In this paper X, Y denote non empty sets. Let X be a non empty set. Observe that every membership function of X is real-yielding. Let f , g be real-yielding functions. The predicate f ⊑ g is defined by: (Def. 1) dom f ⊆ dom g and for every set x such that x ∈ dom f holds f(x) ¬ g(x). Let X be a non empty set and let f , g be membership functions of X. Let us observe that f ⊑ g if and only if: (...

Regular model checking is being developed for algorithmic verification of several classes of infinite-state systems whose configurations can be modeled as words over a finite alphabet. Examples include parameterized systems consisting of an arbitrary number of homogeneous finite-state processes connected in a linear or ring-formed topology, and systems that operate on queues, stacks, integers, ...

Computing transitive closure and reachability information in directed graphs is a fundamental graph problem with many applications. The fastest known algorithms run in O(sm) time for computing all nodes reachable from each of 1 <_ s 5 n source nodes, or, using fast matrix multiplication, in O(n2.38) time for computing the transitive closure, where n is the number of nodes and m the number of ed...

It is essential to provide authentication on mobile nodes in group communication to ensure security and privacy. The nodes that are interested in participating in the group communication form Graphs (V, E). In this paper we authenticate the mobile nodes through transitive closure property of the graph in the routing phase of the On Demand Multicast Routing Protocol (ODMRP) that forms Transitive...

The formalism of constraint databases, in which possibly infinite data sets are described by Boolean combinations of polynomial inequality and equality constraints, has its main application area in spatial databases. The standard query language for polynomial constraint databases is first-order logic over the reals. Because of the limited expressive power of this logic with respect to queries t...

To reason effectively about programs it is important to have some version of a transitive closure operator so that we can describe such notions as the set of nodes reachable from a program’s variables. On the other hand, with a few notable exceptions, adding transitive closure to even very tame logics makes them undecidable. In this paper we explore the boundary between decidability and undecid...

Model theoretic syntax is concerned with studying the descriptive complexity of grammar formalisms for natural languages by defining their derivation trees in suitable logical formalisms. The central tool for model theoretic syntax has been monadic second-order logic (MSO). Much of the recent research in this area has been concerned with finding more expressive logics to capture the derivation ...

The purpose of this paper is twofold. First, we review several basic combinatorial problems that have been stated in terms of directed hypergraphs and have been studied in the literature in the framework of different application domains. Among them, transitive closure, transitive reduction, flow and cut problems, and minimum weight traversal problems. For such problems we illustrate some of the...

The canonical standard description logic reasoning service is classification, that is, the generation of the set of atomic subsumptions which are entailed by some ontology. While this consequence relation is well defined and finite, there is significant variance in the composition of that set. For example, it is common (in tools and in discussion) to exclude some tautologies (e.g., A v >, A v A...

In a random n-vertex digraph, each arc is present with probability p, independently of the presence or absence of other arcs. We investigate the structure of the strong components of a random digraph and present an algorithm for the construction of the transitive closure of a random digraph. We show that, when n is large and np is equal to a constant c greater than 1, it is very likely that all...