The supervisory control problem of discrete event systems with temporal logic specifications is studied. The full branching time logic of CTL* is used for expressing specifications of discrete event systems. The control problem of CTL* is reduced to the decision problem of CTL*. A small model theorem for the control of CTL* is obtained. It is shown that the control problem of CTL* (resp., CTL) ...

A modular formalization of the branching time temporal logic CTL∗ is presented. Our formalization subsumes prior formalizations of propositional linear temporal logic (PTL) and computation tree logic (CTL). Moreover, the modularity allows to instantiate our formalization for different formal security models. Validity of axioms and soundness of inference rules in axiomatizations of PTL, UB, CTL,...

Abstract. The fractional perfect b-matching polytope of an undirected graph G is the polytope of all assignments of nonnegative real numbers to the edges of G such that the sum of the numbers over all edges incident to any vertex v is a prescribed nonnegative number bv. General theorems which provide conditions for nonemptiness, give a formula for the dimension, and characterize the vertices, e...

This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Ω(12.52 ) noncrossing spanning trees and Ω(13.61 ) non-crossing forests. This improves the previous lower bounds on the maximum number of non...

We consider monotonicity problems for graph searching games. Variants of these games – defined by the type of moves allowed for the players – have been found to be closely connected to graph decompositions and associated width measures such as pathor tree-width. Of particular interest is the question whether these games are monotone, i.e. whether the cops can catch a robber without ever allowin...

This document proves the problem of finding a minimum cost Steiner Tree covering k terminals with at most p branching nodes (with outdegree greater than 1), in a directed or an undirected planar graph with n nodes, is hard to approximate within a better ratio than n, even when the parameter p is fixed. 1 Theorem Definition 1. In a undirected (resp. directed) tree, a branching node is a node who...

Clustering procedure for the case where instead of a fixed metric one applies a family of metrics is considered. In this case instead of a classification tree one obtains a classification network (a directed acyclic graph with non directed cycles). Relation to Bruhat–Tits buildings is discussed. Dimension of a general cluster system is considered.