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In computer science and mathematical logic, an infinite-tree automaton is a state machine that deals with infinite tree structures.It can be seen as an extension of top-down finite-tree automata to infinite trees or as an extension of infinite-word automata to infinite trees.
A tree is called fully infinite if all its paths are infinite. Given an alphabet Σ, a Σ-labeled tree is a pair (T,V), where T is a tree and V: T → Σ maps each node of T to a symbol in Σ. A labeled tree formally defines a commonly used term tree structure. A set of labeled trees is called a tree language. A tree is called ordered if there ...
For infinite trees, simple algorithms often fail this. For example, given a binary tree of infinite depth, a depth-first search will go down one side (by convention the left side) of the tree, never visiting the rest, and indeed an in-order or post-order traversal will never visit any nodes, as it has not reached a leaf (and in fact never will ...
A tree whose root node has two subtrees, both of which are full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level (the level of a node defined as the number of edges or links from the root node to a node). [18] A perfect binary tree is a full ...
Infinite tree may refer to: Tree (data structure), a data structure simulating a single-rooted, directed hierarchy (due to the requirement of computer-implementability, only rational trees rather than arbitrary infinite trees are admitted) Tree (graph theory), a connected undirected graph without simple cycles
Such an automaton is called a tree automaton. Infinite tree input : The two extensions above can be combined, so the automaton reads a tree structure with (in)finite branches. Such an automaton is called an infinite tree automaton. States
Interpreting graphs topologically as one-dimensional simplicial complexes, the simply connected infinite tree is the universal cover of the Cayley graph; and the kernel of the mapping is the fundamental group of the Cayley graph. Part of a Cayley graph of the Heisenberg group. (The coloring is only for visual aid.)
Pages in category "Trees (data structures)" The following 122 pages are in this category, out of 122 total. ... Infinite-tree automaton; Internal node; K. K-d tree;