10 Search Results for "Olive, Frédéric"

Document
DOI: 10.4230/LIPIcs.FUN.2026.8
Directed Grabbing Games or How to Politely Grab the Maximum Number of Olives in a Reception

Authors: Jean-Claude Bermond, Michel Cosnard, Frédéric Havet, Takako Kodate, and Stéphane Pérennes

Published in: LIPIcs, Volume 366, 13th International Conference on Fun with Algorithms (FUN 2026)

Abstract
We introduce and study the directed grabbing game, a directed variation of the graph grabbing game played by two players Alice and Bob on a weighted acyclic digraph D. Alice plays first and then they play alternately. At a given odd (resp. even) move, Alice (resp. Bob) chooses a sink, that is a vertex of out-degree 0, grabs the weight (olives) on it and then removes the vertex. The aim of each player is to grab a maximum weight, i.e. a maximum number of olives. This game is inspired by the behaviour that guests are expected to adopt during a reception or cocktail party. We first consider the case where hors d'oeuvre are arranged on slightly spaced parallel lines, such that politeness allows one to take the first hors d'oeuvre from each line. This corresponds to the directed grabbing game on a union of disjoint directed paths. We give an algorithm that, given a weighted digraph D of order n which is the union of q disjoint directed paths, computes an optimal play in O(nlog q) time. Then we consider the "pissaladière case" where the digraph D is a directed (p× q)-grid. We show that, depending on the parity of pq, one player, called Content, has a strategic advantage. Specifically, Content is Alice when pq is odd and Bob when pq is even. We present some strategies that enable Content to remove some large sets of vertices (of order pq/2) in directed grids. We then derive that Content can remove any given vertex that is not in the border of the grid. Finally, in the case where each vertex contains either zero or one olive, we prove that Content can secure the grabbing of around one third of the olives.
Cite as

Jean-Claude Bermond, Michel Cosnard, Frédéric Havet, Takako Kodate, and Stéphane Pérennes. Directed Grabbing Games or How to Politely Grab the Maximum Number of Olives in a Reception. In 13th International Conference on Fun with Algorithms (FUN 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 366, pp. 8:1-8:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bermond_et_al:LIPIcs.FUN.2026.8,
  author =	{Bermond, Jean-Claude and Cosnard, Michel and Havet, Fr\'{e}d\'{e}ric and Kodate, Takako and P\'{e}rennes, St\'{e}phane},
  title =	{{Directed Grabbing Games or How to Politely Grab the Maximum Number of Olives in a Reception}},
  booktitle =	{13th International Conference on Fun with Algorithms (FUN 2026)},
  pages =	{8:1--8:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-417-8},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{366},
  editor =	{Iacono, John},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2026.8},
  URN =		{urn:nbn:de:0030-drops-257273},
  doi =		{10.4230/LIPIcs.FUN.2026.8},
  annote =	{Keywords: grabbing games, paths, directed grids}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2026.3
Building Relational Circuits (Invited Talk)

Authors: Florent Capelli

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
We review two algorithms which allow to build a factorized representation of the answers set of join queries. In a nutshell, the representation builds a circuit representing the answers set of a join query by starting from atomic relations and iteratively combine them by either constructing the Cartesian product or the disjoint union of previously computed relations. The first one can be seen as the trace of the celebrated Yannakakis algorithm, building the answer set from the inputs to the output of the circuit while the second adopts a top-down approach which can be seen as a generalization of the exhaustive DPLL algorithm, originally designed to solve the #SAT problem.
Cite as

Florent Capelli. Building Relational Circuits (Invited Talk). In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{capelli:LIPIcs.ICDT.2026.3,
  author =	{Capelli, Florent},
  title =	{{Building Relational Circuits}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{3:1--3:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.3},
  URN =		{urn:nbn:de:0030-drops-256172},
  doi =		{10.4230/LIPIcs.ICDT.2026.3},
  annote =	{Keywords: Conjunctive queries, factorized databases, knowledge compilation}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2026.9
Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration

Authors: Jinchao Huang, Yufei Tao, and Sibo Wang

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
Previous research on join sampling has focused on joins without selection conditions, even though such conditions are prevalent in everyday queries in database systems. Motivated by this, we undertake a systematic investigation on the complexity of sampling from the result of an acyclic join under equality conditions given only at runtime. When conditions are conjunctive, the goal is to understand when it is possible to precompute a feasible structure that uses Õ(IN) space and supports sampling in Õ(1) time, where IN is the input size. We present a dichotomy to characterize (subject to a widely-accepted conjecture) the existence of such structures based on the conditions supplied and, in every feasible scenario, give an optimal structure of O(IN) space and O(1) sample time. We then extend our investigation to conditions expressed in disjunctive normal form, where the core challenge reduces to the fundamental set union sampling problem. We overcome the challenge with an optimal algorithm and utilize it to develop optimal sampling structures. Our findings also lead to new results on the closely-related random enumeration problem.
Cite as

Jinchao Huang, Yufei Tao, and Sibo Wang. Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 9:1-9:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{huang_et_al:LIPIcs.ICDT.2026.9,
  author =	{Huang, Jinchao and Tao, Yufei and Wang, Sibo},
  title =	{{Acyclic Join Sampling Under Selections: Dichotomy, Union Sampling, and Enumeration}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{9:1--9:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.9},
  URN =		{urn:nbn:de:0030-drops-256231},
  doi =		{10.4230/LIPIcs.ICDT.2026.9},
  annote =	{Keywords: Conjunctive Queries, Acyclic Joins, Sampling, Lower Bounds}
}
Document
Database Theory in Action
DOI: 10.4230/LIPIcs.ICDT.2026.27
Database Theory in Action: Direct Access to Query Answers

Authors: Jiayin Hu and Nikolaos Tziavelis

Published in: LIPIcs, Volume 365, 29th International Conference on Database Theory (ICDT 2026)

Abstract
Direct access asks for the retrieval of query answers by their ranked position, given a query and a desired order. While the time complexity of data structures supporting such accesses has been studied in depth, and efficient algorithms for many queries and common orders are known, their practical performance has received little attention. We provide an implementation covering a wide range of queries and orders; it allows us to investigate intriguing practical aspects, including the comparative performance of database systems and the relationship between direct access and its single-access counterpart.
Cite as

Jiayin Hu and Nikolaos Tziavelis. Database Theory in Action: Direct Access to Query Answers. In 29th International Conference on Database Theory (ICDT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 365, pp. 27:1-27:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hu_et_al:LIPIcs.ICDT.2026.27,
  author =	{Hu, Jiayin and Tziavelis, Nikolaos},
  title =	{{Database Theory in Action: Direct Access to Query Answers}},
  booktitle =	{29th International Conference on Database Theory (ICDT 2026)},
  pages =	{27:1--27:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-413-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{365},
  editor =	{ten Cate, Balder and Funk, Maurice},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2026.27},
  URN =		{urn:nbn:de:0030-drops-256411},
  doi =		{10.4230/LIPIcs.ICDT.2026.27},
  annote =	{Keywords: direct access, conjunctive queries, joins, ranking}
}
Document
DOI: 10.4230/LIPIcs.WADS.2025.19
On the Enumeration of Signatures of XOR-CNF’s

Authors: Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin

Published in: LIPIcs, Volume 349, 19th International Symposium on Algorithms and Data Structures (WADS 2025)

Abstract
Given a CNF formula φ with clauses C_1, … , C_m over a set of variables V, a truth assignment 𝐚: V → {0, 1} generates a binary sequence σ_φ(𝐚) = (C_1(𝐚), …, C_m(𝐚)), called a signature of φ, where C_i(𝐚) = 1 if clause C_i evaluates to 1 under assignment 𝐚, and C_i(𝐚) = 0 otherwise. Signatures and their associated generation problems have given rise to new yet promising research questions in algorithmic enumeration. In a recent paper, Bérczi et al. interestingly proved that generating signatures of a CNF is tractable despite the fact that verifying a solution is hard. They also showed the hardness of finding maximal signatures of an arbitrary CNF due to the intractability of satisfiability in general. Their contribution leaves open the problem of efficiently generating maximal signatures for tractable classes of CNFs, i.e., those for which satisfiability can be solved in polynomial time. Stepping into that direction, we completely characterize the complexity of generating all, minimal, and maximal signatures for XOR-CNF’s.
Cite as

Nadia Creignou, Oscar Defrain, Frédéric Olive, and Simon Vilmin. On the Enumeration of Signatures of XOR-CNF’s. In 19th International Symposium on Algorithms and Data Structures (WADS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 349, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{creignou_et_al:LIPIcs.WADS.2025.19,
  author =	{Creignou, Nadia and Defrain, Oscar and Olive, Fr\'{e}d\'{e}ric and Vilmin, Simon},
  title =	{{On the Enumeration of Signatures of XOR-CNF’s}},
  booktitle =	{19th International Symposium on Algorithms and Data Structures (WADS 2025)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-398-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{349},
  editor =	{Morin, Pat and Oh, Eunjin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WADS.2025.19},
  URN =		{urn:nbn:de:0030-drops-242508},
  doi =		{10.4230/LIPIcs.WADS.2025.19},
  annote =	{Keywords: Algorithmic enumeration, XOR-CNF, signatures, maximal bipartite subgraphs enumeration, extension, proximity search}
}
Document
Research
DOI: 10.4230/OASIcs.Grossi.19
Designing Output Sensitive Algorithms for Subgraph Enumeration

Authors: Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa

Published in: OASIcs, Volume 132, From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday (2025)

Abstract
The enumeration of all subgraphs respecting some structural property is a fundamental task in theoretical computer science, with practical applications in many branches of data mining and network analysis. It is often of interest to only consider solutions (subgraphs) that are maximal under inclusion, and to achieve output-sensitive complexity, i.e., bounding the running time with respect to the number of subgraphs produced. In this paper, we provide a survey of techniques for designing output-sensitive algorithms for subgraph enumeration, including partition-based approaches such as flashlight search, solution-graph traversal methods such as reverse search, and cost amortization strategies such as push-out amortization. We also briefly discuss classes of efficiency, hardness of enumeration, and variants such as approximate enumeration. The paper is meant as an accessible handbook for learning the basics of the field and as a practical reference for selecting state-of-the-art subgraph enumeration strategies fitting to one’s needs.
Cite as

Alessio Conte, Kazuhiro Kurita, Andrea Marino, Giulia Punzi, Takeaki Uno, and Kunihiro Wasa. Designing Output Sensitive Algorithms for Subgraph Enumeration. In From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday. Open Access Series in Informatics (OASIcs), Volume 132, pp. 19:1-19:40, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{conte_et_al:OASIcs.Grossi.19,
  author =	{Conte, Alessio and Kurita, Kazuhiro and Marino, Andrea and Punzi, Giulia and Uno, Takeaki and Wasa, Kunihiro},
  title =	{{Designing Output Sensitive Algorithms for Subgraph Enumeration}},
  booktitle =	{From Strings to Graphs, and Back Again: A Festschrift for Roberto Grossi's 60th Birthday},
  pages =	{19:1--19:40},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-391-1},
  ISSN =	{2190-6807},
  year =	{2025},
  volume =	{132},
  editor =	{Conte, Alessio and Marino, Andrea and Rosone, Giovanna and Vitter, Jeffrey Scott},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.Grossi.19},
  URN =		{urn:nbn:de:0030-drops-238180},
  doi =		{10.4230/OASIcs.Grossi.19},
  annote =	{Keywords: Graph algorithms, Graph enumeration, Output sensitive enumeration}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.26
Dynamic Direct Access of MSO Query Evaluation over Strings

Authors: Pierre Bourhis, Florent Capelli, Stefan Mengel, and Cristian Riveros

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

Abstract
We study the problem of evaluating a Monadic Second Order (MSO) query over strings under updates in the setting of direct access. We present an algorithm that, given an MSO query with first-order free variables represented by an unambiguous variable-set automaton 𝒜 with state set Q and variables X and a string s, computes a data structure in time 𝒪(|Q|^ω⋅ |X|² ⋅ |s|) and, then, given an index i retrieves, using the data structure, the i-th output of the evaluation of 𝒜 over s in time 𝒪(|Q|^ω ⋅ |X|³ ⋅ log(|s|)²) where ω is the exponent for matrix multiplication. Ours is the first efficient direct access algorithm for MSO query evaluation over strings; such algorithms so far had only been studied for first-order queries and conjunctive queries over relational data. Our algorithm gives the answers in lexicographic order where, in contrast to the setting of conjunctive queries, the order between variables can be freely chosen by the user without degrading the runtime. Moreover, our data structure can be updated efficiently after changes to the input string, allowing more powerful updates than in the enumeration literature, e.g. efficient deletion of substrings, concatenation and splitting of strings, and cut-and-paste operations. Our approach combines a matrix representation of MSO queries and a novel data structure for dynamic word problems over semi-groups which yields an overall algorithm that is elegant and easy to formulate.
Cite as

Pierre Bourhis, Florent Capelli, Stefan Mengel, and Cristian Riveros. Dynamic Direct Access of MSO Query Evaluation over Strings. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 26:1-26:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bourhis_et_al:LIPIcs.ICDT.2025.26,
  author =	{Bourhis, Pierre and Capelli, Florent and Mengel, Stefan and Riveros, Cristian},
  title =	{{Dynamic Direct Access of MSO Query Evaluation over Strings}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{26:1--26:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.26},
  URN =		{urn:nbn:de:0030-drops-229675},
  doi =		{10.4230/LIPIcs.ICDT.2025.26},
  annote =	{Keywords: Query evaluation, direct access, MSO queries}
}
Document
DOI: 10.4230/LIPIcs.FUN.2022.12
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.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
DOI: 10.4230/LIPIcs.ICALP.2017.99
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.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
DOI: 10.4230/LIPIcs.CSL.2012.274
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)

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@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.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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