Related papers: O(1) Reversible Tree Navigation Without Cycles
A circular program creates a data structure whose computation depends upon itself or refers to itself. The technique is used to implement the classic data structures circular and doubly-linked lists, threaded trees and queues, in a…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a…
Context-free languages can be characterized in several ways. This article studies projective linearisations of languages of simple dependency trees, i.e., dependency trees in which a node can govern at most one node with a given syntactic…
Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for…
An orientable sequence of order $n$ is a cyclic binary sequence such that each length-$n$ substring appears at most once \emph{in either direction}. Maximal length orientable sequences are known only for $n\leq 7$, and a trivial upper bound…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
Operator precedence languages (OPL) enjoy the local parsability property, which essentially means that a code fragment enclosed within a pair of markers -- playing the role of parentheses -- can be compiled with no knowledge of its external…
We describe here a simple application of rational trees to the implementation of an interpreter for a procedural language written in a logic programming language. This is possible in languages designed to support rational trees (such as…
We solve the problem of designing an O(1) time algorithm for generating adjacent multiset combinations in a different approach from Walsh. By the word adjacent, we mean that two adjacent multiset combinations are different at two places by…
We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any…
We consider a temporal logic EF+F^-1 for unranked, unordered finite trees. The logic has two operators: EF\phi, which says "in some proper descendant \phi holds", and F^-1\phi, which says "in some proper ancestor \phi holds". We present an…
We present a new algorithm for iterating over all permutations of a sequence. The algorithm leverages elementary~$O(1)$ operations on recursive lists. As a result, no new nodes are allocated during the computation. Instead, all elements are…
We show how a few modifications to the red-black trees allow for $O(1)$ worst-case update time (once the position of the inserted or deleted element is known). The resulting structure is based on relaxing some of the properties of the…
In this paper we propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks (causal trees and polytrees). In the conventional algorithms, new evidence in absorbed in time…
We use the recently developed theory of forest algebras to find algebraic characterizations of the languages of unranked trees and forests definable in various logics. These include the temporal logics CTL and EF, and first-order logic over…
We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of…
The recursion operators and symmetries of non-autonomous, (1+1)-dimensional integrable evolution equations are considered. It has been previously observed that the symmetries of the integrable evolution equations obtained through their…
LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…