Markus Lohrey
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Parameterized Complexity of Factorization Problems Open
We study the parameterized complexity of the following factorization problem: given elements $a,a_1, \ldots, a_m$ of a monoid and a parameter $k$, can $a$ be written as the product of at most (or exactly) $k$ elements from $a_1, \ldots, a_…
FO-Query Enumeration over SLP-Compressed Structures of Bounded Degree Open
Enumerating the result set of a first-order query over a relational structure of bounded degree can be done with linear preprocessing and constant delay. In this work, we extend this result towards the compressed perspective where the stru…
Streaming algorithms for products of probabilities Open
We consider streaming algorithms for approximating a product of input probabilities up to multiplicative error of $1-ε$. It is shown that every randomized streaming algorithm for this problem needs space $Ω(\log n + \log b - \log ε) - \mat…
Regular Languages in the Sliding Window Model Open
We study the space complexity of the following problem: For a fixed regular language $L$, we receive a stream of symbols and want to test membership of a sliding window of size $n$ in $L$. For deterministic streaming algorithms we prove a …
Finding cycle types in permutation groups with few generators Open
The problem whether a given permutation group contains a permutation with a given cycle type is studied. This problem is known to be NP-complete. In this paper it is shown that the problem can be solved in logspace for a cyclic permutation…
Compressed decision problems in hyperbolic groups Open
We prove that, for any hyperbolic group, the compressed word and the compressed conjugacy problems are solvable in polynomial time. As a consequence, the word problem for the (outer) automorphism group of a hyperbolic group is solvable in …
Regular Languages in the Sliding Window Model Open
We study the space complexity of the following problem: For a fixed regular language $L$, we receive a stream of symbols and want to test membership of a sliding window of size $n$ in $L$. For deterministic streaming algorithms we prove a …
Streaming in Graph Products Open
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 f…
Parameterized Complexity of Factorization Problems Open
We study the parameterized complexity of the following factorization problem: given elements $a,a_1, \ldots, a_m$ of a monoid and a parameter $k$, can $a$ be written as the product of at most (or exactly) $k$ elements from $a_1, \ldots, a_…
Exponent equations in HNN-extensions Open
We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been inten…
Exponent equations in HNN-extensions Open
We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been inten…
Exponent equations in HNN-extensions Open
We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been inten…
Low-Latency Sliding Window Algorithms for Formal Languages Open
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…
Exponent equations in HNN-extensions Open
We consider exponent equations in finitely generated groups. These are equations, where the variables appear as exponents of group elements and take values from the natural numbers. Solvability of such (systems of) equations has been inten…
Deciding Emptiness for Constraint Automata on Strings with the Prefix and Suffix Order Open
We study constraint automata that accept data languages on finite string values. Each transition of the automaton is labelled with a constraint restricting the string value at the current and the next position of the data word in terms of …
Membership Problems in Finite Groups Open
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 nu…
Low-Latency Sliding Window Algorithms for Formal Languages Open
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 c…
Entropy Bounds for Grammar-Based Tree Compressors Open
The definition of $k^{th}$-order empirical entropy of strings is extended to node labelled binary trees. A suitable binary encoding of tree straight-line programs (that have been used for grammar-based tree compression before) is shown to …
Complexity of word problems for HNN-extensions Open
The computational complexity of the word problem in HNN-extension of groups is studied. HNN-extension is a fundamental construction in combinatorial group theory. It is shown that the word problem for an ascending HNN-extension of a group …
Balancing Straight-line Programs Open
We show that a context-free grammar of size that produces a single string of length (such a grammar is also called a string straight-line program) can be transformed in linear time into a context-free grammar for of size , whose unique der…
Subgroup Membership in GL(2,Z) Open
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 Smallest Grammar Problem Revisited Open
In a seminal paper of Charikar et al. on the smallest grammar problem, the authors derive upper and lower bounds on the approximation ratios for several grammar-based compressors, but in all cases there is a gap between the lower and upper…
Derandomization for Sliding Window Algorithms with Strict Correctness∗ Open
In the sliding window streaming model the goal is to compute an output value that only depends on the last n symbols from the data stream. Thereby, only space sublinear in the window size n should be used. Quite often randomization is used…
The complexity of knapsack problems in wreath products Open
We prove new complexity results for computational problems in certain wreath products of groups and (as an application) for free solvable group. For a finitely generated group we study the so-called power word problem (does a given express…
Knapsack in metabelian Baumslag-Solitar groups Open
In this note, we show that the knapsack problem is decidable in Baumslag-Solitar groups $\mathrm{BS}(1,q)$ for $q\ge 2$.
Knapsack and the power word problem in solvable Baumslag-Solitar groups Open
We prove that the power word problem for certain metabelian subgroups of $\mathsf{GL}(2,\mathbb{C})$ (including the solvable Baumslag-Solitar groups $\mathsf{BS}(1,q) = \langle a,t \mid t a t^{-1} = a^q \rangle$) belongs to the circuit com…
Knapsack and the Power Word Problem in Solvable Baumslag-Solitar Groups Open
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…