In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) which need to be removed to disconnect the remaining nodes from each other. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its robustness as a network.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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St-connectivity
In computer science and computational complexity theory, st-connectivity or STCON is a decision problem asking, for vertices s and t in a directed graph, if t is reachable from s. Formally, the decision problem is given by PATH = {¿D, s, t¿ | D is a directed graph with a path from vertex s to t}.
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SL (complexity)
In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t connectivity), which is the problem of determining whether there exists a path between two vertices in an undirected graph, otherwise described as the problem of determining whether two vertices are in the same connected component. This problem is also called the undirected reachability problem.
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Non-deterministic Turing machine
In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers. In essence, a Turing machine is imagined to be a simple computer that reads and writes symbols one at a time on an endless tape by strictly following a set of rules. It determines what action it should perform next according to its internal "state" and what symbol it currently sees.
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Avi Wigderson
Avi Wigderson is an Israeli mathematician and computer scientist, a professor of mathematics at the Institute for Advanced Study in Princeton. His research interests include complexity theory, parallel algorithms, graph theory, cryptography, distributed computing, and neural networks.
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L (complexity)
In computational complexity theory, L (also known as LSPACE) is the complexity class containing decision problems which can be solved by a deterministic Turing machine using a logarithmic amount of memory space. Logarithmic space is sufficient to hold a constant number of pointers into the input and a logarithmic number of boolean flags and many basic logspace algorithms use the memory in this way.
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DSPACE
In computational complexity theory, DSPACE or SPACE is the computational resource describing the resource of memory space for a deterministic Turing machine. It represents the total amount of memory space that a "normal" physical computer would need to solve a given computational problem with a given algorithm.
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