13 Search Results for "Glasser, Christian"

Document
DOI: 10.4230/LIPIcs.STACS.2026.66
Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

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

Abstract
We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.
Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.112
Lower Bounds Beyond DNF of Parities

Authors: Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract
We consider a subclass of AC⁰[2] circuits that simultaneously captures DNF∘Xor and depth-3 AC⁰ circuits. For this class we show a technique for proving lower bounds inspired by the top-down approach. We give lower bounds for the middle slice function, inner product function, and affine dispersers.
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Artur Riazanov, Anastasia Sofronova, and Dmitry Sokolov. Lower Bounds Beyond DNF of Parities. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 112:1-112:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{riazanov_et_al:LIPIcs.ITCS.2026.112,
  author =	{Riazanov, Artur and Sofronova, Anastasia and Sokolov, Dmitry},
  title =	{{Lower Bounds Beyond DNF of Parities}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{112:1--112:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.112},
  URN =		{urn:nbn:de:0030-drops-253996},
  doi =		{10.4230/LIPIcs.ITCS.2026.112},
  annote =	{Keywords: boolean circuits, top-down, unpredictability}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2025.43
The Complexity of Computing Second Solutions

Authors: Fabian Egidy, Christian Glaßer, and Fynn Godau

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We study the complexity of computing second solutions for NP search problems, i. e., given a problem instance x and a valid solution y, we have to find another valid solution y'. Our main result shows that for typical NP decision problems, the complexity of computing second solutions is completely determined by the choice of the type of solution (i. e., the specific function problem), but independent of the underlying decision problem. More precisely, we show that for every X ∈ NP that is 1-paddable (a weak form of paddability), different choices of the type of solution lead to different second solution problems, which altogether have the same degree structure as the entire class of NP search problems (FNP). In fact, each degree of difficulty within FNP does occur as a second solution problem for X. This proves that typical NP decision problems have no intrinsic complexity w. r. t. the search for a second solution, but only the specification of the type of solution determines this complexity. This explains the empirical observation that the difficulty of computing second solutions strongly depends on the formulation of the problem. Moreover, we show that the complexities of a search problem and its second solution variant are independent in the following sense: For all search problems A and B representing two degrees of difficulty, there exists a search problem C such that 1) C is as difficult as A and 2) computing second solutions for C is as difficult as B.
Cite as

Fabian Egidy, Christian Glaßer, and Fynn Godau. The Complexity of Computing Second Solutions. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 43:1-43:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{egidy_et_al:LIPIcs.MFCS.2025.43,
  author =	{Egidy, Fabian and Gla{\ss}er, Christian and Godau, Fynn},
  title =	{{The Complexity of Computing Second Solutions}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{43:1--43:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.43},
  URN =		{urn:nbn:de:0030-drops-241505},
  doi =		{10.4230/LIPIcs.MFCS.2025.43},
  annote =	{Keywords: function problems, another solution problem, turing machines}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.50
An Oracle with no UP-Complete Sets, but NP = PSPACE

Authors: David Dingel, Fabian Egidy, and Christian Glaßer

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
We construct an oracle relative to which NP = PSPACE, but UP has no many-one complete sets. This combines the properties of an oracle by Hartmanis and Hemachandra [J. Hartmanis and L. A. Hemachandra, 1988] and one by Ogiwara and Hemachandra [Ogiwara and Hemachandra, 1991]. The oracle provides new separations of classical conjectures on optimal proof systems and complete sets in promise classes. This answers several questions by Pudlák [P. Pudlák, 2017], e.g., the implications UP ⟹ CON^𝖭 and SAT ⟹ TFNP are false relative to our oracle. Moreover, the oracle demonstrates that, in principle, it is possible that TFNP-complete problems exist, while at the same time SAT has no p-optimal proof systems.
Cite as

David Dingel, Fabian Egidy, and Christian Glaßer. An Oracle with no UP-Complete Sets, but NP = PSPACE. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 50:1-50:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dingel_et_al:LIPIcs.MFCS.2024.50,
  author =	{Dingel, David and Egidy, Fabian and Gla{\ss}er, Christian},
  title =	{{An Oracle with no UP-Complete Sets, but NP = PSPACE}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{50:1--50:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.50},
  URN =		{urn:nbn:de:0030-drops-206063},
  doi =		{10.4230/LIPIcs.MFCS.2024.50},
  annote =	{Keywords: Computational Complexity, Promise Classes, Complete Sets, Oracle Construction}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.44
Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP

Authors: Fabian Egidy, Christian Glaßer, and Martin Herold

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

Abstract
We study the existence of optimal and p-optimal proof systems for classes in the Boolean hierarchy over NP. Our main results concern DP, i.e., the second level of this hierarchy: - If all sets in DP have p-optimal proof systems, then all sets in coDP have p-optimal proof systems. - The analogous implication for optimal proof systems fails relative to an oracle. As a consequence, we clarify such implications for all classes 𝒞 and 𝒟 in the Boolean hierarchy over NP: either we can prove the implication or show that it fails relative to an oracle. Furthermore, we show that the sets SAT and TAUT have p-optimal proof systems, if and only if all sets in the Boolean hierarchy over NP have p-optimal proof systems which is a new characterization of a conjecture studied by Pudlák.
Cite as

Fabian Egidy, Christian Glaßer, and Martin Herold. Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 44:1-44:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{egidy_et_al:LIPIcs.MFCS.2023.44,
  author =	{Egidy, Fabian and Gla{\ss}er, Christian and Herold, Martin},
  title =	{{Upward Translation of Optimal and P-Optimal Proof Systems in the Boolean Hierarchy over NP}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{44:1--44:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.44},
  URN =		{urn:nbn:de:0030-drops-185784},
  doi =		{10.4230/LIPIcs.MFCS.2023.44},
  annote =	{Keywords: Computational Complexity, Boolean Hierarchy, Proof Complexity, Proof Systems, Oracle Construction}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2022.45
Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP

Authors: Anton Ehrmanntraut, Fabian Egidy, and Christian Glaßer

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

Abstract
We construct an oracle relative to which P = NP ∩ coNP, but there are no many-one complete sets in UP, no many-one complete disjoint NP-pairs, and no many-one complete disjoint coNP-pairs. This contributes to a research program initiated by Pudlák [P. Pudlák, 2017], which studies incompleteness in the finite domain and which mentions the construction of such oracles as open problem. The oracle shows that NP ∩ coNP is indispensable in the list of hypotheses studied by Pudlák. Hence one should consider stronger hypotheses, in order to find a universal one.
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Anton Ehrmanntraut, Fabian Egidy, and Christian Glaßer. Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 45:1-45:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ehrmanntraut_et_al:LIPIcs.MFCS.2022.45,
  author =	{Ehrmanntraut, Anton and Egidy, Fabian and Gla{\ss}er, Christian},
  title =	{{Oracle with P = NP ∩ coNP, but No Many-One Completeness in UP, DisjNP, and DisjCoNP}},
  booktitle =	{47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
  pages =	{45:1--45:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.45},
  URN =		{urn:nbn:de:0030-drops-168435},
  doi =		{10.4230/LIPIcs.MFCS.2022.45},
  annote =	{Keywords: computational complexity, promise classes, proof complexity, complete sets, oracle construction}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.9
NP-Completeness, Proof Systems, and Disjoint NP-Pairs

Authors: Titus Dose and Christian Glaßer

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
The article investigates the relation between three well-known hypotheses. - H_{union}: the union of disjoint ≤^p_m-complete sets for NP is ≤^p_m-complete - H_{opps}: there exist optimal propositional proof systems - H_{cpair}: there exist ≤^{pp}_m-complete disjoint NP-pairs The following results are obtained: - The hypotheses are pairwise independent under relativizable proofs, except for the known implication H_{opps} ⇒ H_{cpair}. - An answer to Pudlák’s question for an oracle relative to which ¬H_{cpair}, ¬H_{opps}, and UP has ≤^p_m-complete sets. - The converse of Köbler, Messner, and Torán’s implication NEE ∩ TALLY ⊆ coNEE ⇒ H_{opps} fails relative to an oracle, where NEE =^{df} NTIME(2^O(2ⁿ)). - New characterizations of H_{union} and two variants in terms of coNP-completeness and p-producibility of the set of hard formulas of propositional proof systems.
Cite as

Titus Dose and Christian Glaßer. NP-Completeness, Proof Systems, and Disjoint NP-Pairs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dose_et_al:LIPIcs.STACS.2020.9,
  author =	{Dose, Titus and Gla{\ss}er, Christian},
  title =	{{NP-Completeness, Proof Systems, and Disjoint NP-Pairs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{9:1--9:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.9},
  URN =		{urn:nbn:de:0030-drops-118707},
  doi =		{10.4230/LIPIcs.STACS.2020.9},
  annote =	{Keywords: NP-complete, propositional proof system, disjoint NP-pair, oracle}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.33
Emptiness Problems for Integer Circuits

Authors: Dominik Barth, Moritz Beck, Titus Dose, Christian Glaßer, Larissa Michler, and Marc Technau

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Abstract
We study the computational complexity of emptiness problems for circuits over sets of natural numbers with the operations union, intersection, complement, addition, and multiplication. For most settings of allowed operations we precisely characterize the complexity in terms of completeness for classes like NL, NP, and PSPACE. The case where intersection, addition, and multiplication is allowed turns out to be equivalent to the complement of polynomial identity testing (PIT). Our results imply the following improvements and insights on problems studied in earlier papers. We improve the bounds for the membership problem MC(\cup,\cap,¯,+,×) studied by McKenzie and Wagner 2007 and for the equivalence problem EQ(\cup,\cap,¯,+,×) studied by Glaßer et al. 2010. Moreover, it turns out that the following problems are equivalent to PIT, which shows that the challenge to improve their bounds is just a reformulation of a major open problem in algebraic computing complexity: 1. membership problem MC(\cap,+,×) studied by McKenzie and Wagner 2007 2. integer membership problems MC_Z(+,×), MC_Z(\cap,+,×) studied by Travers 2006 3. equivalence problem EQ(+,×) studied by Glaßer et al. 2010
Cite as

Dominik Barth, Moritz Beck, Titus Dose, Christian Glaßer, Larissa Michler, and Marc Technau. Emptiness Problems for Integer Circuits. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{barth_et_al:LIPIcs.MFCS.2017.33,
  author =	{Barth, Dominik and Beck, Moritz and Dose, Titus and Gla{\ss}er, Christian and Michler, Larissa and Technau, Marc},
  title =	{{Emptiness Problems for Integer Circuits}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.33},
  URN =		{urn:nbn:de:0030-drops-80641},
  doi =		{10.4230/LIPIcs.MFCS.2017.33},
  annote =	{Keywords: computational complexity, integer expressions, integer circuits, polynomial identity testing}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2011.55
Applications of Discrepancy Theory in Multiobjective Approximation

Authors: Christian Glaßer, Christian Reitwießner, and Maximilian Witek

Published in: LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)

Abstract
We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiablilty problem is 1/2-approximable.
Cite as

Christian Glaßer, Christian Reitwießner, and Maximilian Witek. Applications of Discrepancy Theory in Multiobjective Approximation. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 55-65, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{glaer_et_al:LIPIcs.FSTTCS.2011.55,
  author =	{Gla{\ss}er, Christian and Reitwie{\ss}ner, Christian and Witek, Maximilian},
  title =	{{Applications of Discrepancy Theory in Multiobjective Approximation}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)},
  pages =	{55--65},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-34-7},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{13},
  editor =	{Chakraborty, Supratik and Kumar, Amit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.55},
  URN =		{urn:nbn:de:0030-drops-33233},
  doi =		{10.4230/LIPIcs.FSTTCS.2011.55},
  annote =	{Keywords: Discrepancy Theory, Multiobjective Optimization, Satisfiability, Traveling Salesman}
}
Document
DOI: 10.4230/DagSemProc.10501.1
10501 Abstracts Collection – Advances and Applications of Automata on Words and Trees

Authors: Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas

Published in: Dagstuhl Seminar Proceedings, Volume 10501, Advances and Applications of Automata on Words and Trees (2011)

Abstract
From 12.12.2010 to 17.12.2010, the Dagstuhl Seminar 10501 ``Advances and Applications of Automata on Words and Trees'' was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
Cite as

Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas. 10501 Abstracts Collection – Advances and Applications of Automata on Words and Trees. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{glasser_et_al:DagSemProc.10501.1,
  author =	{Glasser, Christian and Pin, Jean-Eric and Schweikardt, Nicole and Selivanov, Victor and Thomas, Wolfgang},
  title =	{{10501 Abstracts Collection – Advances and Applications of Automata on Words and Trees}},
  booktitle =	{Advances and Applications of Automata on Words and Trees},
  pages =	{1--12},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2011},
  volume =	{10501},
  editor =	{Christian Glasser and Jean-Eric Pin and Nicole Schweikardt and Victor Selivanov and Wolfgang Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10501.1},
  URN =		{urn:nbn:de:0030-drops-31486},
  doi =		{10.4230/DagSemProc.10501.1},
  annote =	{Keywords: Automata theory, logic, verification, data structures, algorithms, complexity, games, infinite games with perfect information, reactive systems, specification and verification, combinatorics, hierarchies and reducibilities}
}
Document
DOI: 10.4230/DagSemProc.10501.2
10501 Executive Summary – Advances and Applications of Automata on Words and Trees

Authors: Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas

Published in: Dagstuhl Seminar Proceedings, Volume 10501, Advances and Applications of Automata on Words and Trees (2011)

Abstract
The aim of the seminar was to discuss and systematize the recent fast progress in automata theory and to identify important directions for future research. For this, the seminar brought together more than 40 researchers from automata theory and related fields of applications. We had 19 talks of 30 minutes and 5 one-hour lectures leaving ample room for discussions. In the following we describe the topics in more detail.
Cite as

Christian Glasser, Jean-Eric Pin, Nicole Schweikardt, Victor Selivanov, and Wolfgang Thomas. 10501 Executive Summary – Advances and Applications of Automata on Words and Trees. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{glasser_et_al:DagSemProc.10501.2,
  author =	{Glasser, Christian and Pin, Jean-Eric and Schweikardt, Nicole and Selivanov, Victor and Thomas, Wolfgang},
  title =	{{10501 Executive Summary – Advances and Applications of Automata on Words and Trees}},
  booktitle =	{Advances and Applications of Automata on Words and Trees},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2011},
  volume =	{10501},
  editor =	{Christian Glasser and Jean-Eric Pin and Nicole Schweikardt and Victor Selivanov and Wolfgang Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10501.2},
  URN =		{urn:nbn:de:0030-drops-31474},
  doi =		{10.4230/DagSemProc.10501.2},
  annote =	{Keywords: Infinite games with perfect information, reactive systems, specification and verification, combinatorics, hierarchies and reducibilities}
}
Document
DOI: 10.4230/DagSemProc.10501.3
Parsing Unary Boolean Grammars Using Online Convolution

Authors: Alexander Okhotin and Christian Reitwießner

Published in: Dagstuhl Seminar Proceedings, Volume 10501, Advances and Applications of Automata on Words and Trees (2011)

Abstract
In contrast to context-free grammars, the extension of these grammars by explicit conjunction, the so-called conjunctive grammars can generate (quite complicated) non-regular languages over a single-letter alphabet (DLT 2007). Given these expressibility results, we study the parsability of Boolean grammars, an extension of context-free grammars by conjunction and negation, over a unary alphabet and show that they can be parsed in time O(|G| log^2(n) M(n)) where M(n) is the time to multiply two n-bit integers. This multiplication algorithm is transformed into a convolution algorithm which in turn is converted to an online convolution algorithm which is used for the parsing.
Cite as

Alexander Okhotin and Christian Reitwießner. Parsing Unary Boolean Grammars Using Online Convolution. In Advances and Applications of Automata on Words and Trees. Dagstuhl Seminar Proceedings, Volume 10501, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{okhotin_et_al:DagSemProc.10501.3,
  author =	{Okhotin, Alexander and Reitwie{\ss}ner, Christian},
  title =	{{Parsing Unary Boolean Grammars Using Online Convolution}},
  booktitle =	{Advances and Applications of Automata on Words and Trees},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2011},
  volume =	{10501},
  editor =	{Christian Glasser and Jean-Eric Pin and Nicole Schweikardt and Victor Selivanov and Wolfgang Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10501.3},
  URN =		{urn:nbn:de:0030-drops-31465},
  doi =		{10.4230/DagSemProc.10501.3},
  annote =	{Keywords: }
}
Document
DOI: 10.4230/LIPIcs.STACS.2008.1355
Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages

Authors: Christian Glasser, Heinz Schmitz, and Victor Selivanov

Published in: LIPIcs, Volume 1, 25th International Symposium on Theoretical Aspects of Computer Science (2008)

Abstract
The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain characterizations for the single levels of these hierarchies and obtain the following results: - The classes of the Boolean hierarchy over level $Sigma_1$ of the dot-depth hierarchy are decidable in $NL$ (previously only the decidability was known). The same remains true if predicates mod $d$ for fixed $d$ are allowed. - If modular predicates for arbitrary $d$ are allowed, then the classes of the Boolean hierarchy over level $Sigma_1$ are decidable. - For the restricted case of a two-letter alphabet, the classes of the Boolean hierarchy over level $Sigma_2$ of the Straubing-Th{'\e}rien hierarchy are decidable in $NL$. This is the first decidability result for this hierarchy. - The membership problems for all mentioned Boolean-hierarchy classes are logspace many-one hard for $NL$. - The membership problems for quasi-aperiodic languages and for $d$-quasi-aperiodic languages are logspace many-one complete for $PSPACE$.
Cite as

Christian Glasser, Heinz Schmitz, and Victor Selivanov. Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 337-348, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{glasser_et_al:LIPIcs.STACS.2008.1355,
  author =	{Glasser, Christian and Schmitz, Heinz and Selivanov, Victor},
  title =	{{Efficient Algorithms for Membership in Boolean Hierarchies of Regular Languages}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{337--348},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Albers, Susanne and Weil, Pascal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2008.1355},
  URN =		{urn:nbn:de:0030-drops-13554},
  doi =		{10.4230/LIPIcs.STACS.2008.1355},
  annote =	{Keywords: Automata and formal languages, computational complexity, dot-depth hierarchy, Boolean hierarchy, decidability, efficient algorithms}
}
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