Document

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

We investigate the streaming space complexity of word problems for groups. Using so-called distinguishers, we prove a transfer theorem for graph products of groups. Moreover, we use distinguishers to obtain a logspace streaming algorithm for the membership problem in a finitely generated subgroup of a free group.

Markus Lohrey and Julio Xochitemol. Streaming in Graph Products. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 71:1-71:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2024.71, author = {Lohrey, Markus and Xochitemol, Julio}, title = {{Streaming in Graph Products}}, booktitle = {49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)}, pages = {71:1--71:17}, 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.2024.71}, URN = {urn:nbn:de:0030-drops-206271}, doi = {10.4230/LIPIcs.MFCS.2024.71}, annote = {Keywords: word problems for groups, streaming algorithms, graph products} }

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

We prove that it is Π₂^𝖯-complete to verify whether the diameter of a given permutation group G = ⟨A⟩ is bounded by a unary encoded number k. This solves an open problem from a paper of Even and Goldreich, where the problem was shown to be NP-hard. Verifying whether the diameter is exactly k is complete for the class consisting of all intersections of a Π₂^𝖯-language and a Σ₂^𝖯-language. A similar result is shown for the length of a given permutation π, which is the minimal k such that π can be written as a product of at most k generators from A. Even and Goldreich proved that it is NP-complete to verify, whether the length of a given π is at most k (with k given in unary encoding). We show that it is DP-complete to verify whether the length is exactly k. Finally, we deduce from our result on the diameter that it is Π₂^𝖯-complete to check whether a given finite automaton with transitions labelled by permutations from S_n produces all permutations from S_n.

Markus Lohrey and Andreas Rosowski. On the Complexity of Diameter and Related Problems in Permutation Groups. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 134:1-134:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lohrey_et_al:LIPIcs.ICALP.2023.134, author = {Lohrey, Markus and Rosowski, Andreas}, title = {{On the Complexity of Diameter and Related Problems in Permutation Groups}}, booktitle = {50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)}, pages = {134:1--134:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-278-5}, ISSN = {1868-8969}, year = {2023}, volume = {261}, editor = {Etessami, Kousha and Feige, Uriel and Puppis, Gabriele}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.134}, URN = {urn:nbn:de:0030-drops-181864}, doi = {10.4230/LIPIcs.ICALP.2023.134}, annote = {Keywords: algorithms for finite groups, diameter of permutation groups, rational subsets in groups} }

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**Published in:** LIPIcs, Volume 250, 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)

Low-latency sliding window algorithms for regular and context-free languages are studied, where latency refers to the worst-case time spent for a single window update or query. For every regular language L it is shown that there exists a constant-latency solution that supports adding and removing symbols independently on both ends of the window (the so-called two-way variable-size model). We prove that this result extends to all visibly pushdown languages. For deterministic 1-counter languages we present a 𝒪(log n) latency sliding window algorithm for the two-way variable-size model where n refers to the window size. We complement these results with a conditional lower bound: there exists a fixed real-time deterministic context-free language L such that, assuming the OMV (online matrix vector multiplication) conjecture, there is no sliding window algorithm for L with latency n^(1/2-ε) for any ε > 0, even in the most restricted sliding window model (one-way fixed-size model). The above mentioned results all refer to the unit-cost RAM model with logarithmic word size. For regular languages we also present a refined picture using word sizes 𝒪(1), 𝒪(log log n), and 𝒪(log n).

Moses Ganardi, Louis Jachiet, Markus Lohrey, and Thomas Schwentick. Low-Latency Sliding Window Algorithms for Formal Languages. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 38:1-38:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ganardi_et_al:LIPIcs.FSTTCS.2022.38, author = {Ganardi, Moses and Jachiet, Louis and Lohrey, Markus and Schwentick, Thomas}, title = {{Low-Latency Sliding Window Algorithms for Formal Languages}}, booktitle = {42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)}, pages = {38:1--38:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-261-7}, ISSN = {1868-8969}, year = {2022}, volume = {250}, editor = {Dawar, Anuj and Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2022.38}, URN = {urn:nbn:de:0030-drops-174301}, doi = {10.4230/LIPIcs.FSTTCS.2022.38}, annote = {Keywords: Streaming algorithms, regular languages, context-free languages} }

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

We show that the subset sum problem, the knapsack problem and the rational subset membership problem for permutation groups are NP-complete. Concerning the knapsack problem we obtain NP-completeness for every fixed n ≥ 3, where n is the number of permutations in the knapsack equation. In other words: membership in products of three cyclic permutation groups is NP-complete. This sharpens a result of Luks [Eugene M. Luks, 1991], which states NP-completeness of the membership problem for products of three abelian permutation groups. We also consider the context-free membership problem in permutation groups and prove that it is PSPACE-complete but NP-complete for a restricted class of context-free grammars where acyclic derivation trees must have constant Horton-Strahler number. Our upper bounds hold for black box groups. The results for context-free membership problems in permutation groups yield new complexity bounds for various intersection non-emptiness problems for DFAs and a single context-free grammar.

Markus Lohrey, Andreas Rosowski, and Georg Zetzsche. Membership Problems in Finite Groups. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 71:1-71:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2022.71, author = {Lohrey, Markus and Rosowski, Andreas and Zetzsche, Georg}, title = {{Membership Problems in Finite Groups}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {71:1--71:16}, 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.2022.71}, URN = {urn:nbn:de:0030-drops-168694}, doi = {10.4230/LIPIcs.MFCS.2022.71}, annote = {Keywords: algorithms for finite groups, intersection non-emptiness problems, knapsack problems in groups} }

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

We study deterministic and randomized streaming algorithms for word problems of finitely generated groups. For finitely generated linear groups, metabelian groups and free solvable groups we show the existence of randomized streaming algorithms with logarithmic space complexity for their word problems. We also show that the class of finitely generated groups with a logspace randomized streaming algorithm for the word problem is closed under several group theoretical constructions: finite extensions, direct products, free products and wreath products by free abelian groups. We contrast these results with several lower bound. An example of a finitely presented group, where the word problem has only a linear space randomized streaming algorithm, is Thompson’s group F.

Markus Lohrey and Lukas Lück. Streaming Word Problems. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 72:1-72:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2022.72, author = {Lohrey, Markus and L\"{u}ck, Lukas}, title = {{Streaming Word Problems}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {72:1--72:15}, 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.2022.72}, URN = {urn:nbn:de:0030-drops-168707}, doi = {10.4230/LIPIcs.MFCS.2022.72}, annote = {Keywords: word problems for groups, streaming algorithms} }

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**Published in:** LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)

It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time where all group elements are represented by so-called power words, i.e., words of the form p_1^{z_1} p_2^{z_2} ⋯ p_k^{z_k}. Here the p_i are explicit words over the generating set of the group and all z_i are binary encoded integers. As a corollary, it follows that the subgroup membership problem for the matrix group GL(2,ℤ) can be decided in polynomial time when all matrix entries are given in binary notation.

Markus Lohrey. Subgroup Membership in GL(2,Z). In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 51:1-51:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lohrey:LIPIcs.STACS.2021.51, author = {Lohrey, Markus}, title = {{Subgroup Membership in GL(2,Z)}}, booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)}, pages = {51:1--51:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-180-1}, ISSN = {1868-8969}, year = {2021}, volume = {187}, editor = {Bl\"{a}ser, Markus and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.51}, URN = {urn:nbn:de:0030-drops-136961}, doi = {10.4230/LIPIcs.STACS.2021.51}, annote = {Keywords: free groups, virtually free groups, subgroup membership, matrix groups} }

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**Published in:** LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

We prove that the power word problem for the solvable Baumslag-Solitar groups BS(1,q) = ⟨ a,t ∣ t a t^{-1} = a^q ⟩ can be solved in TC⁰. In the power word problem, the input consists of group elements g₁, …, g_d and binary encoded integers n₁, …, n_d and it is asked whether g₁^{n₁} ⋯ g_d^{n_d} = 1 holds. Moreover, we prove that the knapsack problem for BS(1,q) is NP-complete. In the knapsack problem, the input consists of group elements g₁, …, g_d,h and it is asked whether the equation g₁^{x₁} ⋯ g_d^{x_d} = h has a solution in ℕ^d.

Markus Lohrey and Georg Zetzsche. Knapsack and the Power Word Problem in Solvable Baumslag-Solitar Groups. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 67:1-67:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2020.67, author = {Lohrey, Markus and Zetzsche, Georg}, title = {{Knapsack and the Power Word Problem in Solvable Baumslag-Solitar Groups}}, booktitle = {45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)}, pages = {67:1--67:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-159-7}, ISSN = {1868-8969}, year = {2020}, volume = {170}, editor = {Esparza, Javier and Kr\'{a}l', Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.67}, URN = {urn:nbn:de:0030-drops-127364}, doi = {10.4230/LIPIcs.MFCS.2020.67}, annote = {Keywords: computational group theory, matrix problems, Baumslag-Solitar groups} }

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**Published in:** LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

We give lower bounds on the complexity of the word problem of certain non-solvable groups: for a large class of non-solvable infinite groups, including in particular free groups, Grigorchuk’s group and Thompson’s groups, we prove that their word problem is ALOGTIME-hard. For some of these groups (including Grigorchuk’s group and Thompson’s groups) we prove that the circuit value problem (which is equivalent to the circuit evaluation problem) is PSPACE-complete.

Laurent Bartholdi, Michael Figelius, Markus Lohrey, and Armin Weiß. Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 29:1-29:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bartholdi_et_al:LIPIcs.CCC.2020.29, author = {Bartholdi, Laurent and Figelius, Michael and Lohrey, Markus and Wei{\ss}, Armin}, title = {{Groups with ALOGTIME-Hard Word Problems and PSPACE-Complete Circuit Value Problems}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {29:1--29:29}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, 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.CCC.2020.29}, URN = {urn:nbn:de:0030-drops-125814}, doi = {10.4230/LIPIcs.CCC.2020.29}, annote = {Keywords: NC^1-hardness, word problem, G-programs, straight-line programs, non-solvable groups, self-similar groups, Thompson’s groups, Grigorchuk’s group} }

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Track B: Automata, Logic, Semantics, and Theory of Programming

**Published in:** LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable groups. For a finitely generated group we study the so-called power word problem (does a given expression u₁^{k₁} … u_d^{k_d}, where u₁, …, u_d are words over the group generators and k₁, …, k_d are binary encoded integers, evaluate to the group identity?) and knapsack problem (does a given equation u₁^{x₁} … u_d^{x_d} = v, where u₁, …, u_d,v are words over the group generators and x₁,…,x_d are variables, have a solution in the natural numbers). We prove that the power word problem for wreath products of the form G ≀ ℤ with G nilpotent and iterated wreath products of free abelian groups belongs to TC⁰. As an application of the latter, the power word problem for free solvable groups is in TC⁰. On the other hand we show that for wreath products G ≀ ℤ, where G is a so called uniformly strongly efficiently non-solvable group (which form a large subclass of non-solvable groups), the power word problem is coNP-hard. For the knapsack problem we show NP-completeness for iterated wreath products of free abelian groups and hence free solvable groups. Moreover, the knapsack problem for every wreath product G ≀ ℤ, where G is uniformly efficiently non-solvable, is Σ₂^p-hard.

Michael Figelius, Moses Ganardi, Markus Lohrey, and Georg Zetzsche. The Complexity of Knapsack Problems in Wreath Products. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 126:1-126:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{figelius_et_al:LIPIcs.ICALP.2020.126, author = {Figelius, Michael and Ganardi, Moses and Lohrey, Markus and Zetzsche, Georg}, title = {{The Complexity of Knapsack Problems in Wreath Products}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {126:1--126:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-138-2}, ISSN = {1868-8969}, year = {2020}, volume = {168}, editor = {Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.126}, URN = {urn:nbn:de:0030-drops-125339}, doi = {10.4230/LIPIcs.ICALP.2020.126}, annote = {Keywords: algorithmic group theory, knapsack, wreath product} }

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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

We study the problem of recognizing regular languages in a variant of the streaming model of computation, called the sliding window model. In this model, we are given a size of the sliding window n and a stream of symbols. At each time instant, we must decide whether the suffix of length n of the current stream ("the active window") belongs to a given regular language.
Recent works [Moses Ganardi et al., 2018; Moses Ganardi et al., 2016] showed that the space complexity of an optimal deterministic sliding window algorithm for this problem is either constant, logarithmic or linear in the window size n and provided natural language theoretic characterizations of the space complexity classes. Subsequently, [Moses Ganardi et al., 2018] extended this result to randomized algorithms to show that any such algorithm admits either constant, double logarithmic, logarithmic or linear space complexity.
In this work, we make an important step forward and combine the sliding window model with the property testing setting, which results in ultra-efficient algorithms for all regular languages. Informally, a sliding window property tester must accept the active window if it belongs to the language and reject it if it is far from the language. We show that for every regular language, there is a deterministic sliding window property tester that uses logarithmic space and a randomized sliding window property tester with two-sided error that uses constant space.

Moses Ganardi, Danny Hucke, Markus Lohrey, and Tatiana Starikovskaya. Sliding Window Property Testing for Regular Languages. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ganardi_et_al:LIPIcs.ISAAC.2019.6, author = {Ganardi, Moses and Hucke, Danny and Lohrey, Markus and Starikovskaya, Tatiana}, title = {{Sliding Window Property Testing for Regular Languages}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {6:1--6:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.6}, URN = {urn:nbn:de:0030-drops-115023}, doi = {10.4230/LIPIcs.ISAAC.2019.6}, annote = {Keywords: Streaming algorithms, approximation algorithms, regular languages} }

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**Published in:** Dagstuhl Reports, Volume 9, Issue 3 (2019)

Since its early days, combinatorial group theory was deeply interwoven with computability theory. In the last 20 years we have seen many new successful interactions between group theory and computer science. On one hand, groups played an important rule in many developments in complexity theory and automata theory. On the other hand, concepts from these computer science fields as well as efficient algorithms, cryptography, and data compression led to the formulation of new questions in group theory. The Dagstuhl Seminar Algorithmic Problems in Group Theory was aimed at bringing together researchers from group theory and computer science so that they can share their expertise. This report documents the material presented during the course of the seminar.

Volker Diekert, Olga Kharlampovich, Markus Lohrey, and Alexei Myasnikov. Algorithmic Problems in Group Theory (Dagstuhl Seminar 19131). In Dagstuhl Reports, Volume 9, Issue 3, pp. 83-110, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@Article{diekert_et_al:DagRep.9.3.83, author = {Diekert, Volker and Kharlampovich, Olga and Lohrey, Markus and Myasnikov, Alexei}, title = {{Algorithmic Problems in Group Theory (Dagstuhl Seminar 19131)}}, pages = {83--110}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2019}, volume = {9}, number = {3}, editor = {Diekert, Volker and Kharlampovich, Olga and Lohrey, Markus and Myasnikov, Alexei}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.9.3.83}, URN = {urn:nbn:de:0030-drops-112939}, doi = {10.4230/DagRep.9.3.83}, annote = {Keywords: algorithmic group theory; generic-case complexity; circuit complexity; diophantine theories} }

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

In this work we introduce a new succinct variant of the word problem in a finitely generated group G, which we call the power word problem: the input word may contain powers p^x, where p is a finite word over generators of G and x is a binary encoded integer. The power word problem is a restriction of the compressed word problem, where the input word is represented by a straight-line program (i.e., an algebraic circuit over G). The main result of the paper states that the power word problem for a finitely generated free group F is AC^0-Turing-reducible to the word problem for F. Moreover, the following hardness result is shown: For a wreath product G Wr Z, where G is either free of rank at least two or finite non-solvable, the power word problem is complete for coNP. This contrasts with the situation where G is abelian: then the power word problem is shown to be in TC^0.

Markus Lohrey and Armin Weiß. The Power Word Problem. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 43:1-43:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lohrey_et_al:LIPIcs.MFCS.2019.43, author = {Lohrey, Markus and Wei{\ss}, Armin}, title = {{The Power Word Problem}}, booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)}, pages = {43:1--43:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-117-7}, ISSN = {1868-8969}, year = {2019}, volume = {138}, editor = {Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.43}, URN = {urn:nbn:de:0030-drops-109871}, doi = {10.4230/LIPIcs.MFCS.2019.43}, annote = {Keywords: word problem, compressed word problem, free groups} }

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**Published in:** LIPIcs, Volume 126, 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)

We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight-line programs defined over a finite generating set for the group. We prove also that, for any infinite hyperbolic group G, the compressed knapsack problem in G is NP-complete.

Derek Holt, Markus Lohrey, and Saul Schleimer. Compressed Decision Problems in Hyperbolic Groups. In 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 126, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{holt_et_al:LIPIcs.STACS.2019.37, author = {Holt, Derek and Lohrey, Markus and Schleimer, Saul}, title = {{Compressed Decision Problems in Hyperbolic Groups}}, booktitle = {36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)}, pages = {37:1--37:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-100-9}, ISSN = {1868-8969}, year = {2019}, volume = {126}, editor = {Niedermeier, Rolf and Paul, Christophe}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2019.37}, URN = {urn:nbn:de:0030-drops-102766}, doi = {10.4230/LIPIcs.STACS.2019.37}, annote = {Keywords: hyperbolic groups, algorithms for compressed words, circuit evaluation problems} }

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**Published in:** LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

We study the space complexity of sliding window streaming algorithms that check membership of the window content in a fixed context-free language. For regular languages, this complexity is either constant, logarithmic or linear [Moses Ganardi et al., 2016]. We prove that every context-free language whose sliding window space complexity is log_2(n) - omega(1) must be regular and has constant space complexity. Moreover, for every c in N, c >= 1 we construct a (nondeterministic) context-free language whose sliding window space complexity is O(n^(1/c)) \ o(n^(1/c)). Finally, we give an example of a deterministic one-counter language whose sliding window space complexity is Theta((log n)^2).

Moses Ganardi, Artur Jez, and Markus Lohrey. Sliding Windows over Context-Free Languages. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.MFCS.2018.15, author = {Ganardi, Moses and Jez, Artur and Lohrey, Markus}, title = {{Sliding Windows over Context-Free Languages}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {15:1--15:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.15}, URN = {urn:nbn:de:0030-drops-95973}, doi = {10.4230/LIPIcs.MFCS.2018.15}, annote = {Keywords: sliding windows, streaming algorithms, context-free languages} }

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**Published in:** LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)

We study the average size of the minimal directed acyclic graph (DAG) with respect to so-called leaf-centric binary tree sources as studied by Zhang, Yang, and Kieffer. A leaf-centric binary tree source induces for every n >= 2 a probability distribution on all binary trees with n leaves. We generalize a result shown by Flajolet, Gourdon, Martinez and Devroye according to which the average size of the minimal DAG of a binary tree that is produced by the binary search tree model is Theta(n / log n).

Louisa Seelbach Benkner and Markus Lohrey. Average Case Analysis of Leaf-Centric Binary Tree Sources. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{seelbachbenkner_et_al:LIPIcs.MFCS.2018.16, author = {Seelbach Benkner, Louisa and Lohrey, Markus}, title = {{Average Case Analysis of Leaf-Centric Binary Tree Sources}}, booktitle = {43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)}, pages = {16:1--16:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-086-6}, ISSN = {1868-8969}, year = {2018}, volume = {117}, editor = {Potapov, Igor and Spirakis, Paul and Worrell, James}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.16}, URN = {urn:nbn:de:0030-drops-95982}, doi = {10.4230/LIPIcs.MFCS.2018.16}, annote = {Keywords: Directed acylic graphs, average case analysis, tree compression} }

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**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

A sliding window algorithm receives a stream of symbols and has to output at each time instant a certain value which only depends on the last n symbols. If the algorithm is randomized, then at each time instant it produces an incorrect output with probability at most epsilon, which is a constant error bound. This work proposes a more relaxed definition of correctness which is parameterized by the error bound epsilon and the failure ratio phi: a randomized sliding window algorithm is required to err with probability at most epsilon at a portion of 1-phi of all time instants of an input stream. This work continues the investigation of sliding window algorithms for regular languages. In previous works a trichotomy theorem was shown for deterministic algorithms: the optimal space complexity is either constant, logarithmic or linear in the window size. The main results of this paper concerns three natural settings (randomized algorithms with failure ratio zero and randomized/deterministic algorithms with bounded failure ratio) and provide natural language theoretic characterizations of the space complexity classes.

Moses Ganardi, Danny Hucke, and Markus Lohrey. Randomized Sliding Window Algorithms for Regular Languages. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 127:1-127:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.ICALP.2018.127, author = {Ganardi, Moses and Hucke, Danny and Lohrey, Markus}, title = {{Randomized Sliding Window Algorithms for Regular Languages}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {127:1--127:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.127}, URN = {urn:nbn:de:0030-drops-91317}, doi = {10.4230/LIPIcs.ICALP.2018.127}, annote = {Keywords: sliding windows, regular languages, randomized complexity} }

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

In a recent paper we analyzed the space complexity of streaming algorithms whose goal is to decide membership of a sliding window to a fixed language. For the class of regular languages we proved a space trichotomy theorem: for every regular language the optimal space bound is either constant, logarithmic or linear. In this paper we continue this line of research: We present natural characterizations for the constant and logarithmic space classes and establish tight relationships to the concept of language growth. We also analyze the space complexity with respect to automata size and prove almost matching lower and upper bounds. Finally, we consider the decision problem whether a language given by a DFA/NFA admits a sliding window algorithm using logarithmic/constant space.

Moses Ganardi, Danny Hucke, Daniel König, Markus Lohrey, and Konstantinos Mamouras. Automata Theory on Sliding Windows. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.31, author = {Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus and Mamouras, Konstantinos}, title = {{Automata Theory on Sliding Windows}}, booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, pages = {31:1--31:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-062-0}, ISSN = {1868-8969}, year = {2018}, volume = {96}, editor = {Niedermeier, Rolf and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.31}, URN = {urn:nbn:de:0030-drops-84851}, doi = {10.4230/LIPIcs.STACS.2018.31}, annote = {Keywords: regular languages, sliding window algorithms} }

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

In recent years, knapsack problems for (in general non-commutative) groups have attracted attention. In this paper, the knapsack problem for wreath products is studied. It turns out that decidability of knapsack is not preserved under wreath product. On the other hand, the class of knapsack-semilinear groups, where solutions sets of knapsack equations are effectively semilinear, is closed under wreath product. As a consequence, we obtain the decidability of knapsack for free solvable groups. Finally, it is shown that for every non-trivial abelian group G, knapsack (as well as the related subset sum problem)
for the wreath product G \wr Z is NP-complete.

Moses Ganardi, Daniel König, Markus Lohrey, and Georg Zetzsche. Knapsack Problems for Wreath Products. In 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 96, pp. 32:1-32:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2018.32, author = {Ganardi, Moses and K\"{o}nig, Daniel and Lohrey, Markus and Zetzsche, Georg}, title = {{Knapsack Problems for Wreath Products}}, booktitle = {35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)}, pages = {32:1--32:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-062-0}, ISSN = {1868-8969}, year = {2018}, volume = {96}, editor = {Niedermeier, Rolf and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2018.32}, URN = {urn:nbn:de:0030-drops-85201}, doi = {10.4230/LIPIcs.STACS.2018.32}, annote = {Keywords: knapsack, wreath products, decision problems in group theory} }

Document

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

Given finite-state automata (or context-free grammars) A,B over the same alphabet and a Parikh vector p, we study the complexity of deciding whether the number of words in the language of A with Parikh image p is greater than the number of such words in the language of B. Recently, this problem turned out to be tightly related to the cost problem for weighted Markov chains. We classify the complexity according to whether A and B are deterministic, the size of the alphabet, and the encoding of p (binary or unary).

Christoph Haase, Stefan Kiefer, and Markus Lohrey. Counting Problems for Parikh Images. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{haase_et_al:LIPIcs.MFCS.2017.12, author = {Haase, Christoph and Kiefer, Stefan and Lohrey, Markus}, title = {{Counting Problems for Parikh Images}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {12:1--12:13}, 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.2017.12}, URN = {urn:nbn:de:0030-drops-80597}, doi = {10.4230/LIPIcs.MFCS.2017.12}, annote = {Keywords: Parikh images, finite automata, counting problems} }

Document

**Published in:** LIPIcs, Volume 68, 20th International Conference on Database Theory (ICDT 2017)

Many XML documents are data-centric and do not make use of the inherent document order. Can we provide stronger compression for such documents through giving up order? We first consider compression via minimal dags (directed acyclic graphs) and study the worst case ratio of the size of the ordered dag divided by the size of the unordered dag, where the worst case is taken for all trees of size n. We prove that this worst case ratio is n / log n for the edge size and n log log n / log n for the node size. In experiments we compare several known compressors on the original document tree versus on a canonical version obtained by length-lexicographical sorting of subtrees. For some documents this difference is surprisingly large: reverse binary dags can be smaller by a factor of 3.7 and other compressors can be smaller by factors of up to 190.

Markus Lohrey, Sebastian Maneth, and Carl Philipp Reh. Compression of Unordered XML Trees. In 20th International Conference on Database Theory (ICDT 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 68, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{lohrey_et_al:LIPIcs.ICDT.2017.18, author = {Lohrey, Markus and Maneth, Sebastian and Reh, Carl Philipp}, title = {{Compression of Unordered XML Trees}}, booktitle = {20th International Conference on Database Theory (ICDT 2017)}, pages = {18:1--18:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-024-8}, ISSN = {1868-8969}, year = {2017}, volume = {68}, editor = {Benedikt, Michael and Orsi, Giorgio}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2017.18}, URN = {urn:nbn:de:0030-drops-70584}, doi = {10.4230/LIPIcs.ICDT.2017.18}, annote = {Keywords: tree compression, directed acyclic graphs, XML} }

Document

**Published in:** Dagstuhl Reports, Volume 6, Issue 10 (2017)

This report documents the program and the outcomes of Dagstuhl Seminar 16431 "Computation over Compressed Structured Data".

Philip Bille, Markus Lohrey, Sebastian Maneth, and Gonzalo Navarro. Computation over Compressed Structured Data (Dagstuhl Seminar 16431). In Dagstuhl Reports, Volume 6, Issue 10, pp. 99-119, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{bille_et_al:DagRep.6.10.99, author = {Bille, Philip and Lohrey, Markus and Maneth, Sebastian and Navarro, Gonzalo}, title = {{Computation over Compressed Structured Data (Dagstuhl Seminar 16431)}}, pages = {99--119}, journal = {Dagstuhl Reports}, ISSN = {2192-5283}, year = {2017}, volume = {6}, number = {10}, editor = {Bille, Philip and Lohrey, Markus and Maneth, Sebastian and Navarro, Gonzalo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagRep.6.10.99}, URN = {urn:nbn:de:0030-drops-69521}, doi = {10.4230/DagRep.6.10.99}, annote = {Keywords: algorithms on compressed structures, data compression, indexing, straight- line programs} }

Document

**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

The circuit evaluation problem for finite semirings is considered, where semirings are not assumed to have an additive or multiplicative identity. The following dichotomy is shown: If a finite semiring R (i) has a solvable multiplicative semigroup and (ii) does not contain a subsemiring with an additive identity 0 and a multiplicative identity 1 != 0, then its circuit evaluation problem is in the complexity class DET (which is contained in NC^2). In all other cases, the circuit evaluation problem is P-complete.

Moses Ganardi, Danny Hucke, Daniel König, and Markus Lohrey. Circuit Evaluation for Finite Semirings. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 35:1-35:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ganardi_et_al:LIPIcs.STACS.2017.35, author = {Ganardi, Moses and Hucke, Danny and K\"{o}nig, Daniel and Lohrey, Markus}, title = {{Circuit Evaluation for Finite Semirings}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {35:1--35:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.35}, URN = {urn:nbn:de:0030-drops-69978}, doi = {10.4230/LIPIcs.STACS.2017.35}, annote = {Keywords: circuit value problem, finite semirings, circuit complexity} }

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**Published in:** LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Myasnikov et al. have introduced the knapsack problem for arbitrary finitely generated groups. In LohreyZ16 the authors proved that for each graph group, the knapsack problem can be solved in NP. Here, we determine the exact complexity of the problem for every graph group. While the problem is TC^0-complete for complete graphs, it is LogCFL-complete for each (non-complete) transitive forest. For every remaining graph, the problem is NP-complete.

Markus Lohrey and Georg Zetzsche. The Complexity of Knapsack in Graph Groups. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 52:1-52:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{lohrey_et_al:LIPIcs.STACS.2017.52, author = {Lohrey, Markus and Zetzsche, Georg}, title = {{The Complexity of Knapsack in Graph Groups}}, booktitle = {34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)}, pages = {52:1--52:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-028-6}, ISSN = {1868-8969}, year = {2017}, volume = {66}, editor = {Vollmer, Heribert and Vall\'{e}e, Brigitte}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.52}, URN = {urn:nbn:de:0030-drops-69810}, doi = {10.4230/LIPIcs.STACS.2017.52}, annote = {Keywords: knapsack, subset sum, graph groups, decision problems in group theory} }

Document

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

We study the space complexity of querying regular languages over data streams in the sliding window model. The algorithm has to answer at any point of time whether the content of the sliding window belongs to a fixed regular language. A trichotomy is shown: For every regular language the optimal space requirement is either in Theta(n), Theta(log(n)), or constant, where $n$ is the size of the sliding window.

Moses Ganardi, Danny Hucke, and Markus Lohrey. Querying Regular Languages over Sliding Windows. 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. 18:1-18:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ganardi_et_al:LIPIcs.FSTTCS.2016.18, author = {Ganardi, Moses and Hucke, Danny and Lohrey, Markus}, title = {{Querying Regular Languages over Sliding Windows}}, booktitle = {36th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2016)}, pages = {18:1--18:14}, 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.2016.18}, URN = {urn:nbn:de:0030-drops-68539}, doi = {10.4230/LIPIcs.FSTTCS.2016.18}, annote = {Keywords: streaming algorithms, regular languages, space complexity} }

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

In this paper the computational complexity of the (bi)simulation problem over restricted graph classes is studied. For trees given as pointer structures or terms the (bi)simulation problem is complete for logarithmic space or NC^1, respectively. This solves an open problem from Balcázar, Gabarró, and Sántha. We also show that the simulation problem is P-complete even for graphs of bounded path-width.

Moses Ganardi, Stefan Göller, and Markus Lohrey. On the Parallel Complexity of Bisimulation on Finite Systems. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ganardi_et_al:LIPIcs.CSL.2016.12, author = {Ganardi, Moses and G\"{o}ller, Stefan and Lohrey, Markus}, title = {{On the Parallel Complexity of Bisimulation on Finite Systems}}, booktitle = {25th EACSL Annual Conference on Computer Science Logic (CSL 2016)}, pages = {12:1--12:17}, 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.2016.12}, URN = {urn:nbn:de:0030-drops-65522}, doi = {10.4230/LIPIcs.CSL.2016.12}, annote = {Keywords: bisimulation, computational complexity, tree width} }

Document

**Published in:** LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

It is shown that the knapsack problem, which was introduced by Myasnikov et al. for arbitrary finitely generated groups, can be solved in NP for graph groups. This result even holds if the group elements are represented in a compressed form by SLPs, which generalizes the classical NP-completeness result of the integer knapsack problem. We also prove general transfer results: NP-membership of the knapsack problem is passed on to finite extensions, HNN-extensions over finite associated subgroups, and amalgamated products with finite identified subgroups.

Markus Lohrey and Georg Zetzsche. Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{lohrey_et_al:LIPIcs.STACS.2016.50, author = {Lohrey, Markus and Zetzsche, Georg}, title = {{Knapsack in Graph Groups, HNN-Extensions and Amalgamated Products}}, booktitle = {33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)}, pages = {50:1--50:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-001-9}, ISSN = {1868-8969}, year = {2016}, volume = {47}, editor = {Ollinger, Nicolas and Vollmer, Heribert}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.50}, URN = {urn:nbn:de:0030-drops-57512}, doi = {10.4230/LIPIcs.STACS.2016.50}, annote = {Keywords: Graph groups, HNN-extensions, amalgamated products, knapsack} }

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Invited Talk

**Published in:** LIPIcs, Volume 41, 24th EACSL Annual Conference on Computer Science Logic (CSL 2015)

Recent decidability results on the satisfiability problem for temporal logics, in particular LTL, CTL* and ECTL*, with constraints over external structures like the integers with the order or infinite trees are surveyed in this paper.

Claudia Carapelle and Markus Lohrey. Temporal Logics with Local Constraints (Invited Talk). In 24th EACSL Annual Conference on Computer Science Logic (CSL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 41, pp. 2-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{carapelle_et_al:LIPIcs.CSL.2015.2, author = {Carapelle, Claudia and Lohrey, Markus}, title = {{Temporal Logics with Local Constraints}}, booktitle = {24th EACSL Annual Conference on Computer Science Logic (CSL 2015)}, pages = {2--13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-90-3}, ISSN = {1868-8969}, year = {2015}, volume = {41}, editor = {Kreutzer, Stephan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2015.2}, URN = {urn:nbn:de:0030-drops-54465}, doi = {10.4230/LIPIcs.CSL.2015.2}, annote = {Keywords: Temporal logics with constraints, concrete domains, LTL, CTL*, ECTL*} }

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**Published in:** LIPIcs, Volume 29, 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)

It is shown that every tree of size n over a fixed set of sigma different ranked symbols can be decomposed into O(n/log_sigma(n)) = O((n * log(sigma))/ log(n)) many hierarchically defined pieces. Formally, such a hierarchical decomposition has the form of a straight-line linear context-free tree grammar of size O(n/log_sigma(n)), which can be used as a compressed representation of the input tree. This generalizes an analogous result for strings. Previous grammar-based tree compressors were not analyzed for the worst-case size of the computed grammar, except for the top dag of Bille et al., for which only the weaker upper bound of O(n/log^{0.19}(n)) for unranked and unlabelled trees has been derived. The main result is used to show that every arithmetical formula of size n, in which only m <= n different variables occur, can be transformed (in time O(n * log(n)) into an arithmetical circuit of size O((n * log(m))/log(n)) and depth O(log(n)). This refines a classical result of Brent, according to which an arithmetical formula of size n can be transformed into a logarithmic depth circuit of size O(n).

Danny Hucke, Markus Lohrey, and Eric Noeth. Constructing Small Tree Grammars and Small Circuits for Formulas. In 34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 29, pp. 457-468, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{hucke_et_al:LIPIcs.FSTTCS.2014.457, author = {Hucke, Danny and Lohrey, Markus and Noeth, Eric}, title = {{Constructing Small Tree Grammars and Small Circuits for Formulas}}, booktitle = {34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)}, pages = {457--468}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-77-4}, ISSN = {1868-8969}, year = {2014}, volume = {29}, editor = {Raman, Venkatesh and Suresh, S. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2014.457}, URN = {urn:nbn:de:0030-drops-48639}, doi = {10.4230/LIPIcs.FSTTCS.2014.457}, annote = {Keywords: grammar-based compression, tree compression, arithmetical circuits} }

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**Published in:** LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

A simple linear-time algorithm for constructing a linear context-free tree grammar of size O(r^2.g.log(n)) for a given input tree T of size n is presented, where g is the size of a minimal linear context-free tree grammar for T, and r is the maximal rank of symbols in T (which is a constant in many applications). This is the first example of a grammar-based tree compression algorithm with an approximation ratio polynomial in g. The analysis of the algorithm uses an extension of the recompression technique (used in the context of grammar-based string compression) from strings to trees.

Artur Jez and Markus Lohrey. Approximation of smallest linear tree grammar. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 445-457, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{jez_et_al:LIPIcs.STACS.2014.445, author = {Jez, Artur and Lohrey, Markus}, title = {{Approximation of smallest linear tree grammar}}, booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)}, pages = {445--457}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-65-1}, ISSN = {1868-8969}, year = {2014}, volume = {25}, editor = {Mayr, Ernst W. and Portier, Natacha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.445}, URN = {urn:nbn:de:0030-drops-44789}, doi = {10.4230/LIPIcs.STACS.2014.445}, annote = {Keywords: Grammar-based compression, Tree compression, Tree-grammars} }

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**Published in:** LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

A Boolean closed full trio is a class of languages that is closed under the Boolean operations (union, intersection, and complementation) and rational transductions. It is well-known that the regular languages constitute such a Boolean closed full trio. It is shown here that every such language class that contains any non-regular language already includes the whole arithmetical hierarchy (and even the one relative to this language).
A consequence of this result is that aside from the regular languages, no full trio generated by one language is closed under complementation.
Our construction also shows that there is a fixed rational Kripke frame such that assigning an arbitrary non-regular language to some variable allows the definition of any language from the arithmetical hierarchy in the corresponding Kripke structure using multimodal logic.

Markus Lohrey and Georg Zetzsche. On Boolean closed full trios and rational Kripke frames. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 530-541, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{lohrey_et_al:LIPIcs.STACS.2014.530, author = {Lohrey, Markus and Zetzsche, Georg}, title = {{On Boolean closed full trios and rational Kripke frames}}, booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)}, pages = {530--541}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-65-1}, ISSN = {1868-8969}, year = {2014}, volume = {25}, editor = {Mayr, Ernst W. and Portier, Natacha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.530}, URN = {urn:nbn:de:0030-drops-44853}, doi = {10.4230/LIPIcs.STACS.2014.530}, annote = {Keywords: rational transductions, full trios, arithmetical hierarchy, Boolean operations} }

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**Published in:** LIPIcs, Volume 21, 24th International Conference on Rewriting Techniques and Applications (RTA 2013)

We adapt the TreeRePair tree compression algorithm and use it as an intermediate step in proving termination of term rewriting systems. We introduce a cost function that approximates the size of constraint systems that specify compatibility of matrix interpretations. We show how to integrate the compression algorithm with the Dependency Pairs transformation. Experiments show that compression reduces running times of constraint solvers, and thus improves the power of automated termination provers.

Alexander Bau, Markus Lohrey, Eric Nöth, and Johannes Waldmann. Compression of Rewriting Systems for Termination Analysis. In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 97-112, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{bau_et_al:LIPIcs.RTA.2013.97, author = {Bau, Alexander and Lohrey, Markus and N\"{o}th, Eric and Waldmann, Johannes}, title = {{Compression of Rewriting Systems for Termination Analysis}}, booktitle = {24th International Conference on Rewriting Techniques and Applications (RTA 2013)}, pages = {97--112}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-53-8}, ISSN = {1868-8969}, year = {2013}, volume = {21}, editor = {van Raamsdonk, Femke}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2013.97}, URN = {urn:nbn:de:0030-drops-40561}, doi = {10.4230/LIPIcs.RTA.2013.97}, annote = {Keywords: termination of rewriting, matrix interpretations, constraint solving, tree compression} }

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

We prove that the complexity of the uniform first-order theory
of ground tree rewrite graphs is in ATIME(2^{2^{poly(n)}},O(n). Providing a matching lower bound, we show that there is some
fixed ground tree rewrite graph whose first-order theory is hard
for ATIME(2^{2^{poly(n)}},poly(n)) with respect to logspace reductions. Finally, we prove that there exists a fixed ground tree rewrite graph together with a single unary predicate in form of a regular tree language such that the resulting structure has a non-elementary first-order theory.

Stefan Göller and Markus Lohrey. The First-Order Theory of Ground Tree Rewrite Graphs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 13, pp. 276-287, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{goller_et_al:LIPIcs.FSTTCS.2011.276, author = {G\"{o}ller, Stefan and Lohrey, Markus}, title = {{The First-Order Theory of Ground Tree Rewrite Graphs}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011)}, pages = {276--287}, 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.2011.276}, URN = {urn:nbn:de:0030-drops-33220}, doi = {10.4230/LIPIcs.FSTTCS.2011.276}, annote = {Keywords: ground tree rewriting systems, first-order theories, complexity} }

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**Published in:** LIPIcs, Volume 5, 27th International Symposium on Theoretical Aspects of Computer Science (2010)

One-counter processes (OCPs) are pushdown processes which operate only on a unary stack alphabet. We study the computational complexity of model checking computation tree logic ($\CTL$) over OCPs. A $\PSPACE$ upper bound is inherited from the modal $\mu$-calculus for this problem. First, we analyze the periodic behaviour of $\CTL$ over OCPs and derive a model checking algorithm whose running time is exponential only in the number of control locations and a syntactic notion of the formula that we call leftward until depth. Thus, model checking fixed OCPs against $\CTL$ formulas with a fixed leftward until depth is in $\P$. This generalizes a result of the first author, Mayr, and To for the expression complexity of $\CTL$'s fragment $\EF$. Second, we prove that already over some fixed OCP, $\CTL$ model checking is $\PSPACE$-hard. Third, we show that there already exists a fixed $\CTL$ formula for which model checking of OCPs is $\PSPACE$-hard. For the latter, we employ two results from complexity theory: (i) Converting a natural number in Chinese remainder presentation into binary presentation is in logspace-uniform $\NC^1$ and (ii) $\PSPACE$ is $\AC^0$-serializable. We demonstrate that our approach can be used to answer further open questions.

Stefan Göller and Markus Lohrey. Branching-time Model Checking of One-counter Processes. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 405-416, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{goller_et_al:LIPIcs.STACS.2010.2472, author = {G\"{o}ller, Stefan and Lohrey, Markus}, title = {{Branching-time Model Checking of One-counter Processes}}, booktitle = {27th International Symposium on Theoretical Aspects of Computer Science}, pages = {405--416}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-16-3}, ISSN = {1868-8969}, year = {2010}, volume = {5}, editor = {Marion, Jean-Yves and Schwentick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2010.2472}, URN = {urn:nbn:de:0030-drops-24722}, doi = {10.4230/LIPIcs.STACS.2010.2472}, annote = {Keywords: Model checking, computation tree logic, complexity theory} }

Document

**Published in:** LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)

Tight connections between leafs languages and strings compressed
via straight-line programs (SLPs) are established. It is shown
that the compressed membership problem for a language $L$ is complete
for the leaf language class defined by $L$ via logspace machines.
A more difficult variant of the compressed membership problem for
$L$ is shown to be complete for the leaf language class defined
by $L$ via polynomial time machines. As a corollary,
a fixed linear visibly pushdown language with
a PSPACE-complete compressed membership problem is obtained.
For XML languages,
the compressed membership problem is shown to be coNP-complete.

Markus Lohrey. Leaf languages and string compression. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 292-303, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{lohrey:LIPIcs.FSTTCS.2008.1761, author = {Lohrey, Markus}, title = {{Leaf languages and string compression}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science}, pages = {292--303}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-08-8}, ISSN = {1868-8969}, year = {2008}, volume = {2}, editor = {Hariharan, Ramesh and Mukund, Madhavan and Vinay, V}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1761}, URN = {urn:nbn:de:0030-drops-17612}, doi = {10.4230/LIPIcs.FSTTCS.2008.1761}, annote = {Keywords: Leaf languages, string compression, grammar-based compression, complexity theory} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 8261, Structure-Based Compression of Complex Massive Data (2008)

From June 22, 2008 to June 27, 2008 the Dagstuhl Seminar 08261 ``Structure-Based Compression of Complex Massive Data'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
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.

Stefan Böttcher, Markus Lohrey, Sebastian Maneth, and Wojciech Rytter. 08261 Abstracts Collection – Structure-Based Compression of Complex Massive Data. In Structure-Based Compression of Complex Massive Data. Dagstuhl Seminar Proceedings, Volume 8261, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bottcher_et_al:DagSemProc.08261.1, author = {B\"{o}ttcher, Stefan and Lohrey, Markus and Maneth, Sebastian and Rytter, Wojciech}, title = {{08261 Abstracts Collection – Structure-Based Compression of Complex Massive Data}}, booktitle = {Structure-Based Compression of Complex Massive Data}, pages = {1--9}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8261}, editor = {Stefan B\"{o}ttcher and Markus Lohrey and Sebastian Maneth and Wojcieh Rytter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08261.1}, URN = {urn:nbn:de:0030-drops-16948}, doi = {10.4230/DagSemProc.08261.1}, annote = {Keywords: Data compression, algorithms for compressed strings and trees, XML-compression} }

Document

**Published in:** Dagstuhl Seminar Proceedings, Volume 8261, Structure-Based Compression of Complex Massive Data (2008)

From 22nd June to 27th of June 2008, the Dagstuhl Seminar
``08261 Structure-Based Compression of
Complex Massive Data'' took place at the
Conference and Research Center (IBFI) in Dagstuhl.
22 researchers with interests in theory and application
of compression and computation on compressed structures
met to present their current work and to discuss
future directions.

Stefan Böttcher, Markus Lohrey, Sebastian Maneth, and Wojciech Rytter. 08261 Executive Summary – Structure-Based Compression of Complex Massive Data. In Structure-Based Compression of Complex Massive Data. Dagstuhl Seminar Proceedings, Volume 8261, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{bottcher_et_al:DagSemProc.08261.2, author = {B\"{o}ttcher, Stefan and Lohrey, Markus and Maneth, Sebastian and Rytter, Wojciech}, title = {{08261 Executive Summary – Structure-Based Compression of Complex Massive Data}}, booktitle = {Structure-Based Compression of Complex Massive Data}, pages = {1--4}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8261}, editor = {Stefan B\"{o}ttcher and Markus Lohrey and Sebastian Maneth and Wojcieh Rytter}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08261.2}, URN = {urn:nbn:de:0030-drops-16814}, doi = {10.4230/DagSemProc.08261.2}, annote = {Keywords: Compression, Succinct Data Structure, Pattern Matching, Text Search, XML Query} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

From 28.10. to 02.11.2007, the Dagstuhl Seminar 07441 ``Algorithmic-Logical Theory of Infinite Structures'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
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.

Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi. 07441 Abstracts Collection – Algorithmic-Logical Theory of Infinite Structures. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{downey_et_al:DagSemProc.07441.1, author = {Downey, Rod and Khoussainov, Bakhadyr and Kuske, Dietrich and Lohrey, Markus and Vardi, Moshe Y.}, title = {{07441 Abstracts Collection – Algorithmic-Logical Theory of Infinite Structures}}, booktitle = {Algorithmic-Logical Theory of Infinite Structures}, pages = {1--13}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7441}, editor = {Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.1}, URN = {urn:nbn:de:0030-drops-14122}, doi = {10.4230/DagSemProc.07441.1}, annote = {Keywords: Theories of infinite structures , computable model theory and automatic structures , model checking infinite systems} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

One of the important research fields of theoretical and applied
computer science and mathematics is the study of algorithmic, logical
and model theoretic properties of structures and their
interactions. By a structure we mean typical objects that arise in
computer science and mathematics such as data structures, programs,
transition systems, graphs, large databases, XML documents, algebraic
systems including groups, integers, fields, Boolean algebras and so
on.

Rod Downey, Bakhadyr Khoussainov, Dietrich Kuske, Markus Lohrey, and Moshe Y. Vardi. 07441 Summary – Algorithmic-Logical Theory of Infinite Structures. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{downey_et_al:DagSemProc.07441.2, author = {Downey, Rod and Khoussainov, Bakhadyr and Kuske, Dietrich and Lohrey, Markus and Vardi, Moshe Y.}, title = {{07441 Summary – Algorithmic-Logical Theory of Infinite Structures}}, booktitle = {Algorithmic-Logical Theory of Infinite Structures}, pages = {1--2}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7441}, editor = {Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.2}, URN = {urn:nbn:de:0030-drops-14111}, doi = {10.4230/DagSemProc.07441.2}, annote = {Keywords: Theories of infinite structures , computable model theory and automatic structures , model checking infinite systems} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

The word problem for inverse monoids generated by
a set $Gamma$ subject to relations of the form $e=f$, where $e$ and $f$
are both idempotents in the free inverse monoid generated by $Gamma$,
is investigated. It is
shown that for every fixed monoid of this form the word problem
can be solved in polynomial time which solves an open problem of
Margolis and Meakin. For the uniform word problem, where the presentation is
part of the input, EXPTIME-completeness is shown.
For the Cayley-graphs of these
monoids, it is shown that the first-order theory with regular path
predicates is decidable. Regular path predicates allow to state
that there is a path from a node $x$ to a node $y$ that is labeled
with a word from some regular language. As a corollary, the decidability
of the generalized word problem is deduced. Finally, some results
on free partially commutative inverse monoids are presented.

Markus Lohrey. Application of verification techniques to inverse monoids. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{lohrey:DagSemProc.07441.3, author = {Lohrey, Markus}, title = {{Application of verification techniques to inverse monoids}}, booktitle = {Algorithmic-Logical Theory of Infinite Structures}, pages = {1--15}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7441}, editor = {Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.3}, URN = {urn:nbn:de:0030-drops-14109}, doi = {10.4230/DagSemProc.07441.3}, annote = {Keywords: Inverse monoids, word problems, Cayley-graphs, complexity} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7441, Algorithmic-Logical Theory of Infinite Structures (2008)

The logic ICPDL is the expressive extension of Propositional
Dynamic Logic (PDL), which admits intersection and converse
as program operators.
The result of this paper is containment
of ICPDL-satisfiability in $2$EXP, which improves the
previously known non-elementary upper bound and implies
$2$EXP-completeness due to an existing lower bound for PDL with intersection (IPDL). The proof proceeds showing that every satisfiable ICPDL formula has model of tree width at most two. Next, we reduce satisfiability in ICPDL to $omega$-regular tree satisfiability in ICPDL. In the latter problem the set of possible models is restricted to trees of an $omega$-regular tree language. In the final step,$omega$-regular tree satisfiability is reduced the emptiness
problem for alternating two-way automata on infinite trees. In this way, a more elegant proof is obtained for Danecki's difficult result that satisfiability in IPDL is in $2EXP$.

Stefan Göller, Markus Lohrey, and Carsten Lutz. PDL with Intersection and Converse is 2EXP-complete. In Algorithmic-Logical Theory of Infinite Structures. Dagstuhl Seminar Proceedings, Volume 7441, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{goller_et_al:DagSemProc.07441.5, author = {G\"{o}ller, Stefan and Lohrey, Markus and Lutz, Carsten}, title = {{PDL with Intersection and Converse is 2EXP-complete}}, booktitle = {Algorithmic-Logical Theory of Infinite Structures}, pages = {1--17}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {7441}, editor = {Rod Downey and Bakhadyr Khoussainov and Dietrich Kuske and Markus Lohrey and Moshe Y. Vardi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07441.5}, URN = {urn:nbn:de:0030-drops-14093}, doi = {10.4230/DagSemProc.07441.5}, annote = {Keywords: Satisfiability, Propositional Dynamic Logic, Computational Complexity} }

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