Related papers: On two Algorithmic Problems about Synchronizing Au…
In this paper, we will find a pseudopolynomial algorithm to solve $Qm \mid \mid L_{\max}$ and then we will prove that it is impossible to get any constant-factor approximation in polynomial time, and thus also impossible to have a PTAS for…
In 1964 \v{C}ern\'{y} conjectured that each $n$-state synchronizing automaton posesses a reset word of length at most $(n-1)^2$. From the other side the best known upper bound on the reset length (minimum length of reset words) is cubic in…
We approach the task of computing a carefully synchronizing word of optimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experiments demonstrate that this…
We consider the problem of minimising the number of states in a multiplicity tree automaton over the field of rational numbers. We give a minimisation algorithm that runs in polynomial time assuming unit-cost arithmetic. We also show that a…
We consider the problem of determining the existence of a sequence of matrices driving a discrete-time consensus system to consensus. We transform this problem into one of the existence of a product of the transition (stochastic) matrices…
In this paper, we work on the notion of k-synchronizability: a system is k-synchronizable if any of its executions, up to reordering causally independent actions, can be divided into a succession of k-bounded interaction phases. We show two…
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
Two topics are presented: synchronization games and synchronization costs. In a synchronization game on a deterministic finite automaton, there are two players, Alice and Bob, whose moves alternate. Alice wants to synchronize the given…
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focus on developing…
A deterministic finite automaton is said to be synchronizing if it has a reset word, i.e. a word that brings all states of the automaton to a particular one. We prove that it is a PSPACE-complete problem to check whether the language of…
The Windows Scheduling Problem, also known as the Pinwheel Problem, is to schedule periodic jobs subject to their processing frequency demands. Instances are given as a set of jobs that have to be processed infinitely often such that the…
The synchronization problem is investigated for the class of locally strongly transitive automata introduced in a previous work of the authors. Some extensions of this problem related to the notions of stable set and word of minimal rank of…
We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be…
We present a few classes of synchronizing automata exhibiting certain extremal properties with regard to synchronization. The first is a series of automata with subsets whose shortest extending words are of length $\varTheta(n^2)$, where…
We present a new series of examples of binary slowly synchronizing automata with sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
We have improved an algorithm generating synchronizing automata with a large length of the shortest reset words. This has been done by refining some known results concerning bounds on the reset length. Our improvements make possible to…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
We introduce two generalizations of synchronizability to automata with transitions weighted in an arbitrary semiring K=(K,+,*,0,1). (or equivalently, to finite sets of matrices in K^nxn.) Let us call a matrix A location-synchronizing if…