We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

This paper addresses the problem of finding an orientation and a minimum radius for directional antennas of a fixed angle placed at the points of a planar set S, that induce a strongly connected communication graph. We consider problem instances in which antenna angles are fixed at 90◦ and 180◦, and establish upper and lower bounds for the minimum radius necessary to guarantee strong connectivi...

Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and character...

We propose two distributed algorithms, one for solving the weight-balance problem and another for solving the bistochastic matrix formation problem, in a distributed system whose components (nodes) can exchange information via interconnection links (edges) that form an arbitrary, possibly directed, strongly connected communication topology (digraph). Both distributed algorithms achieve their go...

The following (solitaire) game is considered: Initially each node of a simple, connected , nite graph contains a nite number of chips. A move consists in ring all nodes with at least as many chips as their degree, where ring a node corresponds to sending one of the node's chips to each one of the node's neighbors. In Bi89] it was conjectured that every parallel chip ring game played on an N nod...

Let D be a strongly connected digraph. The strong distance between two vertices u and v in D, denoted by sdD(u; v) is the minimum size of a strongly connected subdigraph of D containing u and v. The strong eccentricity, se(u), of a vertex u of D, is the strong distance between u and a vertex farthest from u. The minimum strong eccentricity among the vertices of D is the strong radius, srad(D), ...

A subgraph H of an acyclic digraph D is convex if there is no directed path between vertices of H which contains an arc not in H. A digraph D is connected if the underlying undirected graph of D is connected. We construct an algorithm for enumeration of all connected convex subgraphs of a connected acyclic digraph D of order n. The time complexity of the algorithm is O(n · cc(D)), where cc(D) i...

In this paper, we exhibit a sequence of strongly connected aperiodic weakly monotonic automata, whose level increases with the number of states. Mathematics Subject Classification: 20M35, 68Q45, 20M07

Abstract In this paper we prove a characterization for the subclass of nonbalanced TU-games. The result is stated in terms of certain class of cycles of pre-imputations. A cycle is a finite sequence of pre-imputations, where each pair of neighbouring elements are interrelated to each other through a transfer of some amount of utility from members of a certain coalition to the members of the com...

We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertextransitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as...