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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 bottom-up finite tree automaton over F is defined as a tuple (Q, F, Q f, Δ), where Q is a set of states, F is a ranked alphabet (i.e., an alphabet whose symbols have an associated arity), Q f ⊆ Q is a set of final states, and Δ is a set of transition rules of the form f(q 1 (x 1),...,q n (x n)) → q(f(x 1,...,x n)), for an n-ary f ∈ F, q, q i ∈ Q, and x i variables denoting subtrees.
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; Tree (set theory), a generalization of a well-ordered set ...
In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.
Trees with a single root may be viewed as rooted trees in the sense of graph theory in one of two ways: either as a tree (graph theory) or as a trivially perfect graph. In the first case, the graph is the undirected Hasse diagram of the partially ordered set, and in the second case, the graph is simply the underlying (undirected) graph of the ...
Infinite input: An automaton that accepts infinite words . Such automata are called ω-automata. Tree input: The input may be a tree of symbols instead of sequence of symbols. In this case after reading each symbol, the automaton reads all the successor symbols in the input tree.
The most important basic example of this is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: f: [t[1], ..., t[k]] t: v f A forest f consists of a list of trees, while a tree t consists of a pair of a value v and a forest f (its children). This definition is elegant and easy to work with ...
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;