Theory of Computing Systems

We study the expressive power of polynomial recursive sequences, a nonlinear extension of the well-known class of linear recursive sequences. These sequences arise naturally in the study of nonlinear extensions of weighted automata, where (non)...

We show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A max-plus tree automaton is a weighted tree automaton over the max-plus semiring. A max-plus tree automaton is called finitely ambiguous if ...

For quadratic word equations, there exists an algorithm based on rewriting rules which generates a directed graph describing all solutions to the equation. For regular word equations – those for which each variable occurs at most once on each side ...

The study of the complexity of the equation satisfiability problem in finite groups had been initiated by Goldmann and Russell in (Inf. Comput. 178(1), 253–262, 2002) where they showed that this problem is in P for nilpotent groups while it is NP-...

We study the problem of computing an approximate maximum cardinality matching in the semi-streaming model when edges arrive in a random order. In the semi-streaming model, the edges of the input graph $G=(V,E)$ are given as a stream $e_1,\dots ,e_m$, and the ...$$$$$$$\frac{\mathrm{}}{\mathrm{}}$$\mathrm{}$${}^{\mathrm{}}$$$$\frac{\mathrm{}}{\mathrm{}}$$\mathrm{}$$\frac{\mathrm{}}{\mathrm{}}$$\mathrm{}$$\frac{\mathrm{}}{\mathrm{}}\mathrm{}$$$$\mathrm{}\frac{\mathrm{}}{}$$\mathrm{}$${}^{\mathrm{}\mathrm{}\mathrm{}}$$\mathrm{}\mathrm{}\mathrm{}$

In the well known planted clique problem, a clique (or alternatively, an independent set) of size k is planted at random in an Erdos-Renyi random G(n, p) graph, and the goal is to design an algorithm that finds the maximum clique (or independent ...$\sqrt{}$$\frac{\mathrm{}}{\mathrm{}}$$\frac{}{\mathrm{}}$${}^{\frac{\mathrm{}}{\mathrm{}}}$

We give a randomized algorithm that finds a minimum cut in an undirected weighted m-edge n-vertex graph G with high probability in $O(m{log}^{2}n)$ time. This is the first improvement to Karger’s celebrated $O(m{log}^{3}n)$ time algorithm from 1996. Our main ...$$

We study the complexity of the Distributed Constraint Satisfaction Problem (DCSP) on a synchronous, anonymous network from a theoretical standpoint. In this setting, variables and constraints are controlled by agents which communicate with each ...

For a size parameter $s:\mathbb{\mathbb{N}}\to \mathbb{\mathbb{N}}$, the Minimum Circuit Size Problem (denoted by MCSP[s(n)]) is the problem of deciding whether the minimum circuit size of a given function f : {0,1}ⁿ →{0,1} (represented by a string of length N := 2ⁿ) is at most a ...${\mathrm{}}^{{}_{\mathrm{}}}$${\mathrm{}}^{{}_{\mathrm{}}}$${}^{\mathrm{}}$${}^{\mathrm{}\left(\mathrm{}\right)}$$\stackrel{}{}\sqrt{}$${\mathrm{}}^{\stackrel{}{\mathrm{}}}$

Parametric timed automata (PTA) have been introduced by Alur, Henzinger, and Vardi as an extension of timed automata in which clocks can be compared against parameters. The reachability problem asks for the existence of an assignment of the ...

In k-Digraph Coloring we are given a digraph and are asked to partition its vertices into at most k sets, so that each set induces a DAG. This well-known problem is NP-hard, as it generalizes (undirected) k-Coloring, but becomes trivial if the ...${}^{}{\sqrt[\mathrm{}]{\mathrm{}}}^{}$

We present a data structure that, given a graph G of n vertices and m edges, and a suitable pair of nested r-divisions of G, preprocesses G in $O(m+n)$ time and handles any series of edge-deletions in O(m) total time while answering queries to ...

We provide a polynomial-time algorithm for b-Coloring on graphs of constant clique-width. This unifies and extends nearly all previously known polynomial time results on graph classes, and answers open questions posed by Campos and Silva (...$\mathsf{}$$$

It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all group elements are represented by so-called power words, i.e., words of the form $p_1^{z_1}{p}_2^{z_2}\cdots p_k^{z_k}$. Here the $p_i$ are explicit words ...${}_{}$$\mathsf{}\mathrm{}\mathbb{}$$\mathsf{}\mathrm{}\mathbb{}$$\mathsf{}\mathrm{}\mathbb{}$