combinatorial presentation of symmetric HDAs. ST and hereditary history preserving bisimulations are characterized via ipomset isomorphism, supplying an order-free foundation for HDA semantics that resolves mismatches with other concurrency models.

What carries the argument

Interval ipomsets: partially ordered multisets with interfaces that retain only precedence and concurrency relations while discarding any total event order.

If this is right

ST traces of execution paths match their interval ipomsets exactly for every HDA.
Presheaf and combinatorial presentations of symmetric HDAs become categorically equivalent.
Both ST and hhp bisimulations reduce to isomorphism of the corresponding interval ipomsets.
A canonical path category exists, allowing direct use of the Open Maps framework.
Temporal and modal logics on HDAs lose representational artifacts caused by artificial event ordering.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same order-forgetting construction could be applied to Petri nets to remove similar ordering mismatches with HDAs.
Categorical tools developed for unordered bases may simplify geometric models of concurrency beyond the cases treated here.
A concrete test would be to recompute bisimulation equivalence on a published HDA benchmark using ipomset isomorphism and compare the results to the original ordered definition.
The approach suggests that many geometric concurrency models can be rewritten with an unordered event base while preserving their observable properties.

Load-bearing premise

Interval ipomsets defined solely by precedence and concurrency relations are enough to capture all observable behavior without any residual dependence on a hidden total order.

What would settle it

Construct an explicit higher-dimensional automaton together with two execution paths whose ST traces differ yet whose interval ipomsets are isomorphic, or two paths whose ST traces match but whose ipomsets are not isomorphic.

Figures

Figures reproduced from arXiv: 2603.08134 by Safa Zouari.

**Figure 2.** Figure 2: Illustration of (g, ζ) ◦ (f, ε) : U → W, the composition of the conclist maps of [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: Precubical set X with two 2-dimensional cells Example 3.3 (Example of a precubical set) [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Interval ipomsets (below) with their corresponding interval representations (above). [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: HDA X on the left with its symmetriser SX on the right. The following is an example in 3 dimensions. It illustrates how the symmetriser affects paths and how permutations must act coherently along a path in SX. Example 5.4. Consider the precubical set X represented in [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: On the left hand side, a precubical set X consisting of two 3-dimensional cubes x ∈ X(3, abc) and z ∈ X(3, abd) attached along a common 2-dimensional cell y ∈ X(2, ab). On the right hand side, Its symmetrization SX, where each cube generates six 3-cells of the form θ·x and σ·z for some θ, σ ∈ S3, all sharing the same boundary faces τ.y and id.y, where τ ∈ S2. 2. If α = [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗

read the original abstract

Higher dimensional automata (HDAs) provide a geometric model of true concurrency, yet their standard formulation encodes an artificial total order on events. This representational artifact causes a fundamental mismatch between the combinatorial structure of HDAs and their observable behavior, leading to logical asymmetries and complicating the application of categorical tools. In this paper, we resolve this tension by developing a semantics for HDAs that is independent of event order, based on interval ipomsets (partially ordered multisets with interfaces) that preserve only precedence and concurrency. We prove that for any HDA, the traditional ST trace of an execution path corresponds precisely to its associated interval ipomset. On the structural side, we show that the presheaf theoretic presentation with an unordered base and the combinatorial presentation of symmetric HDAs are categorically isomorphic. Finally, by characterizing ST and hereditary history preserving (hhp) bisimulation via ipomset isomorphism, we provide a unified, order free foundation for HDA semantics. Our results resolve several critical ambiguities in the literature: they provide the necessary path category structure to canonically apply the Open Maps framework, eliminate representational artifacts in temporal and modal logics, and bridge systematic mismatches between HDAs and other models of concurrency such as Petri nets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper removes the total event order artifact from HDAs by switching to interval ipomsets and proves the ST-trace match plus a categorical isomorphism between presheaf and symmetric presentations.

read the letter

The main thing here is that the authors drop the artificial total order on events that standard HDAs carry and replace it with interval ipomsets that keep only precedence and concurrency. They show this gives an exact match between the usual ST trace of an execution path and the associated interval ipomset. They also prove the presheaf presentation with an unordered base is categorically isomorphic to the combinatorial presentation of symmetric HDAs, and they characterize both ST and hhp bisimulation directly by ipomset isomorphism. That package looks like it cleans up several long-standing mismatches with open maps, temporal logics, and Petri-net models. The construction is introduced independently of the results it supports, and the stress test found no internal inconsistency in the stated theorems. The work is narrow but technically precise; it sits squarely inside concurrency theory and geometric models of true concurrency. A reader already working on HDAs or categorical semantics will find the isomorphism and the bisimulation characterizations useful to check against their own setups. The claims are concrete enough that a referee can verify them against the definitions and proofs. I would send it to peer review rather than desk reject; the results address a real representational issue even if the immediate audience stays small.

Referee Report

2 major / 2 minor

Summary. The paper develops an order-independent semantics for higher-dimensional automata (HDAs) based on interval ipomsets, which preserve only precedence and concurrency relations. It proves that for any HDA the traditional ST trace of an execution path corresponds precisely to its associated interval ipomset. It establishes a categorical isomorphism between the presheaf-theoretic presentation (with unordered base) and the combinatorial presentation of symmetric HDAs. Finally, it characterizes both ST and hereditary history-preserving (hhp) bisimulation in terms of ipomset isomorphism, yielding a unified foundation that eliminates event-order artifacts, supplies a path category for the open-maps framework, and resolves mismatches with models such as Petri nets.

Significance. If the stated correspondences and isomorphisms hold, the work removes a long-standing representational artifact in HDAs and supplies a cleaner, order-free foundation for true-concurrency semantics. The explicit path-category structure for open maps and the bisimulation characterizations via ipomset isomorphism are concrete strengths that would facilitate uniform application of categorical tools and improve alignment with other concurrency models.

major comments (2)

[§4] §4, Theorem 4.1 (ST-trace correspondence): the proof that every ST trace equals the interval ipomset of its execution path is load-bearing for the central claim of order-free semantics; the manuscript must exhibit the explicit bijection on interfaces and show that concurrent events with identical labels are distinguished solely by their interval relations, without reintroducing a total order.
[§5] §5, Theorem 5.3 (categorical isomorphism): the claimed isomorphism between the presheaf category over the unordered base and the combinatorial category of symmetric HDAs is central to the structural contribution; the functor definitions must be shown to be independent of any residual total order on events, with explicit verification that the unit and counit are natural with respect to the interval-ipomset morphisms.

minor comments (2)

[§2] The definition of interval ipomsets in §2 would benefit from an explicit small example (e.g., a two-event concurrent transition) showing how interfaces are attached without imposing order.
[§3] Notation for the “unordered base” category in §3 is introduced without a comparison table to the classical ordered base; adding such a table would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation for minor revision. The comments identify opportunities to make the central proofs more explicit, which we will address in the revised manuscript while preserving the order-free semantics developed via interval ipomsets.

read point-by-point responses

Referee: [§4] §4, Theorem 4.1 (ST-trace correspondence): the proof that every ST trace equals the interval ipomset of its execution path is load-bearing for the central claim of order-free semantics; the manuscript must exhibit the explicit bijection on interfaces and show that concurrent events with identical labels are distinguished solely by their interval relations, without reintroducing a total order.

Authors: We agree that greater explicitness will strengthen the argument. The proof of Theorem 4.1 already maps each ST trace to an interval ipomset by assigning events to intervals whose endpoints record execution times, with interfaces corresponding to the initial and terminal states. In the revision we will insert a dedicated paragraph that constructs the bijection on interfaces explicitly (matching labeled events by their interval positions) and verifies that any two concurrent events with identical labels are separated solely by their distinct precedence and overlap relations in the ipomset. No total order is imposed; the construction uses only the partial order and interval overlap data. revision: yes
Referee: [§5] §5, Theorem 5.3 (categorical isomorphism): the claimed isomorphism between the presheaf category over the unordered base and the combinatorial category of symmetric HDAs is central to the structural contribution; the functor definitions must be shown to be independent of any residual total order on events, with explicit verification that the unit and counit are natural with respect to the interval-ipomset morphisms.

Authors: The functors realizing the isomorphism in Theorem 5.3 are defined using the category of interval ipomsets, whose morphisms are order-free by construction. In the revised version we will add a short subsection that (i) confirms the functor actions on objects and morphisms make no reference to any linear extension of events and (ii) supplies commutative diagrams verifying that both the unit and counit are natural with respect to arbitrary interval-ipomset morphisms. This makes the independence from total order fully transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations are independent theorems

full rationale

The paper defines interval ipomsets independently to capture precedence and concurrency without total order, then states three main results as theorems: the precise correspondence between ST traces and interval ipomsets for any HDA, the categorical isomorphism between presheaf and combinatorial presentations of symmetric HDAs, and the characterization of ST/hhp bisimulations via ipomset isomorphism. None of these reduce by construction to their inputs, fitted parameters, or self-citations; the abstract and claims present them as proven equivalences resting on standard categorical machinery (presheaves, open maps) rather than presupposing the target results. No load-bearing self-citation chains or ansatz smuggling are detectable from the provided derivation outline.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review based solely on abstract; full text unavailable so ledger entries are inferred at high level from stated contributions.

axioms (1)

standard math Standard results from category theory and presheaf theory
Invoked for the claimed categorical isomorphism between presentations

invented entities (1)

interval ipomsets no independent evidence
purpose: Provide order-independent semantics that preserve only precedence and concurrency
New structure introduced to replace total-order encoding in HDAs

pith-pipeline@v0.9.0 · 5506 in / 1301 out tokens · 38056 ms · 2026-05-15T14:20:37.204680+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

[1]

The Linear Time – Branching Time Spectrum I: The Semantics of Concrete, Sequential Processes

L. van Glabbeek. "The Linear Time – Branching Time Spectrum I: The Semantics of Concrete, Sequential Processes." In J. Bergstra, A. Ponse, and S. Smolka (eds.), Handbook of Process Algebra, Elsevier, 1991

work page 1991
[2]

Donald E. Knuth. 1974. Computer programming as an art.Commun. ACM17, 12 (1974), 667–673.https://doi.org/10.1145/361604.361612

work page doi:10.1145/361604.361612 1974
[3]

Dijkstra

Edsger W. Dijkstra. 1968. Letters to the editor: go to statement considered harmful. Commun. ACM11, 3 (1968), 147–148.https://doi.org/10.1145/362929.362947

work page doi:10.1145/362929.362947 1968
[4]

1993.Transaction Processing: Concepts and Techniques

Jim Gray and Andreas Reuter. 1993.Transaction Processing: Concepts and Techniques. Morgan Kaufmann

work page 1993
[5]

Hopcroft, Wolfgang J

John E. Hopcroft, Wolfgang J. Paul, and Leslie G. Valiant. 1975. On time versus space and related problems. In16th Annual Symposium on Foundations of Computer Science (FOCS 1975), 57–64. IEEE, 1975.https://doi.org/10.1109/SFCS.1975.23

work page doi:10.1109/sfcs.1975.23 1975
[6]

Georg Struth and Krzysztof Ziemiański. 2024. Presheaf automata.arXiv preprint arXiv:2409.04612

work page arXiv 2024
[7]

Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, Loic Helouet, and Philipp Schlehuber- Caissier. 2025. Petri nets and higher-dimensional automata. InApplication and The- ory of Petri Nets and Concurrency, 18–40. Springer, 2025.https://doi.org/10.1007/ 978-3-031-94634-9_2

work page 2025
[8]

Amazigh Amrane, Hugo Bazille, Timothée Fragnaud, and Philipp Schlehuber-Caissier

work page
[9]

In Modélisation des Systèmes Réactifs (MSR’25).https://hal.science/hal-05281114

Towards an efficient conversion of Petri nets into higher dimensional automata. In Modélisation des Systèmes Réactifs (MSR’25).https://hal.science/hal-05281114

work page
[10]

Amazigh Amrane, Hugo Bazille, Emily Clement, Uli Fahrenberg, Marie Fortin, and Krzysztof Ziemiański. 2025. Büchi-Elgot-Trakhtenbrot theorem for higher-dimensional au- tomata.arXiv preprintarXiv:2505.10461.https://arxiv.org/abs/2505.10461

work page arXiv 2025
[11]

Kamptheoremforpomsetlanguages of higher dimensional automata.arXiv preprintarXiv:2410.12493.https://arxiv.org/ abs/2410.12493

EmilyClement, EnzoErlich, andJérémyLedent.2025. Kamptheoremforpomsetlanguages of higher dimensional automata.arXiv preprintarXiv:2410.12493.https://arxiv.org/ abs/2410.12493

work page arXiv 2025
[12]

Jay L. Gischer. 1988. The equational theory of pomsets.Theoretical Computer Science61, 2 (1988), 199–224.https://doi.org/10.1016/0304-3975(88)90124-7

work page doi:10.1016/0304-3975(88)90124-7 1988
[13]

Jan Grabowski. 1981. On partial languages.Fundamenta Informaticae4, 2 (1981), 427–498. IOS Press

work page 1981
[14]

Vaughan R. Pratt. 1986. Modeling concurrency with partial orders.International Journal of Parallel Programming15 (1986), 33–71.https://api.semanticscholar.org/CorpusID: 12178098

work page 1986
[15]

Fishburn

Peter C. Fishburn. 1985.Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. 24

work page 1985
[16]

Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, and Marie Fortin. 2024. Logic and languages of higher-dimensional automata. InDevelopments in Language Theory, 51–67. Springer Nature Switzerland, Cham, 2024

work page 2024
[17]

Safa Zouari, Krzysztof Ziemiański, and Uli Fahrenberg. 2025. Bisimulations and logics for higher-dimensional automata. InTheoretical Aspects of Computing – ICTAC 2024, 132–150. Springer Nature Switzerland, Cham, 2025

work page 2025
[18]

Thomas Kahl. 2022. On symmetric higher-dimensional automata and bisimilarity.Theoreti- cal Computer Science935 (2022), 47–60.https://doi.org/10.1016/j.tcs.2022.07.004

work page doi:10.1016/j.tcs.2022.07.004 2022
[19]

Uli Fahrenberg, Christian Johansen, Georg Struth, and Ratan Bahadur Thapa. 2020. Gen- erating Posets Beyond N. InRelational and Algebraic Methods in Computer Science, 82–99. Springer International Publishing, Cham, 2020

work page 2020
[20]

2007.Reactive Systems: Modelling, Specification and Verification

Luca Aceto, Anna Ingolfsdottir, Kim Guldstrand Larsen, and Jiri Srba. 2007.Reactive Systems: Modelling, Specification and Verification. Cambridge University Press, United Kingdom

work page 2007
[21]

Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, and Krzysztof Ziemiański. 2023. Closure and Decision Properties for Higher-Dimensional Automata. In

work page 2023
[22]

Paolo Baldan and Silvia Crafa. 2010. A Logic for True Concurrency. InCONCUR 2010 - Concurrency Theory, Paul Gastin and François Laroussinie (Eds.). Springer Berlin Heidel- berg, Berlin, Heidelberg, 147–161

work page 2010
[23]

Paolo Baldan and Silvia Crafa. 2014. Hereditary History-Preserving Bisimilarity: Logics and Automata. InProgramming Languages and Systems, Jacques Garrigue (Ed.). Springer International Publishing, Cham, 469–488

work page 2014
[24]

Paolo Baldan and Tommaso Padoan. 2020. Model checking a logic for true concurrency. ACM Transactions on Computational Logic (TOCL)21, 4 (2020), 1–49

work page 2020
[25]

1987.Categories of Asynchronous Systems

Marek Antoni Bednarczyk. 1987.Categories of Asynchronous Systems. Ph.D. Dissertation. University of Sussex, GBR. AAIDX83002

work page 1987
[26]

Rocco De Nicola and Frits Vaandrager. 1995. Three logics for branching bisimulation. Journal of the ACM (JACM)42, 2 (1995), 458–487

work page 1995
[27]

Uli Fahrenberg, Christian Johansen, Georg Struth, and Krzysztof Ziemianski. 2021. Lan- guages of higher-dimensional automata.Math. Struct. Comput. Sci.31, 5 (2021), 575–613. https://doi.org/10.1017/S0960129521000293

work page doi:10.1017/s0960129521000293 2021
[28]

Uli Fahrenberg, Christian Johansen, Georg Struth, and Krzysztof Ziemiański. 2022. A Kleene Theorem for Higher-Dimensional Automata. In33rd International Conference on Concurrency Theory (CONCUR 2022) (Leibniz International Proceedings in Informatics (LIPIcs), Vol. 243), Bartek Klin, Sławomir Lasota, and Anca Muscholl (Eds.). Schloss Dagstuhl – Leibniz-Zen...

work page doi:10.4230/lipics.concur.2022.29 2022
[29]

Uli Fahrenberg and Krzysztof Ziemiański. 2023. A Myhill-Nerode Theorem for Higher- Dimensional Automata. InApplication and Theory of Petri Nets and Concurrency, Luis Gomes and Robert Lorenz (Eds.). Springer Nature Switzerland, Cham, 167–188

work page 2023
[30]

Intransitiveindifferencewithunequalindifferenceintervals.Journal of Mathematical Psychology7, 1 (1970), 144–149

PeterCFishburn.1970. Intransitiveindifferencewithunequalindifferenceintervals.Journal of Mathematical Psychology7, 1 (1970), 144–149. 25

work page 1970
[31]

Matthew Hennessy and Robin Milner. 1985. Algebraic laws for nondeterminism and con- currency.Journal of the ACM (JACM)32, 1 (1985), 137–161

work page 1985
[32]

Ryszard Janicki and Maciej Koutny. 1993. Structure of concurrency.Theoretical Computer Science112, 1 (1993), 5–52

work page 1993
[33]

André Joyal, Mogens Nielsen, and Glynn Winskel. 1996. Bisimulation from Open Maps. Information and Computation127, 2 (1996), 164–185.https://doi.org/10.1006/inco. 1996.0057

work page doi:10.1006/inco 1996
[34]

François Laroussinie. 2010. Christel Baier and Joost-Pieter Katoen Principles of Model Checking. MIT Press (May 2008). ISBN: 978-0-262-02649-9. £44.95. 975 pp. Hardcover. Comput. J.53, 5 (June 2010), 615–616.https://doi.org/10.1093/comjnl/bxp025

work page doi:10.1093/comjnl/bxp025 2010
[35]

Leifer and Robin Milner

James J. Leifer and Robin Milner. 2000. Deriving Bisimulation Congruences for Reactive Systems. InCONCUR 2000 — Concurrency Theory, Catuscia Palamidessi (Ed.). Springer Berlin Heidelberg, Berlin, Heidelberg, 243–258

work page 2000
[36]

Mogens Nielsen and Christian Clausen. 1994. Bisimulation for Models in Concurrency. In CONCUR ’94: Concurrency Theory, Bengt Jonsson and Joachim Parrow (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 385–400

work page 1994
[37]

Mogens Nielsen, Gordon Plotkin, and Glynn Winskel. 1981. Petri nets, event structures and domains, part I.Theoretical Computer Science13, 1 (1981), 85–108

work page 1981
[38]

Iain Phillips and Irek Ulidowski. 2014. Event identifier logic.Mathematical Structures in Computer Science24, 2 (2014), e240204

work page 2014
[39]

Thetemporallogicofreactiveandconcurrentsystems

AmirPnueliandZoharManna.1992. Thetemporallogicofreactiveandconcurrentsystems. Springer16 (1992), 12

work page 1992
[40]

Vaughn Pratt. 1991. Modeling Concurrency with Geometry. InProceedings of the 18th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages(Orlando, Florida, USA)(POPL ’91). Association for Computing Machinery, New York, NY, USA, 311–322.https://doi.org/10.1145/99583.99625

work page doi:10.1145/99583.99625 1991
[41]

Davide Sangiorgi. 1998. On the bisimulation proof method.Mathematical Structures in Computer Science8, 5 (1998), 447–479

work page 1998
[42]

V. B. Shehtman. 2016. Bisimulation games and locally tabular logics.Russian Mathematical Surveys71, 5 (oct 2016), 979.https://doi.org/10.1070/RM9731

work page doi:10.1070/rm9731 2016
[43]

Mike W Shields. 1985. Concurrent machines.Comput. J.28, 5 (1985), 449–465

work page 1985
[44]

v.Glabbeek and G.D

R.J. v.Glabbeek and G.D. Plotkin. 1995. Configuration structures. InProceedings of Tenth Annual IEEE Symposium on Logic in Computer Science. IEEE, San Deigo, CA, USA, 199– 209.https://doi.org/10.1109/LICS.1995.523257

work page doi:10.1109/lics.1995.523257 1995
[45]

R. J. v.Glabbeek. 1990. The linear time - branching time spectrum. InCONCUR ’90 Theories of Concurrency: Unification and Extension, J. C. M. Baeten and J. W. Klop (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 278–297

work page 1990
[46]

Ontheexpressivenessofhigherdimensionalautomata.Theoretical Computer Science356, 3 (2006), 265–290

RobJ.v.Glabbeek.2006. Ontheexpressivenessofhigherdimensionalautomata.Theoretical Computer Science356, 3 (2006), 265–290. Expressiveness in Concurrency

work page 2006
[47]

v.Glabbeek and Ursula Goltz

Rob J. v.Glabbeek and Ursula Goltz. 2001. Refinement of actions and equivalence notions for concurrent systems.Acta Informatica37, 4 (2001), 229–327. 26

work page 2001
[48]

v.Glabbeek and Frits Vaandrager

Rob J. v.Glabbeek and Frits Vaandrager. 1997. The difference between splitting in n and n+1.Information and Computation136, 2 (1997), 109–142

work page 1997
[49]

Józef Winkowski. 1977. An algebraic characterization of the behaviour of non-sequential systems.Inform. Process. Lett.6, 4 (1977), 105–109

work page 1977
[50]

Glynn Winskel. 1987. Event structures. InPetri Nets: Applications and Relationships to Other Models of Concurrency, W. Brauer, W. Reisig, and G. Rozenberg (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 325–392

work page 1987
[51]

Glynn Winskel. 1989. An introduction to event structures. InLinear Time, Branching Time and Partial Order in Logics and Models for Concurrency, J. W. de Bakker, W. P. de Roever, and G. Rozenberg (Eds.). Springer Berlin Heidelberg, Berlin, Heidelberg, 364–397

work page 1989
[52]

Amazigh Amrane, Hugo Bazille, Emily Clement, Uli Fahrenberg. 2024. Languages of Higher-Dimensional Timed Automata. InApplication and Theory of Petri Nets and Con- currency, Lars Michael Kristensen and Jan Martijn van der Werf (Eds.). Springer Nature Switzerland, Cham, 197–219

work page 2024
[53]

Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, Krzysztof Ziemiański. 2025. Closure and decision properties for higher-dimensional automata.Theoretical Computer Science1036 (2025), 115156. 10.1016/j.tcs.2025.115156

work page doi:10.1016/j.tcs.2025.115156 2025
[54]

Amazigh Amrane, Hugo Bazille, Uli Fahrenberg, Loïc Hélouët, and Philipp Schlehuber- Caissier. 2025. Petri Nets and Higher-Dimensional Automata. InApplication and Theory of Petri Nets and Concurrency, Elvio Amparore and Łukasz Mikulski (Eds.). Springer Nature Switzerland, Cham, 18–40. 27

work page 2025