The labels of internal (non-leaf ) nodes are referred to as tags, whose purpose is to describe those data elements.
Using Tree Automata and Regular Expressions to Manipulate Hierarchically Structured Data
However it is easy to see that xr,i is independent of α if the node (r, i) is a leaf of the tree.
Potts Model On Random Trees
The node v of the diagram Σ is called a leaf of the diagram Σ, if v belongs to exactly one edge of Σ.
On simple ideal hyperbolic Coxeter polytopes
Furthermore, since ΣW is a parabolic diagram of order n > 5, one of the nodes u and v of the double edge uv is a leaf.
On simple ideal hyperbolic Coxeter polytopes
In Random-Turn AND-OR, the player who wins the coin toss sets the bit at a leaf node.
Random-Turn Hex and other selection games
We respectively call nodes v2 and v1 right and left children of v . A node without children is called a leaf.
An example of generalized Schur operators involving planar binary trees
These equations can be easily solved, for a given initial satisfying assignment σ, noting that the messages from the leaf variable nodes i satisfy the boundary condition ~ni→a (σi ) = ~o(σi ), where we deﬁne [~o(σ)]τ = I(σ 6= τ ).
On the freezing of variables in random constraint satisfaction problems
Example 2.11 Let K = Kk (∃path ) be the set of all trees in ∆Mk such that all the nodes along at least one path from the root to a leaf are labeled 1n (for appropriate values of n).
Algebraic characterization of logically defined tree languages
Then (t, λ) satisﬁes QK x · hϕn in if and only if there exists a root-to-leaf path such that, for every node v ∈ NV(t) along this path, (t, λv ) |= ϕn (x) (where n is the rank of v).
Algebraic characterization of logically defined tree languages
If x ∈ Z but y 6∈ Z, we let ϕ′ = true or false depending whether the node of U where x occurs in an ancestor of the (k1 + 1)-st variable leaf.
Algebraic characterization of logically defined tree languages
The ob ject of our study was to ﬁnd what happens when we constrain to connected graphs only. A simple argument indicated that correlations would appear: a neighbor of a node with degree one (leaf ) must have its degree greater than 1; otherwise, they would form a separate connected component.
Correlations in connected random graphs
Proposition 3.1: Given BL and Fmax, there exists an optimal solution of BLOCK-ALL that can be represented as a pruned subtree of LCP-tree(BL) with: the same root, up to Fmax leaves, and non-leaf nodes having exactly two children.
Optimal Filtering of Malicious IP Sources
The same argument recursively applies to descendant nodes, until either we reach a leaf node, or we have only one ﬁlter available.
Optimal Filtering of Malicious IP Sources
We note that since any LCP-tree is also a binary tree, there are at most log(N ) predecessors of any leaf node, thus the above procedure requires O(log(N )Fmax ) operations.
Optimal Filtering of Malicious IP Sources
Suppose that at each inner node (i.e., node that is not a leaf ) a total ordering of its children is given.
Note: Random-to-front shuffles on trees
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