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We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…
Complementation and determinization are two fundamental notions in automata theory. The close relationship between the two has been well observed in the literature. In the case of nondeterministic finite automata on finite words (NFA),…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
We introduce the class of tree constraint automata with data values in Z (equipped with the less than relation and equality predicates to constants) and we show that the nonemptiness problem is ExpTime-complete. Using an automata-based…
We consider the problems of maintaining an approximate maximum matching and an approximate minimum vertex cover in a dynamic graph undergoing a sequence of edge insertions/deletions. Starting with the seminal work of Onak and Rubinfeld…
Sorting is a fundamental algorithmic pre-processing technique which often allows to represent data more compactly and, at the same time, speeds up search queries on it. In this paper, we focus on the well-studied problem of sorting and…
A synchronizing word of a deterministic finite complete automaton is a word whose action maps every state to a single one. Finding a shortest or a short synchronizing word is a central computational problem in the theory of synchronizing…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
The purpose of the present study is to search one-dimensional Cellular Automata (CA) rules which will solve the density classification task (DCT) perfectly. The mathematical analysis of number conserving functions over binary strings of…
The work presents some new algorithms realized recently in the package TESTAS. They decide whether or not deterministic finite automaton (DFA) is synchronizing, several procedures find relatively short synchronizing words and a…
This paper investigates the (quasi-)periodicity of a string when the string is edited. A string $C$ is called a cover (as known as a quasi-period) of a string $T$ if each character of $T$ lies within some occurrence of $C$. By definition, a…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
In the stochastic submodular cover problem, the goal is to select a subset of stochastic items of minimum expected cost to cover a submodular function. Solutions in this setting correspond to sequential decision processes that select items…
Given a non-invertible dynamical system with a transfer operator, we show there is a minimal cover with a transfer operator that preserves continuous functions. We also introduce an essential cover with even stronger continuity properties.…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…
Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…
We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation of the constrained problem. Then…
We study the algorithmic problem of optimally covering a tree with $k$ mobile robots. The tree is known to all robots, and our goal is to assign a walk to each robot in such a way that the union of these walks covers the whole tree. We…
We develop deterministic approximation algorithms for the minimum dominating set problem in the CONGEST model with an almost optimal approximation guarantee. For $\epsilon>1/{\text{{poly}}}\log \Delta$ we obtain two algorithms with…