Showing papers on "Tree (data structure) published in 1969"

Proving Properties of Programs by Structural Induction

Abstract: This paper discusses the technique of structural induction for proving theorems about programs. This technique is closely related to recursion induction but makes use of the inductive definition of the data structures handled by the programs. It treats programs with recursion but without assignments or jumps. Some syntactic extensions to Landin's functional programming language ISWIM are suggested which make it easier to program the manipulation of data structures and to develop proofs about such programs. Two sample proofs are given to demonstrate the technique, one for a tree sorting algorithm and one for a simple compiler for expressions. (First received April 1968 and in revised form August 1968)

Tree Generating Regular Systems

Abstract: Trees are defined as mappings from tree structures (in the graph-theoretic sense) into sets of symbols. Regular systems are defined in which the production rules are of the form Φ → ψ , where Φ and ψ are trees. An application of a rule involves replacing a subtree Φ by the tree ψ . The main result is that the sets of trees generated by regular systems are exactly those that are accepted by tree automata. This generalizes a theorem of BUchi, proved for strings.

Some studies in machine learning using the game of checkers. II—Recent progress

Abstract: A new signature-table technique is described together with an improved book-learning procedure which is thought to be much superior to the linear polynomial method. Full use is made of the so-called “alpha-beta” pruning and several forms of forward pruning to restrict the spread of the move tree and to permit the program to look ahead to a much greater depth than it otherwise could do. While still unable to outplay checker masters, the program's playing ability has been greatly improved.tplay checker masters, the

On arithmetic expressions and trees

Abstract: A description is given of how a tree representing the evaluation of an arithmetic expression can be drawn in such a way that the number of accumulators needed for the computation can be represented in a straightforward manner. This representation reduces the choice of the best order of computation to a specific problem under the theory of graphs. An algorithm to solve this problem is presented.

Properties of the distance matrix of a tree

Abstract: In a recent paper, Hakimi and Yau [1] have given the necessary and sufficient conditions for a matrix D to be the distance matrix of a linear graph. They also give a computational technique for determining a tree realization if it exists. The purpose of this note is to exhibit certain interesting algebraic properties of the distance matrix of a tree. Two algorithms for tree realization emerge from these properties. However, these algorithms are not elaborated on as there are many computational techniques which are faster than the original method proposed by Hakimi and Yau. Let G be a nonoriented weighted linear graph with n + 1 vertices and m edges, such that the weight assigned to edge i is a positive number . The length of any path from node i to node j is the sum of the weights of the edges in that path; the distance da between nodes i and j is the length of the shortest path from i to j, with dti taken as zero. The matrix whose elements are da is the distance matrix D. This development is limited to graphs which are trees [2], It is convenient to introduce the path matrix of a tree. If an arbitrary vertex r is taken as a reference vertex, then the path matrix P is defined as follows.

Collapsible artificial tree construction adapted for christmas decoration

Abstract: A COLLAPSIBLE ARTIFICIAL TREE CONSTRUCTION PARTICULARLY ADAPTED FOR CHRISTMAS DECORATION IN WHICH SIMULATED BRANCHES ARE FREELY FOLDABLE SUBSTANTIALLY PARALLEL TO THE SIMULATED TREE TRUNK IN ONE DIRECTION AND FREELY PIVOT TO AN UNFOLDED LATERALLY EXTENDING DIRECTION WHEN THE ARTIFICIAL TREE IS TO BE ERECTED AND USED, AND IN WHICH THE BRANCHES FREELY GRAVITATE TO AN UNFOLDED CONDITION WHEREBY INSERTION OF THE TREE TRUNK INTO A TUBULAR CONTAINER AUTOMATICALLY FOLDS THE BRANCHES UPWARDLY AND ALONG THE TRUNK, AND REMOVAL OF THE TREE FROM A TUBULAR CONTAINER RESULTS IN THE BRANCHES BEING AUTOMATICALLY UNFOLDED

Chain saw tree-felling apparatus

Abstract: The present invention pertains to a tree-felling device that is adapted to be mounted on the front of a vehicle and that incorporates a pivotally mounted chain saw. The chain saw is associated with means for assisting the directional felling of the tree.

Unusual lesions of the larynx, trachea and bronchial tree.

Abstract: This paper deals with three unusual problems and demonstrates the necessity for early diagnosis and a definitive course of management. The first problem is the so-called scimitar sign, a bronchovascular syndrome known better to the radiologist, cardiologist and cardiovascular surgeon than to the otolaryngologist. It is of great importance in the differential diagnosis of opacifications of the right chest. The second lesion is that of a hemangioma of the laryngotracheal area and is presented because of the additional use of corticosteroids in possibly reducing the morbidity of this lesion. An attempt is made to clarify the confusing aspects and recommendations of the treatment of this lesion. The third lesion is an anomaly of the airway with a tracheo-pharyngeal communication, a condition difficult to diagnose. It presents all the difficulties an endoscopist may encounter in the treatment of such a rare anomaly.

Directed random generation of sentences

Abstract: The problem of producing sentences of a transformational grammar by using a random generator to create phrase structure trees for input to the lexical insertion and transformational phases is discussed. A purely random generator will produce base trees which will be blocked by the transformations, and which are frequently too long to be of practical interest. A solution is offered in the form of a computer program which allows the user to constrain and direct the generation by the simple but powerful device of restricted subtrees. The program is a directed random generator which accepts as input a subtree with restrictions and produces around it a tree which satisfies the restrictions and is ready for the next phase of the grammar. The underlying linguistic model is that of Noam Chomsky, as presented in Aspects of the Theory of Syntax. The program is written in FORTRAN IV for the IBM 360/67 and is part of a unified computer system for transformational grammar. It is currently being used with several partial grammars of English.

Clinical significance of white bile in the biliary tree.

Abstract: 'White bile' is a clear, colourless, watery fluid found occasionally in the biliary tree proximal to an extrahepatic biliary obstruction. Thus it is neither white nor bilious; and it is not viscid and opaque like the fluid found in the obstructed gall bladder. With the exception of the paper by Judd and Lyons (1923) previous reports on white bile dealt either with a single patient (Edington and McCallum, 1930; Lake, 1934; Flint, 1937; Griffiths, Haber, Rees, and Smith, 1963; Bouchier and Cooperband, 1965), or with several patients (Aronsohn, 1936; Hawthorne and Sterling, 1955), or with experiments carried oult in animals (Rous and McMaster, 1921; McMaster, Broun, and Rous, 1923; Cameron and Oakley, 1932; Aronsohn, 1935; Haber and Rees, 1963). These reports contain certain generalizations about the possible clinical significance of white bile. It could be assumed that it is found most frequently in those obstructions due to stone (Flint, 1937; Hawthorne and Sterling, 1955) or either stone or stricture (Judd and Lyons, 1923); that it will be found only when the gall bladder is either distal to the obstruction or when it is not functioning (Rous and McMaster, 1921; McMaster et al, 1923; Judd and Lyons, 1923; Lake, 1934; Griffith et al, 1963); that it occurs only when there is infection in the fluid (Aronsohn, 1935 and 1936); that total obstruction is always present (Aronsohn, 1936); and that it signifies severe liver damage and a grave immediate prognosis (Flint, 1937). In this paper we report the findings in nine patients admitted to Prince Henry Hospital each with obstructive jaundice and each with clear, colourless, watery fluid in the biliary tree. The findings in these patients have been examined to appraise the clinical significance of finding white bile at operation.

Planting tool for tree seedlings

Abstract: A tool having a punch for forming a hole in the ground and a guide for directing a tree seedling into the hole.

Tree excavating machine

Abstract: A tree digger which, when mounted on the base of a tree, digs a trench inclined from the vertical about same, the distance of the trench from the tree and the depth of the trench being adjustable.

Artificial tree branch of foliage stamped from a ribbon of plastic material

Abstract: The invention is an artificial tree branch made of foliage which is cut or stamped from a broad ribbon of sheet plastic material. The leaves of the branch extend from a supporting strip of the plastic which is supported by a stem, such as a wire, to which the leaf supporting strip is attached.

Fruit workers platform

Abstract: A fruit workers platform includes a support frame which can be moved from tree to tree and at least one working station thereon. Means are provided to dispose the workers at all levels of each tree for picking, pruning, etc.

Procedure and device for felling of timber

Abstract: Timber-felling method according to which the tree is drawn up with its roots by a mechanical device, the tree being first pulled out of the ground in a vertical direction and thereafter prized at an increasing angle thereto.

Adaptive-logic trees for use in multilevel-circuit design

Abstract: A logic tree employing only 2-input gates is described which is capable of mechanising any desired function of the variable set. The tree can therefore represent either a fixed relationship, or vary adaptively by adjusting the input parameters. It is shown that this structure can be used to derive economic multilevel representations of functions directly from the canonical form which require only 2-input gates. The design procedure can operate effectively with only a simple set of design rules.

Double grip pruner

Abstract: A PRUNER COMPRISING TWO SEPARATED SQUEEZE-GRIP OPERATING HANDLES ADAPTED FOR SIMULTANEOUS SQUEEZING-GRIP OPERATION BY BOTH HANDS FOR INCREASING THE CUTTING POWER TRANSMITTED TO THE PRUNER CUTTING JAWS, AND WHICH OPERATING HANDLES ARE IN LONGITUDINALLY SPACED RELATION ALONG THE PRUNER SHAFT TO FACILITATE THE MANEUVERING OF THE JAWS RELATIVELY TO THE BRANCHES OF A TREE, BUSH OR THE LIKE.