Generalized symbolic trajectory evaluation (GSTE) is an extension of symbolic trajectory evaluation (STE). In GSTE, assertion graphs are used to specify properties in a special form of regular automata with antecedent and consequent pairs. This paper presents a new model characterization, called maximal models, for an assertion graph with important properties. Besides their own theoretical sign...

We consider the maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition or deletion of edges. When the set of edges in a graph changes, we are interested in knowing the change in the set of maximal bicliques (the “change”), rather than in knowing the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to ...

We consider incremental maintenance of maximal bicliques from a dynamic bipartite graph that changes over time due to the addition of edges. When new edges are added to the graph, we seek to enumerate the change in the set of maximal bicliques, without enumerating the set of maximal bicliques that remain unaffected. The challenge in an efficient algorithm is to enumerate the change without expl...

It is shown that matrices over algebraically closed fields that are farthest apart in the commuting graph must be non-derogatory. Rank-one matrices and diagonalizable matrices are also characterized in terms of the commuting graph.

Consider a family of sets and a single set, called query set. How can one quickly find a member of the family which has a maximal intersection with the query set? Strict time constraints on the query and on a possible preprocessing of the set family make this problem challenging. Such maximal intersection queries arise in a wide range of applications, including web search, recommendation system...

A graph is hamiltonian if it has a hamiltonian cycle. It is well-known that Tutte proved that any 4connected planar graph is hamiltonian. It is also well-known that the problem of determining whether a 3-connected planar graph is hamiltonian is NP-complete. In particular, Chvátal and Wigderson had independently shown that the problem of determining whether a maximal planar graph is hamiltonian ...

Generating all configurations that satisfy a given specification is a well-studied problem in Combinatorics and in Graph theory suggesting many interesting problems. Among them, generating all maximal independent sets of a given graph is one that has attracted considerable attention [3,4,7]. A maximal independent set of a graph G = (V,E) is a subset V ′ ⊆ V such that no two vertices in V ′ are ...

the rings considered in this article are commutative with identity $1neq 0$. by a proper ideal of a ring $r$,  we mean an ideal $i$ of $r$ such that $ineq r$.  we say that a proper ideal $i$ of a ring $r$ is a  maximal non-prime ideal if $i$ is not a prime ideal of $r$ but any proper ideal $a$ of $r$ with $ isubseteq a$ and $ineq a$ is a prime ideal. that is, among all the proper ideals of $r$,...

Abstract In this article we introduce a simple tool to derive polynomial upper bounds for the probability of observing unusually large maximal components in some models random graphs when considered at criticality. Specifically, apply our method model intersection graph, graph obtained through p -bond percolation on general d -regular and an inhomogeneous graph.

A potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph. It is known that if these objects can be listed in polynomial time for a class of graphs, the treewidth and the minimum 5ll-in are polynomially tractable for these graphs. We show here that the potential maximal cliques of a graph can be generated in polynomial time i...