4 Search Results for "Intrigila, Benedetto"

Document
DOI: 10.4230/LIPIcs.MFCS.2025.27
Cops and Robbers for Graphs on Surfaces with Crossings

Authors: Prosenjit Bose, Pat Morin, and Karthik Murali

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
Cops and Robbers is a game played on a graph where a set of cops attempt to capture a single robber. The game proceeds in rounds, where each round first consists of the cops' turn, followed by the robber’s turn. In the first round, the cops place themselves on a subset of vertices, after which the robber chooses a vertex to place himself. From the next round onwards, in the cops' turn, every cop can choose to either stay on the same vertex or move to an adjacent vertex, and likewise the robber in his turn. The robber is considered to be captured if, at any point in time, there is some cop on the same vertex as the robber. The cops win if they can capture the robber within a finite number of rounds; else the robber wins. A natural question in this game concerns the cop-number of a graph - the minimum number of cops needed to capture a robber. It has long been known that graphs embeddable (without crossings) on surfaces of bounded genus have bounded cop-number. In contrast, it was shown recently that the class of 1-planar graphs - graphs that can be drawn on the plane with at most one crossing per edge - does not have bounded cop-number. This paper initiates an investigation into how the distance between crossing pairs of edges influences a graph’s cop number. In particular, we look at Distance d Cops and Robbers, a variant of the classical game, where the robber is considered to be captured if there is a cop within distance d of the robber. Let c_d(G) denote the minimum number of cops required in the graph G to capture a robber within distance d. We look at various classes of graphs, such as 1-plane graphs, k-plane graphs (graphs where each edge is crossed at most k times), and even general graph drawings, and show that if every crossing pair of edges can be connected by a path of small length, then c_d(G) is bounded, for small values of d. For example, we show that if a graph G admits a drawing in which every pair of crossing edges is contained in a path of length at most 3, then c₄(G) ≤ 21. And if the drawing permits a stronger assumption that the endpoints of every crossing induce the complete graph K₄, then c₃(G) ≤ 9. The tools and techniques that we develop in this paper are sufficiently general, enabling us to examine graphs drawn not only on the sphere but also on orientable and non-orientable surfaces.
Cite as

Prosenjit Bose, Pat Morin, and Karthik Murali. Cops and Robbers for Graphs on Surfaces with Crossings. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 27:1-27:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bose_et_al:LIPIcs.MFCS.2025.27,
  author =	{Bose, Prosenjit and Morin, Pat and Murali, Karthik},
  title =	{{Cops and Robbers for Graphs on Surfaces with Crossings}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{27:1--27:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.27},
  URN =		{urn:nbn:de:0030-drops-241349},
  doi =		{10.4230/LIPIcs.MFCS.2025.27},
  annote =	{Keywords: Cops and Robbers, Crossings, 1-Planar, Surfaces}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2025.12
Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!

Authors: Rémy Cerda, Giulio Manzonetto, and Alexis Saurin

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Although the λI-calculus is a natural fragment of the λ-calculus, obtained by forbidding the erasure, its equational theories did not receive much attention. The reason is that all proper denotational models studied in the literature equate all non-normalizable λI-terms, whence the associated theory is not very informative. The goal of this paper is to introduce a previously unknown theory of the λI-calculus, induced by a notion of evaluation trees that we call "Ohana trees". The Ohana tree of a λI-term is an annotated version of its Böhm tree, remembering all free variables that are hidden within its meaningless subtrees, or pushed into infinity along its infinite branches. We develop the associated theories of program approximation: the first approach - more classic - is based on finite trees and continuity, the second adapts Ehrhard and Regnier’s Taylor expansion. We then prove a Commutation Theorem stating that the normal form of the Taylor expansion of a λI-term coincides with the Taylor expansion of its Ohana tree. As a corollary, we obtain that the equality induced by Ohana trees is compatible with abstraction and application. We conclude by discussing the cases of Lévy-Longo and Berarducci trees, and generalizations to the full λ-calculus.
Cite as

Rémy Cerda, Giulio Manzonetto, and Alexis Saurin. Ohana Trees and Taylor Expansion for the λI-Calculus: No variable gets left behind or forgotten!. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cerda_et_al:LIPIcs.FSCD.2025.12,
  author =	{Cerda, R\'{e}my and Manzonetto, Giulio and Saurin, Alexis},
  title =	{{Ohana Trees and Taylor Expansion for the \lambdaI-Calculus: No variable gets left behind or forgotten!}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.12},
  URN =		{urn:nbn:de:0030-drops-236277},
  doi =		{10.4230/LIPIcs.FSCD.2025.12},
  annote =	{Keywords: \lambda-calculus, program approximation, Taylor expansion, \lambdaI-calculus, persistent free variables, B\"{o}hm trees, Ohana trees}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.FSCD.2025.3
Unsolvable Terms in Filter Models (Invited Talk)

Authors: Mariangiola Dezani-Ciancaglini, Paola Giannini, and Furio Honsell

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Intersection type theories (itt’s) and filter models, i.e. λ-calculus models generated by itt’s, are reviewed in full generality. In this framework, which subsumes most λ-calculus models in the literature based on Scott-continuous functions, we discuss the interpretation of unsolvable terms. We give a necessary, but not sufficient, condition on an itt for the interpretation of some unsolvable term to be non-trivial in the filter model it generates. This result is obtained building on a type theoretic characterisation of the fine structure of unsolvables.
Cite as

Mariangiola Dezani-Ciancaglini, Paola Giannini, and Furio Honsell. Unsolvable Terms in Filter Models (Invited Talk). In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dezaniciancaglini_et_al:LIPIcs.FSCD.2025.3,
  author =	{Dezani-Ciancaglini, Mariangiola and Giannini, Paola and Honsell, Furio},
  title =	{{Unsolvable Terms in Filter Models}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{3:1--3:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.3},
  URN =		{urn:nbn:de:0030-drops-236181},
  doi =		{10.4230/LIPIcs.FSCD.2025.3},
  annote =	{Keywords: \lambda-calculus, Intersection Types, Unsolvable Terms, Filter Models}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2017.20
Refutation of Sallé's Longstanding Conjecture

Authors: Benedetto Intrigila, Giulio Manzonetto, and Andrew Polonsky

Published in: LIPIcs, Volume 84, 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)

Abstract
The lambda-calculus possesses a strong notion of extensionality, called "the omega-rule", which has been the subject of many investigations. It is a longstanding open problem whether the equivalence obtained by closing the theory of Böhm trees under the omega-rule is strictly included in Morris's original observational theory, as conjectured by Sallé in the seventies. In a recent work, Breuvart et al. have shown that Morris's theory satisfies the omega-rule. In this paper we demonstrate that the two aforementioned theories actually coincide, thus disproving Sallé's conjecture.
Cite as

Benedetto Intrigila, Giulio Manzonetto, and Andrew Polonsky. Refutation of Sallé's Longstanding Conjecture. In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, pp. 20:1-20:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{intrigila_et_al:LIPIcs.FSCD.2017.20,
  author =	{Intrigila, Benedetto and Manzonetto, Giulio and Polonsky, Andrew},
  title =	{{Refutation of Sall\'{e}'s Longstanding Conjecture}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{20:1--20:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-047-7},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{84},
  editor =	{Miller, Dale},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.20},
  URN =		{urn:nbn:de:0030-drops-77236},
  doi =		{10.4230/LIPIcs.FSCD.2017.20},
  annote =	{Keywords: lambda calculus, observational equivalence, B\"{o}hm trees, omega-rule}
}
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