61 Search Results for "J�hnichen, Stefan"


Document
Direct Access for Conjunctive Queries with Negations

Authors: Florent Capelli and Oliver Irwin

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)


Abstract
Given a conjunctive query Q and a database 𝐃, a direct access to the answers of Q over 𝐃 is the operation of returning, given an index j, the j-th answer for some order on its answers. While this problem is #P-hard in general with respect to combined complexity, many conjunctive queries have an underlying structure that allows for a direct access to their answers for some lexicographical ordering that takes polylogarithmic time in the size of the database after a polynomial time precomputation. Previous work has precisely characterised the tractable classes and given fine-grained lower bounds on the precomputation time needed depending on the structure of the query. In this paper, we generalise these tractability results to the case of signed conjunctive queries, that is, conjunctive queries that may contain negative atoms. Our technique is based on a class of circuits that can represent relational data. We first show that this class supports tractable direct access after a polynomial time preprocessing. We then give bounds on the size of the circuit needed to represent the answer set of signed conjunctive queries depending on their structure. Both results combined together allow us to prove the tractability of direct access for a large class of conjunctive queries. On the one hand, we recover the known tractable classes from the literature in the case of positive conjunctive queries. On the other hand, we generalise and unify known tractability results about negative conjunctive queries - that is, queries having only negated atoms. In particular, we show that the class of β-acyclic negative conjunctive queries and the class of bounded nest set width negative conjunctive queries admit tractable direct access.

Cite as

Florent Capelli and Oliver Irwin. Direct Access for Conjunctive Queries with Negations. In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 13:1-13:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{capelli_et_al:LIPIcs.ICDT.2024.13,
  author =	{Capelli, Florent and Irwin, Oliver},
  title =	{{Direct Access for Conjunctive Queries with Negations}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{13:1--13:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.13},
  URN =		{urn:nbn:de:0030-drops-197958},
  doi =		{10.4230/LIPIcs.ICDT.2024.13},
  annote =	{Keywords: Conjunctive queries, factorized databases, direct access, hypertree decomposition}
}
Document
History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs

Authors: Khalil Esper and Jürgen Teich

Published in: OASIcs, Volume 117, Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024)


Abstract
Embedded system applications usually have requirements regarding non-functional properties of their execution like latency or power consumption. Enforcement of such requirements can be implemented by a reactive control loop, where an enforcer determines based on a system response (feedback) how to control the system, e.g., by selecting the number of active cores allocated to a program or by scaling their voltage/frequency mode. It is of a particular interest to design enforcement strategies for which it is possible to provide formal guarantees with respect to requirement violations, especially under a largely varying environmental input (workload) per execution. In this paper, we consider enforcement strategies that are modeled by a finite state machine (FSM) and the environment by a discrete-time Markov chain. Such a formalization enables the formal verification of temporal properties (verification goals) regarding the satisfaction of requirements of a given enforcement strategy. In this paper, we propose history-based enforcement FSMs which compute a reaction not just on the current, but on a fixed history of K previously observed system responses. We then analyze the quality of such enforcement FSMs in terms of the probability of satisfying a given set of verification goals and compare them to enforcement FSMs that react solely on the current system response. As experimental results, we present three use cases while considering requirements on latency and power consumption. The results show that history-based enforcement FSMs outperform enforcement FSMs that only consider the current system response regarding the probability of satisfying a given set of verification goals.

Cite as

Khalil Esper and Jürgen Teich. History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs. In Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024). Open Access Series in Informatics (OASIcs), Volume 117, pp. 4:1-4:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{esper_et_al:OASIcs.NG-RES.2024.4,
  author =	{Esper, Khalil and Teich, J\"{u}rgen},
  title =	{{History-Based Run-Time Requirement Enforcement of Non-Functional Properties on MPSoCs}},
  booktitle =	{Fifth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2024)},
  pages =	{4:1--4:11},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-313-3},
  ISSN =	{2190-6807},
  year =	{2024},
  volume =	{117},
  editor =	{Yomsi, Patrick Meumeu and Wildermann, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2024.4},
  URN =		{urn:nbn:de:0030-drops-197074},
  doi =		{10.4230/OASIcs.NG-RES.2024.4},
  annote =	{Keywords: Verification, Runtime Requirement Enforcement, History, Latency}
}
Document
SAT Encodings and Beyond (Dagstuhl Seminar 23261)

Authors: Marijn J. H. Heule, Inês Lynce, Stefan Szeider, and Andre Schidler

Published in: Dagstuhl Reports, Volume 13, Issue 6 (2024)


Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23261 "SAT Encodings and Beyond." The seminar facilitated an intense examination and discussion of current results and challenges related to encodings for SAT and related solving paradigms. The seminar featured presentations and group work that provided theoretical, practical, and industrial viewpoints. The goal was to foster more profound insights and advancements in encoding techniques, which are pivotal in enhancing solvers' efficiency.

Cite as

Marijn J. H. Heule, Inês Lynce, Stefan Szeider, and Andre Schidler. SAT Encodings and Beyond (Dagstuhl Seminar 23261). In Dagstuhl Reports, Volume 13, Issue 6, pp. 106-122, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@Article{heule_et_al:DagRep.13.6.106,
  author =	{Heule, Marijn J. H. and Lynce, In\^{e}s and Szeider, Stefan and Schidler, Andre},
  title =	{{SAT Encodings and Beyond (Dagstuhl Seminar 23261)}},
  pages =	{106--122},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{6},
  editor =	{Heule, Marijn J. H. and Lynce, In\^{e}s and Szeider, Stefan and Schidler, Andre},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagRep.13.6.106},
  URN =		{urn:nbn:de:0030-drops-196409},
  doi =		{10.4230/DagRep.13.6.106},
  annote =	{Keywords: constraint propagation, lower and upper bounds, problem formulation, propositional satisfiability, symmetry breaking}
}
Document
Online Algorithms with Randomly Infused Advice

Authors: Yuval Emek, Yuval Gil, Maciej Pacut, and Stefan Schmid

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer ℬ from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 ≤ α ≤ 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - α, then the buffer ℬ contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter α increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.

Cite as

Yuval Emek, Yuval Gil, Maciej Pacut, and Stefan Schmid. Online Algorithms with Randomly Infused Advice. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 44:1-44:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{emek_et_al:LIPIcs.ESA.2023.44,
  author =	{Emek, Yuval and Gil, Yuval and Pacut, Maciej and Schmid, Stefan},
  title =	{{Online Algorithms with Randomly Infused Advice}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{44:1--44:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.44},
  URN =		{urn:nbn:de:0030-drops-186970},
  doi =		{10.4230/LIPIcs.ESA.2023.44},
  annote =	{Keywords: Online algorithms, competitive analysis, advice}
}
Document
Learned Monotone Minimal Perfect Hashing

Authors: Paolo Ferragina, Hans-Peter Lehmann, Peter Sanders, and Giorgio Vinciguerra

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
A Monotone Minimal Perfect Hash Function (MMPHF) constructed on a set S of keys is a function that maps each key in S to its rank. On keys not in S, the function returns an arbitrary value. Applications range from databases, search engines, data encryption, to pattern-matching algorithms. In this paper, we describe LeMonHash, a new technique for constructing MMPHFs for integers. The core idea of LeMonHash is surprisingly simple and effective: we learn a monotone mapping from keys to their rank via an error-bounded piecewise linear model (the PGM-index), and then we solve the collisions that might arise among keys mapping to the same rank estimate by associating small integers with them in a retrieval data structure (BuRR). On synthetic random datasets, LeMonHash needs 34% less space than the next larger competitor, while achieving about 16 times faster queries. On real-world datasets, the space usage is very close to or much better than the best competitors, while achieving up to 19 times faster queries than the next larger competitor. As far as the construction of LeMonHash is concerned, we get an improvement by a factor of up to 2, compared to the competitor with the next best space usage. We also investigate the case of keys being variable-length strings, introducing the so-called LeMonHash-VL: it needs space within 13% of the best competitors while achieving up to 3 times faster queries than the next larger competitor.

Cite as

Paolo Ferragina, Hans-Peter Lehmann, Peter Sanders, and Giorgio Vinciguerra. Learned Monotone Minimal Perfect Hashing. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 46:1-46:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{ferragina_et_al:LIPIcs.ESA.2023.46,
  author =	{Ferragina, Paolo and Lehmann, Hans-Peter and Sanders, Peter and Vinciguerra, Giorgio},
  title =	{{Learned Monotone Minimal Perfect Hashing}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{46:1--46:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.46},
  URN =		{urn:nbn:de:0030-drops-186990},
  doi =		{10.4230/LIPIcs.ESA.2023.46},
  annote =	{Keywords: compressed data structure, monotone minimal perfect hashing, retrieval}
}
Document
Tight Algorithms for Connectivity Problems Parameterized by Clique-Width

Authors: Falko Hegerfeld and Stefan Kratsch

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
The complexity of problems involving global constraints is usually much more difficult to understand than the complexity of problems only involving local constraints. In the realm of graph problems, connectivity constraints are a natural form of global constraints. We study connectivity problems from a fine-grained parameterized perspective. In a breakthrough result, Cygan et al. (TALG 2022) first obtained Monte-Carlo algorithms with single-exponential running time α^{tw} n^𝒪(1) for connectivity problems parameterized by treewidth by introducing the cut-and-count-technique, which reduces many connectivity problems to locally checkable counting problems. Furthermore, the obtained bases α were shown to be optimal under the Strong Exponential-Time Hypothesis (SETH). However, since only sparse graphs may admit small treewidth, we lack knowledge of the fine-grained complexity of connectivity problems with respect to dense structure. The most popular graph parameter to measure dense structure is arguably clique-width, which intuitively measures how easily a graph can be constructed by repeatedly adding bicliques. Bergougnoux and Kanté (TCS 2019) have shown, using the rank-based approach, that also parameterized by clique-width many connectivity problems admit single-exponential algorithms. Unfortunately, the obtained running times are far from optimal under SETH. We show how to obtain optimal running times parameterized by clique-width for two benchmark connectivity problems, namely Connected Vertex Cover and Connected Dominating Set. These are the first tight results for connectivity problems with respect to clique-width and these results are obtained by developing new algorithms based on the cut-and-count-technique and novel lower bound constructions. Precisely, we show that there exist one-sided error Monte-Carlo algorithms that given a k-clique-expression solve - Connected Vertex Cover in time 6^k n^𝒪(1), and - Connected Dominating Set in time 5^k n^𝒪(1). Both results are shown to be tight under SETH.

Cite as

Falko Hegerfeld and Stefan Kratsch. Tight Algorithms for Connectivity Problems Parameterized by Clique-Width. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{hegerfeld_et_al:LIPIcs.ESA.2023.59,
  author =	{Hegerfeld, Falko and Kratsch, Stefan},
  title =	{{Tight Algorithms for Connectivity Problems Parameterized by Clique-Width}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{59:1--59:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.59},
  URN =		{urn:nbn:de:0030-drops-187124},
  doi =		{10.4230/LIPIcs.ESA.2023.59},
  annote =	{Keywords: Parameterized Complexity, Connectivity, Clique-width, Cut\&Count, Lower Bound}
}
Document
Tight Algorithmic Applications of Clique-Width Generalizations

Authors: Vera Chekan and Stefan Kratsch

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
In this work, we study two natural generalizations of clique-width introduced by Martin Fürer. Multi-clique-width (mcw) allows every vertex to hold multiple labels [ITCS 2017], while for fusion-width (fw) we have a possibility to merge all vertices of a certain label [LATIN 2014]. Fürer has shown that both parameters are upper-bounded by treewidth thus making them more appealing from an algorithmic perspective than clique-width and asked for applications of these parameters for problem solving. First, we determine the relation between these two parameters by showing that mcw ≤ fw + 1. Then we show that when parameterized by multi-clique-width, many problems (e.g., Connected Dominating Set) admit algorithms with the same running time as for clique-width despite the exponential gap between these two parameters. For some problems (e.g., Hamiltonian Cycle) we show an analogous result for fusion-width: For this we present an alternative view on fusion-width by introducing so-called glue-expressions which might be interesting on their own. All algorithms obtained in this work are tight up to (Strong) Exponential Time Hypothesis.

Cite as

Vera Chekan and Stefan Kratsch. Tight Algorithmic Applications of Clique-Width Generalizations. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 35:1-35:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chekan_et_al:LIPIcs.MFCS.2023.35,
  author =	{Chekan, Vera and Kratsch, Stefan},
  title =	{{Tight Algorithmic Applications of Clique-Width Generalizations}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{35:1--35:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.35},
  URN =		{urn:nbn:de:0030-drops-185699},
  doi =		{10.4230/LIPIcs.MFCS.2023.35},
  annote =	{Keywords: Parameterized complexity, connectivity problems, clique-width}
}
Document
Positive Data Languages

Authors: Florian Frank, Stefan Milius, and Henning Urbat

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
Positive data languages are languages over an infinite alphabet closed under possibly non-injective renamings of data values. Informally, they model properties of data words expressible by assertions about equality, but not inequality, of data values occurring in the word. We investigate the class of positive data languages recognizable by nondeterministic orbit-finite nominal automata, an abstract form of register automata introduced by Bojańczyk, Klin, and Lasota. As our main contribution we provide a number of equivalent characterizations of that class in terms of positive register automata, monadic second-order logic with positive equality tests, and finitely presentable nondeterministic automata in the categories of nominal renaming sets and of presheaves over finite sets.

Cite as

Florian Frank, Stefan Milius, and Henning Urbat. Positive Data Languages. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 48:1-48:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{frank_et_al:LIPIcs.MFCS.2023.48,
  author =	{Frank, Florian and Milius, Stefan and Urbat, Henning},
  title =	{{Positive Data Languages}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.48},
  URN =		{urn:nbn:de:0030-drops-185828},
  doi =		{10.4230/LIPIcs.MFCS.2023.48},
  annote =	{Keywords: Data Languages, Register Automata, MSO, Nominal Sets, Presheaves}
}
Document
Deciding Predicate Logical Theories Of Real-Valued Functions

Authors: Stefan Ratschan

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)


Abstract
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that reason about real-valued functions. This paper defines a first-order predicate language for reasoning about multi-dimensional smooth real-valued functions and their derivatives, and demonstrates that - despite the obvious undecidability barriers - certain positive decidability results for such a language are indeed possible.

Cite as

Stefan Ratschan. Deciding Predicate Logical Theories Of Real-Valued Functions. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 76:1-76:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{ratschan:LIPIcs.MFCS.2023.76,
  author =	{Ratschan, Stefan},
  title =	{{Deciding Predicate Logical Theories Of Real-Valued Functions}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{76:1--76:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.76},
  URN =		{urn:nbn:de:0030-drops-186101},
  doi =		{10.4230/LIPIcs.MFCS.2023.76},
  annote =	{Keywords: decision procedures, first-order predicate logical theories, real numbers, real-valued functions}
}
Document
RAVEN: Reinforcement Learning for Generating Verifiable Run-Time Requirement Enforcers for MPSoCs

Authors: Khalil Esper, Jan Spieck, Pierre-Louis Sixdenier, Stefan Wildermann, and Jürgen Teich

Published in: OASIcs, Volume 108, Fourth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2023)


Abstract
In embedded systems, applications frequently have to meet non-functional requirements regarding, e.g., real-time or energy consumption constraints, when executing on a given MPSoC target platform. Feedback-based controllers have been proposed that react to transient environmental factors by adapting the DVFS settings or degree of parallelism following some predefined control strategy. However, it is, in general, not possible to give formal guarantees for the obtained controllers to satisfy a given set of non-functional requirements. Run-time requirement enforcement has emerged as a field of research for the enforcement of non-functional requirements at run-time, allowing to define and formally verify properties on respective control strategies specified by automata. However, techniques for the automatic generation of such controllers have not yet been established. In this paper, we propose a technique using reinforcement learning to automatically generate verifiable feedback-based enforcers. For that, we train a control policy based on a representative input sequence at design time. The learned control strategy is then transformed into a verifiable enforcement automaton which constitutes our run-time control model that can handle unseen input data. As a case study, we apply the approach to generate controllers that are able to increase the probability of satisfying a given set of requirement verification goals compared to multiple state-of-the-art approaches, as can be verified by model checkers.

Cite as

Khalil Esper, Jan Spieck, Pierre-Louis Sixdenier, Stefan Wildermann, and Jürgen Teich. RAVEN: Reinforcement Learning for Generating Verifiable Run-Time Requirement Enforcers for MPSoCs. In Fourth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2023). Open Access Series in Informatics (OASIcs), Volume 108, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{esper_et_al:OASIcs.NG-RES.2023.7,
  author =	{Esper, Khalil and Spieck, Jan and Sixdenier, Pierre-Louis and Wildermann, Stefan and Teich, J\"{u}rgen},
  title =	{{RAVEN: Reinforcement Learning for Generating Verifiable Run-Time Requirement Enforcers for MPSoCs}},
  booktitle =	{Fourth Workshop on Next Generation Real-Time Embedded Systems (NG-RES 2023)},
  pages =	{7:1--7:16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-268-6},
  ISSN =	{2190-6807},
  year =	{2023},
  volume =	{108},
  editor =	{Terraneo, Federico and Cattaneo, Daniele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.NG-RES.2023.7},
  URN =		{urn:nbn:de:0030-drops-177380},
  doi =		{10.4230/OASIcs.NG-RES.2023.7},
  annote =	{Keywords: Verification, Runtime Requirement Enforcement, Reinforcement Learning}
}
Document
Graph Realization of Distance Sets

Authors: Amotz Bar-Noy, David Peleg, Mor Perry, and Dror Rawitz

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
The Distance Realization problem is defined as follows. Given an n × n matrix D of nonnegative integers, interpreted as inter-vertex distances, find an n-vertex weighted or unweighted graph G realizing D, i.e., whose inter-vertex distances satisfy dist_G(i,j) = D_{i,j} for every 1 ≤ i < j ≤ n, or decide that no such realizing graph exists. The problem was studied for general weighted and unweighted graphs, as well as for cases where the realizing graph is restricted to a specific family of graphs (e.g., trees or bipartite graphs). An extension of Distance Realization that was studied in the past is where each entry in the matrix D may contain a range of consecutive permissible values. We refer to this extension as Range Distance Realization (or Range-DR). Restricting each range to at most k values yields the problem k-Range Distance Realization (or k-Range-DR). The current paper introduces a new extension of Distance Realization, in which each entry D_{i,j} of the matrix may contain an arbitrary set of acceptable values for the distance between i and j, for every 1 ≤ i < j ≤ n. We refer to this extension as Set Distance Realization (Set-DR), and to the restricted problem where each entry may contain at most k values as k-Set Distance Realization (or k-Set-DR). We first show that 2-Range-DR is NP-hard for unweighted graphs (implying the same for 2-Set-DR). Next we prove that 2-Set-DR is NP-hard for unweighted and weighted trees. We then explore Set-DR where the realization is restricted to the families of stars, paths, or cycles. For the weighted case, our positive results are that for each of these families there exists a polynomial time algorithm for 2-Set-DR. On the hardness side, we prove that 6-Set-DR is NP-hard for stars and 5-Set-DR is NP-hard for paths and cycles. For the unweighted case, our results are the same, except for the case of unweighted stars, for which k-Set-DR is polynomially solvable for any k.

Cite as

Amotz Bar-Noy, David Peleg, Mor Perry, and Dror Rawitz. Graph Realization of Distance Sets. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{barnoy_et_al:LIPIcs.MFCS.2022.13,
  author =	{Bar-Noy, Amotz and Peleg, David and Perry, Mor and Rawitz, Dror},
  title =	{{Graph Realization of Distance Sets}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.13},
  URN =		{urn:nbn:de:0030-drops-168119},
  doi =		{10.4230/LIPIcs.MFCS.2022.13},
  annote =	{Keywords: Graph Realization, distance realization, network design}
}
Document
Conflict-Free Coloring on Claw-Free Graphs and Interval Graphs

Authors: Sriram Bhyravarapu, Subrahmanyam Kalyanasundaram, and Rogers Mathew

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
A Conflict-Free Open Neighborhood coloring, abbreviated CFON^* coloring, of a graph G = (V,E) using k colors is an assignment of colors from a set of k colors to a subset of vertices of V(G) such that every vertex sees some color exactly once in its open neighborhood. The minimum k for which G has a CFON^* coloring using k colors is called the CFON^* chromatic number of G, denoted by χ_{ON}^*(G). The analogous notion for closed neighborhood is called CFCN^* coloring and the analogous parameter is denoted by χ_{CN}^*(G). The problem of deciding whether a given graph admits a CFON^* (or CFCN^*) coloring that uses k colors is NP-complete. Below, we describe briefly the main results of this paper. - For k ≥ 3, we show that if G is a K_{1,k}-free graph then χ_{ON}^*(G) = O(k²log Δ), where Δ denotes the maximum degree of G. Dębski and Przybyło in [J. Graph Theory, 2021] had shown that if G is a line graph, then χ_{CN}^*(G) = O(log Δ). As an open question, they had asked if their result could be extended to claw-free (K_{1,3}-free) graphs, which are a superclass of line graphs. Since it is known that the CFCN^* chromatic number of a graph is at most twice its CFON^* chromatic number, our result positively answers the open question posed by Dębski and Przybyło. - We show that if the minimum degree of any vertex in G is Ω(Δ/{log^ε Δ}) for some ε ≥ 0, then χ_{ON}^*(G) = O(log^{1+ε}Δ). This is a generalization of the result given by Dębski and Przybyło in the same paper where they showed that if the minimum degree of any vertex in G is Ω(Δ), then χ_{ON}^*(G)= O(logΔ). - We give a polynomial time algorithm to compute χ_{ON}^*(G) for interval graphs G. This answers in positive the open question posed by Reddy [Theoretical Comp. Science, 2018] to determine whether the CFON^* chromatic number can be computed in polynomial time on interval graphs. - We explore biconvex graphs, a subclass of bipartite graphs and give a polynomial time algorithm to compute their CFON^* chromatic number. This is interesting as Abel et al. [SIDMA, 2018] had shown that it is NP-complete to decide whether a planar bipartite graph G has χ_{ON}^*(G) = k where k ∈ {1, 2, 3}.

Cite as

Sriram Bhyravarapu, Subrahmanyam Kalyanasundaram, and Rogers Mathew. Conflict-Free Coloring on Claw-Free Graphs and Interval Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 19:1-19:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{bhyravarapu_et_al:LIPIcs.MFCS.2022.19,
  author =	{Bhyravarapu, Sriram and Kalyanasundaram, Subrahmanyam and Mathew, Rogers},
  title =	{{Conflict-Free Coloring on Claw-Free Graphs and Interval Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{19:1--19:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.19},
  URN =		{urn:nbn:de:0030-drops-168173},
  doi =		{10.4230/LIPIcs.MFCS.2022.19},
  annote =	{Keywords: Conflict-free coloring, Interval graphs, Bipartite graphs, Claw-free graphs}
}
Document
Sample Compression Schemes for Balls in Graphs

Authors: Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
One of the open problems in machine learning is whether any set-family of VC-dimension d admits a sample compression scheme of size O(d). In this paper, we study this problem for balls in graphs. For balls of arbitrary radius r, we design proper sample compression schemes of size 4 for interval graphs, of size 6 for trees of cycles, and of size 22 for cube-free median graphs. We also design approximate sample compression schemes of size 2 for balls of δ-hyperbolic graphs.

Cite as

Jérémie Chalopin, Victor Chepoi, Fionn Mc Inerney, Sébastien Ratel, and Yann Vaxès. Sample Compression Schemes for Balls in Graphs. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chalopin_et_al:LIPIcs.MFCS.2022.31,
  author =	{Chalopin, J\'{e}r\'{e}mie and Chepoi, Victor and Mc Inerney, Fionn and Ratel, S\'{e}bastien and Vax\`{e}s, Yann},
  title =	{{Sample Compression Schemes for Balls in Graphs}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{31:1--31:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.31},
  URN =		{urn:nbn:de:0030-drops-168298},
  doi =		{10.4230/LIPIcs.MFCS.2022.31},
  annote =	{Keywords: Proper Sample Compression Schemes, Balls, Graphs, VC-dimension}
}
Document
On Algorithms Based on Finitely Many Homomorphism Counts

Authors: Yijia Chen, Jörg Flum, Mingjun Liu, and Zhiyang Xun

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
It is well known [L. Lovász, 1967] that up to isomorphism a graph G is determined by the homomorphism counts hom(F, G), i.e., by the number of homomorphisms from F to G where F ranges over all graphs. Moreover, it suffices that F ranges over the graphs with at most as many vertices as G. Thus, in principle, we can answer any query concerning G with only accessing the hom(⋅, G)’s instead of G itself. In this paper, we deal with queries for which there is a hom algorithm, i.e., there are finitely many graphs F₁, …, F_k such that for any graph G whether it is a Yes-instance of the query is already determined by the vector hom^⟶_{F₁, …, F_k}(G): = (hom(F₁, G), …, hom(F_k, G)). We observe that planarity of graphs and 3-colorability of graphs, properties expressible in monadic second-order logic, have no hom algorithm. On the other hand, queries expressible as a Boolean combination of universal sentences in first-order logic FO have a hom algorithm. Even though it is not easy to find FO definable queries without a hom algorithm, we succeed to show this for the non-existence of an isolated vertex, a property expressible by the FO sentence ∀ x∃ y Exy, somehow the "simplest" graph property not definable by a Boolean combination of universal sentences. These results provide a characterization of the prefix classes of first-order logic with the property that each query definable by a sentence of the prefix class has a hom algorithm. For adaptive hom algorithms, i.e., algorithms that might access a hom(F_{i+1}, G) with F_{i+1} depending on hom(F_j, G) for 1 ≤ j ≤ i we show that three homomorphism counts hom(⋅, G) are sufficient and in general necessary to determine the (isomorphism type of) G. In particular, by three adaptive queries we can answer any question on G. Moreover, adaptively accessing two hom(⋅, G)’s is already enough to detect an isolated vertex. In 1993 Chaudhuri and Vardi [S. Chaudhuri and M. Y. Vardi, 1993] showed the analogue of the Lovász Isomorphism Theorem for the right homomorphism vector of a graph G, i.e, the vector of values hom(G,F) where F ranges over all graphs characterizes the isomorphism type of G. We study to what extent our results carry over to the right homomorphism vector.

Cite as

Yijia Chen, Jörg Flum, Mingjun Liu, and Zhiyang Xun. On Algorithms Based on Finitely Many Homomorphism Counts. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{chen_et_al:LIPIcs.MFCS.2022.32,
  author =	{Chen, Yijia and Flum, J\"{o}rg and Liu, Mingjun and Xun, Zhiyang},
  title =	{{On Algorithms Based on Finitely Many Homomorphism Counts}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.32},
  URN =		{urn:nbn:de:0030-drops-168301},
  doi =		{10.4230/LIPIcs.MFCS.2022.32},
  annote =	{Keywords: homomorphism numbers, hom algorithms, adaptive hom algorithms}
}
Document
Countdown μ-Calculus

Authors: Jędrzej Kołodziejski and Bartek Klin

Published in: LIPIcs, Volume 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)


Abstract
We introduce the countdown μ-calculus, an extension of the modal μ-calculus with ordinal approximations of fixpoint operators. In addition to properties definable in the classical calculus, it can express (un)boundedness properties such as the existence of arbitrarily long sequences of specific actions. The standard correspondence with parity games and automata extends to suitably defined countdown games and automata. However, unlike in the classical setting, the scalar fragment is provably weaker than the full vectorial calculus and corresponds to automata satisfying a simple syntactic condition. We establish some facts, in particular decidability of the model checking problem and strictness of the hierarchy induced by the maximal allowed nesting of our new operators.

Cite as

Jędrzej Kołodziejski and Bartek Klin. Countdown μ-Calculus. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{kolodziejski_et_al:LIPIcs.MFCS.2022.64,
  author =	{Ko{\l}odziejski, J\k{e}drzej and Klin, Bartek},
  title =	{{Countdown \mu-Calculus}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{64:1--64:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-256-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{241},
  editor =	{Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.64},
  URN =		{urn:nbn:de:0030-drops-168624},
  doi =		{10.4230/LIPIcs.MFCS.2022.64},
  annote =	{Keywords: countdown \mu-calculus, games, automata}
}
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