Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posets with Interfaces for Concurrent Kleene Algebra   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
series-parallel 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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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga