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In graph theory, reachability refers to the ability to get from one vertex to another within a graph. A vertex s {\displaystyle s} can reach a vertex t {\displaystyle t} (and t {\displaystyle t} is reachable from s {\displaystyle s} ) if there exists a sequence of adjacent vertices (i.e. a walk ) which starts with s {\displaystyle s} and ends ...
The reachability problem consists of attaining a final situation from an initial situation. Reachability is a fundamental problem which can be formulated as follows: Given a computational system with a set of allowed rules or transformations, decide whether a certain state of a system is reachable from a given initial state of the system.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. If each strongly connected component is contracted to a single vertex, the resulting graph is a directed acyclic graph, the condensation of G.
A Petri net (graph) is called (structurally) bounded if it is bounded for every possible initial marking. A Petri net is bounded if and only if its reachability graph is finite. Boundedness is decidable by looking at covering, by constructing the Karp–Miller Tree. It can be useful to explicitly impose a bound on places in a given net.
The transitive closure of the adjacency relation of a directed acyclic graph (DAG) is the reachability relation of the DAG and a strict partial order. A cluster graph, the transitive closure of an undirected graph. The transitive closure of an undirected graph produces a cluster graph, a disjoint union of cliques.
The television term “pilot” is likely inspired by the aviation industry, given it's the first time a show lifts off or "airs." Like an airline pilot operating a plane, these episodes steer ...
Reachability analysis was introduced in a paper of 1978 for the analysis and verification of communication protocols. [1] This paper was inspired by a paper by Bartlett et al. of 1968 [2] which presented the alternating bit protocol using finite-state modeling of the protocol entities, and also pointed out that a similar protocol described earlier had a design flaw.