Generating Posets Beyond N

Fahrenberg, Uli; Johansen, Christian; Struth, Georg; Thapa, Ratan Bahadur

doi:10.1007/978-3-030-43520-2_6

Cited by 14 publications

(19 citation statements)

References 33 publications

(32 reference statements)

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“…Whether gluing-parallel iposets form the free structure in some algebraic variety remains open. Such a result is claimed in [8,Thm. 19], but its proof builds on a so-called Levi lemma, [8, Lemma 16], which does not hold.…”

Section: Gluing-parallel Iposetssupporting

confidence: 52%

“…This paper is based on [8] but contains significant improvements. We make precise the notion of lax tensors on strict 2-categories in Definition 5 and show in Theorem 1 that iposets form such a structure.…”

Section: Introductionmentioning

confidence: 99%

“…We also make more precise the hierarchies in Section 7 and expose several more forbidden induced subposets in Proposition 26. Whether the gluing-parallel iposets form the free algebras in some algebraic variety remains open, and we are obliged to retract [8,Thm. 19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Posets with Interfaces for Concurrent Kleene Algebra

Fahrenberg¹,

Johansen²,

Struth³

et al. 2021

Preprint

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We introduce posets with interfaces (iposets) and generalise the serial composition of posets to a new gluing composition of iposets. In partial order semantics of concurrency, this amounts to designate events that continue their execution across components. Alternatively, in terms of decomposing concurrent systems, it allows cutting through some events, whereas serial composition may cut through edges only.We show that iposets under gluing composition form a category, extending the monoid of posets under serial composition, and a 2-category when enriched with a subsumption order and a suitable parallel composition as a lax tensor. This generalises the interchange monoids used in concurrent Kleene algebra.We also consider gp-iposets, which are generated from singletons by finitary gluing and parallel compositions. We show that the class includes the seriesparallel posets as well as the interval orders, which are also well studied in concurrency theory. Finally, we show that not all posets are gp-iposets, exposing several posets that cannot occur as induced substructures of gp-iposets.

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Section: Gluing-parallel Iposetssupporting

confidence: 52%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Posets with Interfaces for Concurrent Kleene Algebra

Fahrenberg¹,

Johansen²,

Struth³

et al. 2021

Preprint

Self Cite

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show abstract

“…Since N-shapes appear in pomsets that describe message passing between threads, we would like to be able to learn such languages as well. We do not see an obvious way to extend our algorithm to include these pomsets, but perhaps recent techniques from [10] can provide a solution.…”

Section: Discussionmentioning

confidence: 98%

Learning Pomset Automata

Heerdt

Kappé

Rot

et al. 2021

Lecture Notes in Computer Science

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We extend the $$\mathtt {L}^{\!\star }$$ L ⋆ algorithm to learn bimonoids recognising pomset languages. We then identify a class of pomset automata that accepts precisely the class of pomset languages recognised by bimonoids and show how to convert between bimonoids and automata.

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“…General d-paths underpin more complicated schedules, for which parallel composition is involved in the description; cf, e.g. Fanchon and Morin (2009) for a detailed description of finite step transition systems accepting pomset languages and Fahrenberg et al (2020) for newer developments.…”

Section: Posets Poset Categories and Algebraic Topologymentioning

confidence: 99%

Strictifying and taming directed paths in Higher Dimensional Automata

Raussen¹

2021

Math. Struct. Comp. Sci.

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Directed paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate whether one obtains different topological properties of such a space of executions if one restricts attention to schedulings with “nice” properties, e.g. involving synchronisations. This note shows that this is not the case, i.e. that one may operate with nice schedulings without inflicting any harm. Several of the results in this note had previously been obtained by Ziemiański in Ziemiański (2017. Applicable Algebra in Engineering, Communication and Computing28 497–525; 2020a. Journal of Applied and Computational Topology4 (1) 45–78). We attempt to make them accessible for a wider audience by giving an easier proof for these findings by an application of quite elementary results from algebraic topology; notably the nerve lemma.

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Generating Posets Beyond N

Cited by 14 publications

References 33 publications

Posets with Interfaces for Concurrent Kleene Algebra

Posets with Interfaces for Concurrent Kleene Algebra

Learning Pomset Automata

Strictifying and taming directed paths in Higher Dimensional Automata

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