4 Search Results for "Hughes, Dominic J. D."

Document
DOI: 10.4230/LIPIcs.SEA.2024.23
Engineering A* Search for the Flip Distance of Plane Triangulations

Authors: Philip Mayer and Petra Mutzel

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The flip distance for two triangulations of a point set is defined as the smallest number of edge flips needed to transform one triangulation into another, where an edge flip is the act of replacing an edge of a triangulation by a different edge such that the result remains a triangulation. We adapt and engineer a sophisticated A* search algorithm acting on the so-called flip graph. In particular, we prove that previously proposed lower bounds for the flip distance form consistent heuristics for A* and show that they can be computed efficiently using dynamic algorithms. As an alternative approach, we present an integer linear program (ILP) for the flip distance problem. We experimentally evaluate our approaches on a new real-world benchmark data set based on an application in geodesy, namely sea surface reconstruction. Our evaluation reveals that A* search consistently outperforms our ILP formulation as well as a naive baseline, which is bidirectional breadth-first search. In particular, the runtime of our approach improves upon the baseline by more than two orders of magnitude. Furthermore, our A* search successfully solves most of the considered sea surface instances with up to 41 points. This is a substantial improvement compared to the baseline, which struggles with subsets of the real-world data of size 25. Lastly, to allow the consideration of global sea level data, we developed a decomposition-based heuristic for the flip distance. In our experiments it yields optimal flip distance values for most of the considered sea level data and it can be applied to large data sets due to its fast runtime.
Cite as

Philip Mayer and Petra Mutzel. Engineering A* Search for the Flip Distance of Plane Triangulations. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mayer_et_al:LIPIcs.SEA.2024.23,
  author =	{Mayer, Philip and Mutzel, Petra},
  title =	{{Engineering A* Search for the Flip Distance of Plane Triangulations}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{23:1--23:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.23},
  URN =		{urn:nbn:de:0030-drops-203887},
  doi =		{10.4230/LIPIcs.SEA.2024.23},
  annote =	{Keywords: Computational Geometry, Triangulations, Flip Distance, A-star Search, Integer Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2024.15
Adjoint Natural Deduction

Authors: Junyoung Jang, Sophia Roshal, Frank Pfenning, and Brigitte Pientka

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has been defined in the form of a sequent calculus because the central concept of independence is most clearly understood in this form, and because it permits a proof of cut elimination following standard techniques. In this paper we present a natural deduction formulation of adjoint logic and show how it is related to the sequent calculus. As a consequence, every provable proposition has a verification (sometimes called a long normal form). We also give a computational interpretation of adjoint logic in the form of a functional language and prove properties of computations that derive from the structure of modes, including freedom from garbage (for modes without weakening and contraction), strictness (for modes disallowing weakening), and erasure (based on a preorder between modes). Finally, we present a surprisingly subtle algorithm for type checking.
Cite as

Junyoung Jang, Sophia Roshal, Frank Pfenning, and Brigitte Pientka. Adjoint Natural Deduction. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 15:1-15:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jang_et_al:LIPIcs.FSCD.2024.15,
  author =	{Jang, Junyoung and Roshal, Sophia and Pfenning, Frank and Pientka, Brigitte},
  title =	{{Adjoint Natural Deduction}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{15:1--15:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.15},
  URN =		{urn:nbn:de:0030-drops-203441},
  doi =		{10.4230/LIPIcs.FSCD.2024.15},
  annote =	{Keywords: Substructural Logic, Type Systems, Functional Programming}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2022.19
Normalization Without Syntax

Authors: Willem B. Heijltjes, Dominic J. D. Hughes, and Lutz Straßburger

Published in: LIPIcs, Volume 228, 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)

Abstract
We present normalization for intuitionistic combinatorial proofs (ICPs) and relate it to the simply-typed lambda-calculus. We prove confluence and strong normalization. Combinatorial proofs, or "proofs without syntax", form a graphical semantics of proof in various logics that is canonical yet complexity-aware: they are a polynomial-sized representation of sequent proofs that factors out exactly the non-duplicating permutations. Our approach to normalization aligns with these characteristics: it is canonical (free of permutations) and generic (readily applied to other logics). Our reduction mechanism is a canonical representation of reduction in sequent calculus with closed cuts (no abstraction is allowed below a cut), and relates to closed reduction in lambda-calculus and supercombinators. While we will use ICPs concretely, the notion of reduction is completely abstract, and can be specialized to give a reduction mechanism for any representation of typed normal forms.
Cite as

Willem B. Heijltjes, Dominic J. D. Hughes, and Lutz Straßburger. Normalization Without Syntax. In 7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 228, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{heijltjes_et_al:LIPIcs.FSCD.2022.19,
  author =	{Heijltjes, Willem B. and Hughes, Dominic J. D. and Stra{\ss}burger, Lutz},
  title =	{{Normalization Without Syntax}},
  booktitle =	{7th International Conference on Formal Structures for Computation and Deduction (FSCD 2022)},
  pages =	{19:1--19:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-233-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{228},
  editor =	{Felty, Amy P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2022.19},
  URN =		{urn:nbn:de:0030-drops-163004},
  doi =		{10.4230/LIPIcs.FSCD.2022.19},
  annote =	{Keywords: combinatorial proofs, intuitionistic logic, lambda-calculus, Curry-Howard, proof nets}
}
Document
DOI: 10.4230/LIPIcs.FSCD.2019.22
Proof Nets for First-Order Additive Linear Logic

Authors: Willem B. Heijltjes, Dominic J. D. Hughes, and Lutz Straßburger

Published in: LIPIcs, Volume 131, 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)

Abstract
We present canonical proof nets for first-order additive linear logic, the fragment of linear logic with sum, product, and first-order universal and existential quantification. We present two versions of our proof nets. One, witness nets, retains explicit witnessing information to existential quantification. For the other, unification nets, this information is absent but can be reconstructed through unification. Unification nets embody a central contribution of the paper: first-order witness information can be left implicit, and reconstructed as needed. Witness nets are canonical for first-order additive sequent calculus. Unification nets in addition factor out any inessential choice for existential witnesses. Both notions of proof net are defined through coalescence, an additive counterpart to multiplicative contractibility, and for witness nets an additional geometric correctness criterion is provided. Both capture sequent calculus cut-elimination as a one-step global composition operation.
Cite as

Willem B. Heijltjes, Dominic J. D. Hughes, and Lutz Straßburger. Proof Nets for First-Order Additive Linear Logic. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 22:1-22:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{heijltjes_et_al:LIPIcs.FSCD.2019.22,
  author =	{Heijltjes, Willem B. and Hughes, Dominic J. D. and Stra{\ss}burger, Lutz},
  title =	{{Proof Nets for First-Order Additive Linear Logic}},
  booktitle =	{4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)},
  pages =	{22:1--22:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-107-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{131},
  editor =	{Geuvers, Herman},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2019.22},
  URN =		{urn:nbn:de:0030-drops-105297},
  doi =		{10.4230/LIPIcs.FSCD.2019.22},
  annote =	{Keywords: linear logic, first-order logic, proof nets, Herbrand’s theorem}
}
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