21 Search Results for "P�gel, Tobias"


Document
Weakly Markov Categories and Weakly Affine Monads

Authors: Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta

Published in: LIPIcs, Volume 270, 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)


Abstract
Introduced in the 1990s in the context of the algebraic approach to graph rewriting, gs-monoidal categories are symmetric monoidal categories where each object is equipped with the structure of a commutative comonoid. They arise for example as Kleisli categories of commutative monads on cartesian categories, and as such they provide a general framework for effectful computation. Recently proposed in the context of categorical probability, Markov categories are gs-monoidal categories where the monoidal unit is also terminal, and they arise for example as Kleisli categories of commutative affine monads, where affine means that the monad preserves the monoidal unit. The aim of this paper is to study a new condition on the gs-monoidal structure, resulting in the concept of weakly Markov categories, which is intermediate between gs-monoidal categories and Markov ones. In a weakly Markov category, the morphisms to the monoidal unit are not necessarily unique, but form a group. As we show, these categories exhibit a rich theory of conditional independence for morphisms, generalising the known theory for Markov categories. We also introduce the corresponding notion for commutative monads, which we call weakly affine, and for which we give two equivalent characterisations. The paper argues that these monads are relevant to the study of categorical probability. A case at hand is the monad of finite non-zero measures, which is weakly affine but not affine. Such structures allow to investigate probability without normalisation within an elegant categorical framework.

Cite as

Tobias Fritz, Fabio Gadducci, Paolo Perrone, and Davide Trotta. Weakly Markov Categories and Weakly Affine Monads. In 10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 270, pp. 16:1-16:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{fritz_et_al:LIPIcs.CALCO.2023.16,
  author =	{Fritz, Tobias and Gadducci, Fabio and Perrone, Paolo and Trotta, Davide},
  title =	{{Weakly Markov Categories and Weakly Affine Monads}},
  booktitle =	{10th Conference on Algebra and Coalgebra in Computer Science (CALCO 2023)},
  pages =	{16:1--16:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-287-7},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{270},
  editor =	{Baldan, Paolo and de Paiva, Valeria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2023.16},
  URN =		{urn:nbn:de:0030-drops-188133},
  doi =		{10.4230/LIPIcs.CALCO.2023.16},
  annote =	{Keywords: String diagrams, gs-monoidal and Markov categories, categorical probability, affine monads}
}
Document
Track A: Algorithms, Complexity and Games
Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances

Authors: Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, and Martin Schirneck

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We construct data structures for extremal and pairwise distances in directed graphs in the presence of transient edge failures. Henzinger et al. [ITCS 2017] initiated the study of fault-tolerant (sensitivity) oracles for the diameter and vertex eccentricities. We extend this with a special focus on space efficiency. We present several new data structures, among them the first fault-tolerant eccentricity oracle for dual failures in subcubic space. We further prove lower bounds that show limits to approximation vs. space and diameter vs. space trade-offs for fault-tolerant oracles. They highlight key differences between data structures for undirected and directed graphs. Initially, our oracles are randomized leaning on a sampling technique frequently used in sensitivity analysis. Building on the work of Alon, Chechik, and Cohen [ICALP 2019] as well as Karthik and Parter [SODA 2021], we develop a hierarchical framework to derandomize fault-tolerant data structures. We first apply it to our own diameter and eccentricity oracles and then show its versatility by derandomizing algorithms from the literature: the distance sensitivity oracle of Ren [JCSS 2022] and the Single-Source Replacement Path algorithm of Chechik and Magen [ICALP 2020]. This way, we obtain the first deterministic distance sensitivity oracle with subcubic preprocessing time.

Cite as

Davide Bilò, Keerti Choudhary, Sarel Cohen, Tobias Friedrich, and Martin Schirneck. Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bilo_et_al:LIPIcs.ICALP.2022.22,
  author =	{Bil\`{o}, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Schirneck, Martin},
  title =	{{Deterministic Sensitivity Oracles for Diameter, Eccentricities and All Pairs Distances}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{22:1--22:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.22},
  URN =		{urn:nbn:de:0030-drops-163633},
  doi =		{10.4230/LIPIcs.ICALP.2022.22},
  annote =	{Keywords: derandomization, diameter, eccentricity, fault-tolerant data structure, sensitivity oracle, space lower bound}
}
Document
Track A: Algorithms, Complexity and Games
Social Distancing Network Creation

Authors: Tobias Friedrich, Hans Gawendowicz, Pascal Lenzner, and Anna Melnichenko

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
During a pandemic people have to find a trade-off between meeting others and staying safely at home. While meeting others is pleasant, it also increases the risk of infection. We consider this dilemma by introducing a game-theoretic network creation model in which selfish agents can form bilateral connections. They benefit from network neighbors, but at the same time, they want to maximize their distance to all other agents. This models the inherent conflict that social distancing rules impose on the behavior of selfish agents in a social network. Besides addressing this familiar issue, our model can be seen as the inverse to the well-studied Network Creation Game by Fabrikant et al. [PODC 2003] where agents aim at being as central as possible in the created network. Thus, our work is in-line with studies that compare minimization problems with their maximization versions. We look at two variants of network creation governed by social distancing. In the first variant, there are no restrictions on the connections being formed. We characterize optimal and equilibrium networks, and we derive asymptotically tight bounds on the Price of Anarchy and Price of Stability. The second variant is the model’s generalization that allows restrictions on the connections that can be formed. As our main result, we prove that Swap-Maximal Routing-Cost Spanning Trees, an efficiently computable weaker variant of Maximum Routing-Cost Spanning Trees, actually resemble equilibria for a significant range of the parameter space. Moreover, we give almost tight bounds on the Price of Anarchy and Price of Stability. These results imply that, compared the well-studied inverse models, under social distancing the agents' selfish behavior has a significantly stronger impact on the quality of the equilibria, i.e., allowing socially much worse stable states.

Cite as

Tobias Friedrich, Hans Gawendowicz, Pascal Lenzner, and Anna Melnichenko. Social Distancing Network Creation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 62:1-62:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{friedrich_et_al:LIPIcs.ICALP.2022.62,
  author =	{Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Melnichenko, Anna},
  title =	{{Social Distancing Network Creation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{62:1--62:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.62},
  URN =		{urn:nbn:de:0030-drops-164038},
  doi =		{10.4230/LIPIcs.ICALP.2022.62},
  annote =	{Keywords: Algorithmic Game Theory, Equilibrium Existence, Price of Anarchy, Network Creation Game, Social Distancing, Maximization vs. Minimization Problems}
}
Document
Crazy New Idea
Mind the Gap: Language Data, Their Producers, and the Scientific Process (Crazy New Idea)

Authors: Tobias Weber

Published in: OASIcs, Volume 93, 3rd Conference on Language, Data and Knowledge (LDK 2021)


Abstract
This paper discusses the role of low-resource languages in NLP through the lens of different stakeholders. It argues that the current "consumerist approach" to language data reinforces a vicious circle which increases the technological exclusion of minority communities. Researchers' decisions directly affect these processes to the detriment of minorities and practitioners engaging in language work in these communities. In line with the conference topic, the paper concludes with strategies and prerequisites for creating a positive feedback loop in our research benefiting language work within the next decade.

Cite as

Tobias Weber. Mind the Gap: Language Data, Their Producers, and the Scientific Process (Crazy New Idea). In 3rd Conference on Language, Data and Knowledge (LDK 2021). Open Access Series in Informatics (OASIcs), Volume 93, pp. 6:1-6:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{weber:OASIcs.LDK.2021.6,
  author =	{Weber, Tobias},
  title =	{{Mind the Gap: Language Data, Their Producers, and the Scientific Process}},
  booktitle =	{3rd Conference on Language, Data and Knowledge (LDK 2021)},
  pages =	{6:1--6:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-199-3},
  ISSN =	{2190-6807},
  year =	{2021},
  volume =	{93},
  editor =	{Gromann, Dagmar and S\'{e}rasset, Gilles and Declerck, Thierry and McCrae, John P. and Gracia, Jorge and Bosque-Gil, Julia and Bobillo, Fernando and Heinisch, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.LDK.2021.6},
  URN =		{urn:nbn:de:0030-drops-145424},
  doi =		{10.4230/OASIcs.LDK.2021.6},
  annote =	{Keywords: minority languages, data integration, sociology of technology, documentary linguistics, exclusion}
}
Document
Track A: Algorithms, Complexity and Games
On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order

Authors: J. A. Gregor Lagodzinski, Andreas Göbel, Katrin Casel, and Tobias Friedrich

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)


Abstract
We study the problem of counting the number of homomorphisms from an input graph G to a fixed (quantum) graph ̄{H} in any finite field of prime order ℤ_p. The subproblem with graph H was introduced by Faben and Jerrum [ToC'15] and its complexity is still uncharacterised despite active research, e.g. the very recent work of Focke, Goldberg, Roth, and Zivný [SODA'21]. Our contribution is threefold. First, we introduce the study of quantum graphs to the study of modular counting homomorphisms. We show that the complexity for a quantum graph ̄{H} collapses to the complexity criteria found at dimension 1: graphs. Second, in order to prove cases of intractability we establish a further reduction to the study of bipartite graphs. Lastly, we establish a dichotomy for all bipartite (K_{3,3}$1{e}, {domino})-free graphs by a thorough structural study incorporating both local and global arguments. This result subsumes all results on bipartite graphs known for all prime moduli and extends them significantly. Even for the subproblem with p = 2 this establishes new results.

Cite as

J. A. Gregor Lagodzinski, Andreas Göbel, Katrin Casel, and Tobias Friedrich. On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 91:1-91:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{lagodzinski_et_al:LIPIcs.ICALP.2021.91,
  author =	{Lagodzinski, J. A. Gregor and G\"{o}bel, Andreas and Casel, Katrin and Friedrich, Tobias},
  title =	{{On Counting (Quantum-)Graph Homomorphisms in Finite Fields of Prime Order}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{91:1--91:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.91},
  URN =		{urn:nbn:de:0030-drops-141608},
  doi =		{10.4230/LIPIcs.ICALP.2021.91},
  annote =	{Keywords: Algorithms, Theory, Quantum Graphs, Bipartite Graphs, Graph Homomorphisms, Modular Counting, Complexity Dichotomy}
}
Document
The Minimization of Random Hypergraphs

Authors: Thomas Bläsius, Tobias Friedrich, and Martin Schirneck

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
We investigate the maximum-entropy model B_{n,m,p} for random n-vertex, m-edge multi-hypergraphs with expected edge size pn. We show that the expected size of the minimization min(B_{n,m,p}), i.e., the number of inclusion-wise minimal edges of B_{n,m,p}, undergoes a phase transition with respect to m. If m is at most 1/(1-p)^{(1-p)n}, then E[|min(B_{n,m,p})|] is of order Θ(m), while for m ≥ 1/(1-p)^{(1-p+ε)n} for any ε > 0, it is Θ(2^{(H(α) + (1-α) log₂ p) n}/√n). Here, H denotes the binary entropy function and α = - (log_{1-p} m)/n. The result implies that the maximum expected number of minimal edges over all m is Θ((1+p)ⁿ/√n). Our structural findings have algorithmic implications for minimizing an input hypergraph. This has applications in the profiling of relational databases as well as for the Orthogonal Vectors problem studied in fine-grained complexity. We make several technical contributions that are of independent interest in probability. First, we improve the Chernoff-Hoeffding theorem on the tail of the binomial distribution. In detail, we show that for a binomial variable Y ∼ Bin(n,p) and any 0 < x < p, it holds that P[Y ≤ xn] = Θ(2^{-D(x‖p) n}/√n), where D is the binary Kullback-Leibler divergence between Bernoulli distributions. We give explicit upper and lower bounds on the constants hidden in the big-O notation that hold for all n. Secondly, we establish the fact that the probability of a set of cardinality i being minimal after m i.i.d. maximum-entropy trials exhibits a sharp threshold behavior at i^* = n + log_{1-p} m.

Cite as

Thomas Bläsius, Tobias Friedrich, and Martin Schirneck. The Minimization of Random Hypergraphs. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 21:1-21:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{blasius_et_al:LIPIcs.ESA.2020.21,
  author =	{Bl\"{a}sius, Thomas and Friedrich, Tobias and Schirneck, Martin},
  title =	{{The Minimization of Random Hypergraphs}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{21:1--21:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.21},
  URN =		{urn:nbn:de:0030-drops-128871},
  doi =		{10.4230/LIPIcs.ESA.2020.21},
  annote =	{Keywords: Chernoff-Hoeffding theorem, maximum entropy, maximization, minimization, phase transition, random hypergraphs}
}
Document
Invited Talk
An Algebraic Framework to Reason About Concurrency (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)


Abstract
Kleene algebra with tests (KAT) is an algebraic framework for reasoning about the control flow of sequential programs. Hoare, Struth, and collaborators proposed a concurrent extension of Kleene Algebra (CKA) as a first step towards developing algebraic reasoning for concurrent programs. Completing their research program and extending KAT to encompass concurrent behaviour has however proven to be more challenging than initially expected. The core problem appears because when generalising KAT to reason about concurrent programs, axioms native to KAT in conjunction with expected axioms for reasoning about concurrency lead to an unexpected equation about programs. In this talk, we will revise the literature on CKA(T) and explain the challenges and solutions in the development of an algebraic framework for concurrency. The talk is based on a series of papers joint with Tobias Kappé, Paul Brunet, Bas Luttik, Jurriaan Rot, Jana Wagemaker, and Fabio Zanasi [Tobias Kappé et al., 2017; Tobias Kappé et al., 2019; Kappé et al., 2018]. Additional references can be found on the CoNeCo project website: https://coneco-project.org/.

Cite as

Alexandra Silva. An Algebraic Framework to Reason About Concurrency (Invited Talk). In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, p. 6:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{silva:LIPIcs.FSTTCS.2019.6,
  author =	{Silva, Alexandra},
  title =	{{An Algebraic Framework to Reason About Concurrency}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{6:1--6:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Chattopadhyay, Arkadev and Gastin, Paul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.6},
  URN =		{urn:nbn:de:0030-drops-115687},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.6},
  annote =	{Keywords: Kleene Algebra, Concurrency, Automata}
}
Document
Invited Talk
Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk)

Authors: Alexandra Silva

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
Guarded Kleene Algebra with Tests (GKAT) is a variation on Kleene Algebra with Tests (KAT) that arises by restricting the union (+) and iteration (*) operations from KAT to predicate-guarded versions. We develop the (co)algebraic theory of GKAT and show how it can be efficiently used to reason about imperative programs. In contrast to KAT, whose equational theory is PSPACE-complete, we show that the equational theory of GKAT is (almost) linear time. We also provide a full Kleene theorem and prove completeness for an analogue of Salomaa’s axiomatization of Kleene Algebra. We will also discuss how this result has practical implications in the verification of programs, with examples from network and probabilistic programming. This is joint work with Nate Foster, Justin Hsu, Tobias Kappe, Dexter Kozen, and Steffen Smolka.

Cite as

Alexandra Silva. Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time (Invited Talk). In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{silva:LIPIcs.MFCS.2019.2,
  author =	{Silva, Alexandra},
  title =	{{Guarded Kleene Algebra with Tests: Verification of Uninterpreted Programs in Nearly Linear Time}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.2},
  URN =		{urn:nbn:de:0030-drops-109462},
  doi =		{10.4230/LIPIcs.MFCS.2019.2},
  annote =	{Keywords: Kleene algebra, verification, decision procedures}
}
Document
On the Complexity of Reachability in Parametric Markov Decision Processes

Authors: Tobias Winkler, Sebastian Junges, Guillermo A. Pérez, and Joost-Pieter Katoen

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)


Abstract
This paper studies parametric Markov decision processes (pMDPs), an extension to Markov decision processes (MDPs) where transitions probabilities are described by polynomials over a finite set of parameters. Fixing values for all parameters yields MDPs. In particular, this paper studies the complexity of finding values for these parameters such that the induced MDP satisfies some reachability constraints. We discuss different variants depending on the comparison operator in the constraints and the domain of the parameter values. We improve all known lower bounds for this problem, and notably provide ETR-completeness results for distinct variants of this problem. Furthermore, we provide insights in the functions describing the induced reachability probabilities, and how pMDPs generalise concurrent stochastic reachability games.

Cite as

Tobias Winkler, Sebastian Junges, Guillermo A. Pérez, and Joost-Pieter Katoen. On the Complexity of Reachability in Parametric Markov Decision Processes. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{winkler_et_al:LIPIcs.CONCUR.2019.14,
  author =	{Winkler, Tobias and Junges, Sebastian and P\'{e}rez, Guillermo A. and Katoen, Joost-Pieter},
  title =	{{On the Complexity of Reachability in Parametric Markov Decision Processes}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.14},
  URN =		{urn:nbn:de:0030-drops-109162},
  doi =		{10.4230/LIPIcs.CONCUR.2019.14},
  annote =	{Keywords: Parametric Markov decision processes, Formal verification, ETR, Complexity}
}
Document
Extended Abstract
Can Computational Meta-Documentary Linguistics Provide for Accountability and Offer an Alternative to "Reproducibility" in Linguistics?

Authors: Tobias Weber

Published in: OASIcs, Volume 70, 2nd Conference on Language, Data and Knowledge (LDK 2019)


Abstract
As an answer to the need for accountability in linguistics, computational methodology and big data approaches offer an interesting perspective to the field of meta-documentary linguistics. The focus of this paper lies on the scientific process of citing published data and the insights this gives to the workings of a discipline. The proposed methodology shall aid to bring out the narratives of linguistic research within the literature. This can be seen as an alternative, philological approach to documentary linguistics.

Cite as

Tobias Weber. Can Computational Meta-Documentary Linguistics Provide for Accountability and Offer an Alternative to "Reproducibility" in Linguistics?. In 2nd Conference on Language, Data and Knowledge (LDK 2019). Open Access Series in Informatics (OASIcs), Volume 70, pp. 26:1-26:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{weber:OASIcs.LDK.2019.26,
  author =	{Weber, Tobias},
  title =	{{Can Computational Meta-Documentary Linguistics Provide for Accountability and Offer an Alternative to "Reproducibility" in Linguistics?}},
  booktitle =	{2nd Conference on Language, Data and Knowledge (LDK 2019)},
  pages =	{26:1--26:8},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-105-4},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{70},
  editor =	{Eskevich, Maria and de Melo, Gerard and F\"{a}th, Christian and McCrae, John P. and Buitelaar, Paul and Chiarcos, Christian and Klimek, Bettina and Dojchinovski, Milan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.LDK.2019.26},
  URN =		{urn:nbn:de:0030-drops-103900},
  doi =		{10.4230/OASIcs.LDK.2019.26},
  annote =	{Keywords: Language Documentation, meta-documentary Linguistics, Citation, Methodology, Digital Humanities, Philology, Intertextuality}
}
Document
Approximating Airports and Railways

Authors: Anna Adamaszek, Antonios Antoniadis, Amit Kumar, and Tobias Mömke

Published in: LIPIcs, Volume 96, 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)


Abstract
In this paper we consider the airport and railway problem (AR), which combines capacitated facility location with network design, both in the general metric and the two-dimensional Euclidean space. An instance of the airport and railway problem consists of a set of points in the corresponding metric, together with a non-negative weight for each point, and a parameter k. The points represent cities, the weights denote costs of opening an airport in the corresponding city, and the parameter k is a maximum capacity of an airport. The goal is to construct a minimum cost network of airports and railways connecting all the cities, where railways correspond to edges connecting pairs of points, and the cost of a railway is equal to the distance between the corresponding points. The network is partitioned into components, where each component contains an open airport, and spans at most k cities. For the Euclidean case, any points in the plane can be used as Steiner vertices of the network. We obtain the first bicriteria approximation algorithm for AR for the general metric case, which yields a 4-approximate solution with a resource augmentation of the airport capacity k by a factor of 2. More generally, for any parameter 0 < p <= 1 where pk is an integer we develop a (4/3)(2 + 1/p)-approximation algorithm for metric AR with a resource augmentation by a factor of 1 + p. Furthermore, we obtain the first constant factor approximation algorithm that does not resort to resource augmentation for AR in the Euclidean plane. Additionally, for the Euclidean setting we provide a quasi-polynomial time approximation scheme for the same problem with a resource augmentation by a factor of 1 + mu on the airport capacity, for any fixed mu > 0.

Cite as

Anna Adamaszek, Antonios Antoniadis, Amit Kumar, and Tobias Mömke. Approximating Airports and Railways. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 5:1-5:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{adamaszek_et_al:LIPIcs.STACS.2018.5,
  author =	{Adamaszek, Anna and Antoniadis, Antonios and Kumar, Amit and M\"{o}mke, Tobias},
  title =	{{Approximating Airports and Railways}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{5:1--5:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Niedermeier, Rolf and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.5},
  URN =		{urn:nbn:de:0030-drops-85183},
  doi =		{10.4230/LIPIcs.STACS.2018.5},
  annote =	{Keywords: Network Design, Facility Location, Approximation Algorithms, PTAS, Metric, Euclidean}
}
Document
Invited Talk
Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk)

Authors: Alexandra Silva

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


Abstract
Concurrent Kleene Algebra (CKA) is a mathematical formalism to study programs that exhibit concurrent behaviour. As with previous extensions of Kleene Algebra, characterizing the free model is crucial in order to develop the foundations of the theory and potential applications. For CKA, this has been an open question for a few years and this talk will overview why the problem is so difficult. We will then pave the way towards a solution, by presenting a new automaton model and a Kleene-like theorem for CKA. More precisely, we connect a relaxed version of CKA to series-parallel pomset languages, which are a natural candidate for the free model. There are two substantial differences with previous work: from expressions to automata, we use Brzozowski derivatives, which enable a direct construction of the automaton; from automata to expressions, we provide a syntactic characterization of the automata that denote valid CKA behaviours. We also survey how the present work can be used to to extend the network specification language NetKAT with primitives for concurrency so as to model and reason about concurrency within networks. This is joint work with Tobias Kappe, Paul Brunet, Bas Luttik, and Fabio Zanasi.

Cite as

Alexandra Silva. Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages (Invited Talk). In 2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 84, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{silva:LIPIcs.FSCD.2017.3,
  author =	{Silva, Alexandra},
  title =	{{Brzozowski Goes Concurrent - A Kleene Theorem for Pomset Languages}},
  booktitle =	{2nd International Conference on Formal Structures for Computation and Deduction (FSCD 2017)},
  pages =	{3:1--3:1},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2017.3},
  URN =		{urn:nbn:de:0030-drops-77445},
  doi =		{10.4230/LIPIcs.FSCD.2017.3},
  annote =	{Keywords: Kleene algebras, Pomset languages, concurrency, NetKAT}
}
Document
Charting the Replica Symmetric Phase

Authors: Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)


Abstract
Random graph models and associated inference problems such as the stochastic block model play an eminent role in computer science, discrete mathematics and statistics. Based on non-rigorous arguments physicists predicted the existence of a generic phase transition that separates a "replica symmetric phase" where statistical inference is impossible from a phase where the detection of the "ground truth" is information-theoretically possible. In this paper we prove a contiguity result that shows that detectability is indeed impossible within the replica-symmetric phase for a broad class of models. In particular, this implies the detectability conjecture for the disassortative stochastic block model from [Decelle et al.: Phys Rev E 2011]. Additionally, we investigate key features of the replica symmetric phase such as the nature of point-to-set correlations (`reconstruction').

Cite as

Amin Coja-Oghlan, Charilaos Efthymiou, Nor Jaafari, Mihyun Kang, and Tobias Kapetanopoulos. Charting the Replica Symmetric Phase. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 40:1-40:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{cojaoghlan_et_al:LIPIcs.APPROX-RANDOM.2017.40,
  author =	{Coja-Oghlan, Amin and Efthymiou, Charilaos and Jaafari, Nor and Kang, Mihyun and Kapetanopoulos, Tobias},
  title =	{{Charting the Replica Symmetric Phase}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{40:1--40:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  URN =		{urn:nbn:de:0030-drops-75895},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.40},
  annote =	{Keywords: Random factor graph, bounds for condensation phase transition, Potts antiferromagnet, diluted k-spin model, stochastic block model}
}
Document
Practical Range Minimum Queries Revisited

Authors: Niklas Baumstark, Simon Gog, Tobias Heuer, and Julian Labeit

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)


Abstract
Finding the position of the minimal element in a subarray A[i..j] of an array A of size n is a fundamental operation in many applications. In 2011, Fischer and Heun presented the first index of size 2n+o(n) bits which answers the operation in constant time for any subarray. The index can be computed in linear time and queries can be answered without consulting the original array. The most recent and currently fastest practical index is due to Ferrada and Navarro (DCC'16). It reduces the range minimum query (RMQ) to more fundamental and well studied queries on binary vectors, namely rank and select, and a RMQ query on an array of sublinear size derived from A. A range min-max tree is employed to solve this recursive RMQ call. In this paper, we review their practical design and suggest a series of changes which result in consistently faster query times. Specifically, we provide a customized select implementation, switch to two levels of recursion, and use the sparse table solution for the recursion base case instead of a range min-max tree. We provide an extensive empirical evaluation of our new implementation and also compare it to the state of the art. Our experimental study shows that our proposal significantly outperforms the previous solutions on established benchmarks (up to a factor of three) and furthermore accelerates real world applications such as traversing a succinct tree or listing all distinct elements in an interval of an array.

Cite as

Niklas Baumstark, Simon Gog, Tobias Heuer, and Julian Labeit. Practical Range Minimum Queries Revisited. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{baumstark_et_al:LIPIcs.SEA.2017.12,
  author =	{Baumstark, Niklas and Gog, Simon and Heuer, Tobias and Labeit, Julian},
  title =	{{Practical Range Minimum Queries Revisited}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.12},
  URN =		{urn:nbn:de:0030-drops-76158},
  doi =		{10.4230/LIPIcs.SEA.2017.12},
  annote =	{Keywords: Succinct Data Structures, Range Minimum Queries, Algorithm Engineering}
}
Document
The Quantile Index - Succinct Self-Index for Top-k Document Retrieval

Authors: Niklas Baumstark, Simon Gog, Tobias Heuer, and Julian Labeit

Published in: LIPIcs, Volume 75, 16th International Symposium on Experimental Algorithms (SEA 2017)


Abstract
One of the central problems in information retrieval is that of finding the k documents in a large text collection that best match a query given by a user. A recent result of Navarro & Nekrich (SODA 2012) showed that single term and phrase queries of length m can be solved in optimal O(m+k) time using a linear word sized index. While a verbatim implementation of the index would be at least an order of magnitude larger than the original collection, various authors incrementally improved the index to a point where the space requirement is currently within a factor of 1.5 to 2.0 of the text size for standard collections. In this paper, we propose a new time/space trade-off for different top-k indexes. This is achieved by sampling only a quantile of the postings in the original inverted file or suffix array-based index. For those queries that cannot be answered using the sampled version of the index we show how to compute the query results on the fly efficiently. As an example, we apply our method to the top-k framework by Navarro & Nekrich. Under probabilistic assumptions that hold for most standard texts, and for a standard scoring function called term frequency, our index can be represented with only sublinearly many bits plus the space needed for a compressed suffix array of the text, while maintaining poly-logarithmic query times. We evaluate our solution on real-world datasets and compare its practical space usage and performance against state-of-the-art implementations. Our experiments show that our index compresses below the size of the original text. To our knowledge it is the first suffix array-based text index that is able to break this bound in practice even for non-repetitive collections, while still maintaining reasonable query times of under half a millisecond on average for top-10 queries.

Cite as

Niklas Baumstark, Simon Gog, Tobias Heuer, and Julian Labeit. The Quantile Index - Succinct Self-Index for Top-k Document Retrieval. In 16th International Symposium on Experimental Algorithms (SEA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 75, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{baumstark_et_al:LIPIcs.SEA.2017.15,
  author =	{Baumstark, Niklas and Gog, Simon and Heuer, Tobias and Labeit, Julian},
  title =	{{The Quantile Index - Succinct Self-Index for Top-k Document Retrieval}},
  booktitle =	{16th International Symposium on Experimental Algorithms (SEA 2017)},
  pages =	{15:1--15:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-036-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{75},
  editor =	{Iliopoulos, Costas S. and Pissis, Solon P. and Puglisi, Simon J. and Raman, Rajeev},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2017.15},
  URN =		{urn:nbn:de:0030-drops-76183},
  doi =		{10.4230/LIPIcs.SEA.2017.15},
  annote =	{Keywords: Text Indexing, Succinct Data Structures, Top-k Document Retrieval}
}
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