7 Search Results for "Weinert, Alexander"

Document
DOI: 10.4230/LIPIcs.STACS.2026.73
Colouring Probe H-Free Graphs

Authors: Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
The NP-complete problems Colouring and k-Colouring (k ≥ 3) are well studied on H-free graphs, i.e., graphs that do not contain some fixed graph H as an induced subgraph. We research to what extent the known polynomial-time algorithms for H-free graphs can be generalized if we only know some of the edges of the input graph. We do this by considering the classical probe graph model introduced in the early nineties. For a graph H, a partitioned probe H-free graph (G,P,N) consists of a graph G = (V,E), together with a set P ⊆ V of probes and an independent set N = V ⧵ P of non-probes, such that G+F is H-free for some edge set F ⊆ binom(N,2). We show the following: - We fully classify Colouring on partitioned probe H-free graphs and show that the obtained complexity dichotomy differs from the known dichotomy of Colouring for H-free graphs. - We fully classify 3-Colouring on partitioned probe P_t-free graphs: we prove polynomial-time solvability for t ≤ 5 and NP-completeness for t ≥ 6. In contrast, 3-Colouring on P_t-free graphs is known to be polynomial-time solvable for t ≤ 7 and quasi-polynomial-time solvable for t ≥ 8. Our main result is our polynomial-time algorithm for 3-Colouring on partitioned P₅-free graphs. For this result, and also for all our other polynomial-time results, we do not need to know the edge set F; we only need to know its existence. Moreover, the class of probe P₅-free graphs includes not only paths of arbitrary length but even all bipartite graphs and is much richer than the class of P₅-free graphs. The latter is also evidenced by the fact that there exist graph problems, such as Matching Cut, that are known to be polynomial-time solvable for P₅-free graphs but NP-complete for partitioned probe P₅-free graphs. In particular, unlike the class of 3-colourable P₅-free graphs, the class of 3-colourable probe P₅-free graphs has unbounded mim-width. Hence, our polynomial-time result for 3-Colouring for probe P₅-free graphs suggests that there may be another, deeper overarching reason why 3-Colouring is polynomial-time solvable for P₅-free graphs.
Cite as

Daniël Paulusma, Johannes Rauch, and Erik Jan van Leeuwen. Colouring Probe H-Free Graphs. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 73:1-73:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paulusma_et_al:LIPIcs.STACS.2026.73,
  author =	{Paulusma, Dani\"{e}l and Rauch, Johannes and van Leeuwen, Erik Jan},
  title =	{{Colouring Probe H-Free Graphs}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{73:1--73:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.73},
  URN =		{urn:nbn:de:0030-drops-255621},
  doi =		{10.4230/LIPIcs.STACS.2026.73},
  annote =	{Keywords: colouring, probe graph, forbidden induced subgraph, complexity dichotomy}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2025.19
Time for Timed Monitorability

Authors: Thomas M. Grosen, Sean Kauffman, Kim G. Larsen, and Martin Zimmermann

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract
Monitoring is an important part of the verification toolbox, in particular in situations where exhaustive verification using, e.g., model-checking is infeasible. The goal of online monitoring is to determine the satisfaction or violation of a specification during runtime, i.e., based on finite execution prefixes. However, not every specification is amenable to monitoring, e.g., properties for which no finite execution can witness satisfaction or violation. Monitorability is the question of whether a given specification is amenable to monitoring, and has been extensively studied in discrete time. Here, we study the monitorability problem for real-time properties expressed as Timed Automata. For specifications given by deterministic Timed Muller Automata, we prove decidability while we show that the problem is undecidable for specifications given by nondeterministic Timed Büchi automata. Furthermore, we refine monitorability to also determine bounds on the number of events as well as the time that must pass before monitoring the property may yield an informative verdict. We prove that for deterministic Timed Muller automata, such bounds can be effectively computed. In contrast we show that for nondeterministic Timed Büchi automata such bounds are not computable.
Cite as

Thomas M. Grosen, Sean Kauffman, Kim G. Larsen, and Martin Zimmermann. Time for Timed Monitorability. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 19:1-19:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{grosen_et_al:LIPIcs.CONCUR.2025.19,
  author =	{Grosen, Thomas M. and Kauffman, Sean and Larsen, Kim G. and Zimmermann, Martin},
  title =	{{Time for Timed Monitorability}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{19:1--19:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.19},
  URN =		{urn:nbn:de:0030-drops-239690},
  doi =		{10.4230/LIPIcs.CONCUR.2025.19},
  annote =	{Keywords: Monitorability, Monitoring, Timed Automata, MITL}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.34
Synthesizing Optimally Resilient Controllers

Authors: Daniel Neider, Alexander Weinert, and Martin Zimmermann

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Recently, Dallal, Neider, and Tabuada studied a generalization of the classical game-theoretic model used in program synthesis, which additionally accounts for unmodeled intermittent disturbances. In this extended framework, one is interested in computing optimally resilient strategies, i.e., strategies that are resilient against as many disturbances as possible. Dallal, Neider, and Tabuada showed how to compute such strategies for safety specifications. In this work, we compute optimally resilient strategies for a much wider range of winning conditions and show that they do not require more memory than winning strategies in the classical model. Our algorithms only have a polynomial overhead in comparison to the ones computing winning strategies. In particular, for parity conditions optimally resilient strategies are positional and can be computed in quasipolynomial time.
Cite as

Daniel Neider, Alexander Weinert, and Martin Zimmermann. Synthesizing Optimally Resilient Controllers. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 34:1-34:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{neider_et_al:LIPIcs.CSL.2018.34,
  author =	{Neider, Daniel and Weinert, Alexander and Zimmermann, Martin},
  title =	{{Synthesizing Optimally Resilient Controllers}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{34:1--34:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.34},
  URN =		{urn:nbn:de:0030-drops-97010},
  doi =		{10.4230/LIPIcs.CSL.2018.34},
  annote =	{Keywords: Controller Synthesis, Infinite Games, Resilient Strategies, Disturbances}
}
Document
DOI: 10.4230/LIPIcs.CSL.2018.36
Parity Games with Weights

Authors: Sven Schewe, Alexander Weinert, and Martin Zimmermann

Published in: LIPIcs, Volume 119, 27th EACSL Annual Conference on Computer Science Logic (CSL 2018)

Abstract
Quantitative extensions of parity games have recently attracted significant interest. These extensions include parity games with energy and payoff conditions as well as finitary parity games and their generalization to parity games with costs. Finitary parity games enjoy a special status among these extensions, as they offer a native combination of the qualitative and quantitative aspects in infinite games: the quantitative aspect of finitary parity games is a quality measure for the qualitative aspect, as it measures the limit superior of the time it takes to answer an odd color by a larger even one. Finitary parity games have been extended to parity games with costs, where each transition is labelled with a non-negative weight that reflects the costs incurred by taking it. We lift this restriction and consider parity games with costs with arbitrary integer weights. We show that solving such games is in NP cap co-NP, the signature complexity for games of this type. We also show that the protagonist has finite-state winning strategies, and provide tight exponential bounds for the memory he needs to win the game. Naturally, the antagonist may need infinite memory to win. Finally, we present tight bounds on the quality of winning strategies for the protagonist.
Cite as

Sven Schewe, Alexander Weinert, and Martin Zimmermann. Parity Games with Weights. In 27th EACSL Annual Conference on Computer Science Logic (CSL 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 119, pp. 36:1-36:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{schewe_et_al:LIPIcs.CSL.2018.36,
  author =	{Schewe, Sven and Weinert, Alexander and Zimmermann, Martin},
  title =	{{Parity Games with Weights}},
  booktitle =	{27th EACSL Annual Conference on Computer Science Logic (CSL 2018)},
  pages =	{36:1--36:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-088-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{119},
  editor =	{Ghica, Dan R. and Jung, Achim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2018.36},
  URN =		{urn:nbn:de:0030-drops-97037},
  doi =		{10.4230/LIPIcs.CSL.2018.36},
  annote =	{Keywords: Infinite Games, Quantitative Games, Parity Games}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2017.47
VLDL Satisfiability and Model Checking via Tree Automata

Authors: Alexander Weinert

Published in: LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

Abstract
We present novel algorithms solving the satisfiability problem and the model checking problem for Visibly Linear Dynamic Logic (VLDL) in asymptotically optimal time via a reduction to the emptiness problem for tree automata with Büchi acceptance. Since VLDL allows for the specification of important properties of recursive systems, this reduction enables the efficient analysis of such systems. Furthermore, as the problem of tree automata emptiness is well-studied, this reduction enables leveraging the mature algorithms and tools for that problem in order to solve the satisfiability problem and the model checking problem for VLDL.
Cite as

Alexander Weinert. VLDL Satisfiability and Model Checking via Tree Automata. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 47:1-47:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{weinert:LIPIcs.FSTTCS.2017.47,
  author =	{Weinert, Alexander},
  title =	{{VLDL Satisfiability and Model Checking via Tree Automata}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{47:1--47:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Lokam, Satya and Ramanujam, R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.47},
  URN =		{urn:nbn:de:0030-drops-83871},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.47},
  annote =	{Keywords: Visibly Linear Dynamic Logic, Visibly Pushdown Languages, Satisfiability, Model Checking, Tree Automata}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2016.28
Visibly Linear Dynamic Logic

Authors: Alexander Weinert and Martin Zimmermann

Published in: LIPIcs, Volume 65, 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)

Abstract
We introduce Visibly Linear Dynamic Logic (VLDL), which extends Linear Temporal Logic (LTL) by temporal operators that are guarded by visibly pushdown languages over finite words. In VLDL one can, e.g., express that a function resets a variable to its original value after its execution, even in the presence of an unbounded number of intermediate recursive calls. We prove that VLDL describes exactly the omega-visibly pushdown languages. Thus it is strictly more expressive than LTL and able to express recursive properties of programs with unbounded call stacks. The main technical contribution of this work is a translation of VLDL into omega-visibly pushdown automata of exponential size via one-way alternating jumping automata. This translation yields exponential-time algorithms for satisfiability, validity, and model checking. We also show that visibly pushdown games with VLDL winning conditions are solvable in triply-exponential time.We prove all these problems to be complete for their respective complexity classes.
Cite as

Alexander Weinert and Martin Zimmermann. Visibly Linear Dynamic Logic. In 36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 65, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{weinert_et_al:LIPIcs.FSTTCS.2016.28,
  author =	{Weinert, Alexander and Zimmermann, Martin},
  title =	{{Visibly Linear Dynamic Logic}},
  booktitle =	{36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)},
  pages =	{28:1--28:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-027-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{65},
  editor =	{Lal, Akash and Akshay, S. and Saurabh, Saket and Sen, Sandeep},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2016.28},
  URN =		{urn:nbn:de:0030-drops-68639},
  doi =		{10.4230/LIPIcs.FSTTCS.2016.28},
  annote =	{Keywords: Temporal Logic, Visibly Pushdown Languages, Satisfiability, Model Checking, Infinite Games}
}
Document
DOI: 10.4230/LIPIcs.CSL.2016.31
Easy to Win, Hard to Master: Optimal Strategies in Parity Games with Costs

Authors: Alexander Weinert and Martin Zimmermann

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)

Abstract
The winning condition of a parity game with costs requires an arbitrary, but fixed bound on the distance between occurrences of odd colors and the next occurrence of a larger even one. Such games quantitatively extend parity games while retaining most of their attractive properties, i.e, determining the winner is in NP and co-NP and one player has positional winning strategies. We show that the characteristics of parity games with costs are vastly different when asking for strategies realizing the minimal such bound: the solution problem becomes PSPACE-complete and exponential memory is both necessary in general and always sufficient. Thus, playing parity games with costs optimally is harder than just winning them. Moreover, we show that the tradeoff between the memory size and the realized bound is gradual in general.
Cite as

Alexander Weinert and Martin Zimmermann. Easy to Win, Hard to Master: Optimal Strategies in Parity Games with Costs. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{weinert_et_al:LIPIcs.CSL.2016.31,
  author =	{Weinert, Alexander and Zimmermann, Martin},
  title =	{{Easy to Win, Hard to Master: Optimal Strategies in Parity Games with Costs}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.31},
  URN =		{urn:nbn:de:0030-drops-65714},
  doi =		{10.4230/LIPIcs.CSL.2016.31},
  annote =	{Keywords: Parity Games with Costs, Optimal Strategies, Memory Requirements, Tradeoffs}
}
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