3 Search Results for "Olive, Fr�d�ric"


Document
Grabbing Olives on Linear Pizzas and Pissaladières

Authors: Jean-Claude Bermond, Frédéric Havet, and Michel Cosnard

Published in: LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)


Abstract
In this paper we revisit the problem entitled Sharing a Pizza stated by P. Winkler by considering a new puzzle called Sharing a Pissaladiere. The game is played by two polite coatis Alice and Bob who share a pissaladière (a p×q grid) which is divided into rectangular slices. Alice starts in a corner and then the coatis alternate removing a remaining slice adjacent to at most two other slices. On some slices there are precious olives of Nice and the aim of each coati is to grab the maximum number of olives. We first study the particular case of 1×n grid (i.e. a path) where the game is a graph grabbing game known as Sharing a linear pizza. In that case each player can take only an end vertex of the remaining path. These problems are particular cases of a new class of games called d-degenerate games played on a graph with non negative weights assigned to the vertices with the rule that coatis alternatively take a vertex of degree at most d. Our main results are the following. We give optimal strategies for paths (linear pizzas) with no two adjacent weighty vertices. We also give a recurrence formula to compute the gains which depend only on the parity of n and of the respective parities of weighty vertices with a complexity in O(h²) where h denotes the number of parity changes in the weighty vertices. When the weights are only {0,1} we reduce the computation of the average number of olives collected by each player to a word counting problem. We solve Sharing a pissaladière with {0,1} weights, when there is one olive or 2 olives. In that case Alice (resp. Bob) grabs almost all the olives if the number of vertices of the grid n = p×q is odd (resp. even). We prove that for a 2×q grid with a fixed number k of olives Bob grabs at least ⌈(k-1)/3⌉ olives and almost always grabs all the k olives.

Cite as

Jean-Claude Bermond, Frédéric Havet, and Michel Cosnard. Grabbing Olives on Linear Pizzas and Pissaladières. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 12:1-12:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bermond_et_al:LIPIcs.FUN.2022.12,
  author =	{Bermond, Jean-Claude and Havet, Fr\'{e}d\'{e}ric and Cosnard, Michel},
  title =	{{Grabbing Olives on Linear Pizzas and Pissaladi\`{e}res}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{12:1--12:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.12},
  URN =		{urn:nbn:de:0030-drops-159826},
  doi =		{10.4230/LIPIcs.FUN.2022.12},
  annote =	{Keywords: Grabbing game, degenerate graph, path, grid}
}
Document
Definability by Horn Formulas and Linear Time on Cellular Automata

Authors: Nicolas Bacquey, Etienne Grandjean, and Frédéric Olive

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)


Abstract
We establish an exact logical characterization of linear time complexity of cellular automata of dimension d, for any fixed d: a set of pictures of dimension d belongs to this complexity class iff it is definable in existential second-order logic restricted to monotonic Horn formulas with built-in successor function and d+1 first-order variables. This logical characterization is optimal modulo an open problem in parallel complexity. Furthermore, its proof provides a systematic method for transforming an inductive formula defining some problem into a cellular automaton that computes it in linear time.

Cite as

Nicolas Bacquey, Etienne Grandjean, and Frédéric Olive. Definability by Horn Formulas and Linear Time on Cellular Automata. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 99:1-99:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bacquey_et_al:LIPIcs.ICALP.2017.99,
  author =	{Bacquey, Nicolas and Grandjean, Etienne and Olive, Fr\'{e}d\'{e}ric},
  title =	{{Definability by Horn Formulas and Linear Time on Cellular Automata}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{99:1--99:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.99},
  URN =		{urn:nbn:de:0030-drops-74174},
  doi =		{10.4230/LIPIcs.ICALP.2017.99},
  annote =	{Keywords: picture languages, linear time, cellular automata of any dimension, local induction, descriptive complexity, second-order logic, horn formulas, logic}
}
Document
Descriptive complexity for pictures languages

Authors: Etienne Grandjean and Frédéric Olive

Published in: LIPIcs, Volume 16, Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL (2012)


Abstract
This paper deals with logical characterizations of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: - the class of "recognizable" picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages to any dimension; - the class of picture languages recognized on "nondeterministic cellular automata in linear time" : cellular automata are the simplest and most natural model of parallel computation and linear time is the minimal time-bounded class allowing synchronization of nondeterministic cellular automata. We uniformly generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of "recognizable" picture languages in existential monadic second-order logic. We state several logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata. They are the first machine-independent characterizations of complexity classes of cellular automata. Our characterizations are essentially deduced from normalization results we prove for first-order and existential second-order logics over pictures. They are obtained in a general and uniform framework that allows to extend them to other "regular" structures.

Cite as

Etienne Grandjean and Frédéric Olive. Descriptive complexity for pictures languages. In Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL. Leibniz International Proceedings in Informatics (LIPIcs), Volume 16, pp. 274-288, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


Copy BibTex To Clipboard

@InProceedings{grandjean_et_al:LIPIcs.CSL.2012.274,
  author =	{Grandjean, Etienne and Olive, Fr\'{e}d\'{e}ric},
  title =	{{Descriptive complexity for pictures languages}},
  booktitle =	{Computer Science Logic (CSL'12) - 26th International Workshop/21st Annual Conference of the EACSL},
  pages =	{274--288},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-42-2},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{16},
  editor =	{C\'{e}gielski, Patrick and Durand, Arnaud},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2012.274},
  URN =		{urn:nbn:de:0030-drops-36783},
  doi =		{10.4230/LIPIcs.CSL.2012.274},
  annote =	{Keywords: Picture languages, locality and tiling, recognizability, linear time, cellular automata, logical characterizations, second-order logic}
}
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