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Documents authored by Corradini, Andrea

Document
DOI: 10.4230/LIPIcs.CONCUR.2024.11
Left-Linear Rewriting in Adhesive Categories

Authors: Paolo Baldan, Davide Castelnovo, Andrea Corradini, and Fabio Gadducci

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
When can two sequential steps performed by a computing device be considered (causally) independent? This is a relevant question for concurrent and distributed systems, since independence means that they could be executed in any order, and potentially in parallel. Equivalences identifying rewriting sequences which differ only for independent steps are at the core of the theory of concurrency of many formalisms. We investigate the issue in the context of the double pushout approach to rewriting in the general setting of adhesive categories. While a consolidated theory exists for linear rules, which can consume, preserve and generate entities, this paper focuses on left-linear rules which may also "merge" parts of the state. This is an apparently minimal, yet technically hard enhancement, since a standard characterisation of independence that - in the linear case - allows one to derive a number of properties, essential in the development of a theory of concurrency, no longer holds. The paper performs an in-depth study of the notion of independence for left-linear rules: it introduces a novel characterisation of independence, identifies well-behaved classes of left-linear rewriting systems, and provides some fundamental results including a Church-Rosser property and the existence of canonical equivalence proofs for concurrent computations. These results properly extends the class of formalisms that can be modelled in the adhesive framework.
Cite as

Paolo Baldan, Davide Castelnovo, Andrea Corradini, and Fabio Gadducci. Left-Linear Rewriting in Adhesive Categories. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baldan_et_al:LIPIcs.CONCUR.2024.11,
  author =	{Baldan, Paolo and Castelnovo, Davide and Corradini, Andrea and Gadducci, Fabio},
  title =	{{Left-Linear Rewriting in Adhesive Categories}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.11},
  URN =		{urn:nbn:de:0030-drops-207835},
  doi =		{10.4230/LIPIcs.CONCUR.2024.11},
  annote =	{Keywords: Adhesive categories, double-pushout rewriting, left-linear rules, switch equivalence, local Church-Rosser property}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.39
Coinductive Techniques for Checking Satisfiability of Generalized Nested Conditions

Authors: Lara Stoltenow, Barbara König, Sven Schneider, Andrea Corradini, Leen Lambers, and Fernando Orejas

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
We study nested conditions, a generalization of first-order logic to a categorical setting, and provide a tableau-based (semi-decision) procedure for checking (un)satisfiability and finite model generation. This generalizes earlier results on graph conditions. Furthermore we introduce a notion of witnesses, allowing the detection of infinite models in some cases. To ensure completeness, paths in a tableau must be fair, where fairness requires that all parts of a condition are processed eventually. Since the correctness arguments are non-trivial, we rely on coinductive proof methods and up-to techniques that structure the arguments. We distinguish between two types of categories: categories where all sections are isomorphisms, allowing for a simpler tableau calculus that includes finite model generation; in categories where this requirement does not hold, model generation does not work, but we still obtain a sound and complete calculus.
Cite as

Lara Stoltenow, Barbara König, Sven Schneider, Andrea Corradini, Leen Lambers, and Fernando Orejas. Coinductive Techniques for Checking Satisfiability of Generalized Nested Conditions. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{stoltenow_et_al:LIPIcs.CONCUR.2024.39,
  author =	{Stoltenow, Lara and K\"{o}nig, Barbara and Schneider, Sven and Corradini, Andrea and Lambers, Leen and Orejas, Fernando},
  title =	{{Coinductive Techniques for Checking Satisfiability of Generalized Nested Conditions}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.39},
  URN =		{urn:nbn:de:0030-drops-208113},
  doi =		{10.4230/LIPIcs.CONCUR.2024.39},
  annote =	{Keywords: satisfiability, graph conditions, coinductive techniques, category theory}
}
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