Kensei Tsuchida

Optimal Attribute-Efficient Learning of Disjunction, Parity and Threshold Functions

Decision trees are a very general computation model. Here the problem is to identify a Boolean function f out of a given set of Boolean functions F by asking for the value of f at adaptively chosen inputs. For classes F consisting of functions which may be obtained from one function g on n inputs by replacing arbitrary n−k inputs by given constants this problem is known as attribute-efficient learning with k essential attributes. Results on general classes of functions are known. More precise and often optimal results are presented for the cases where g is one of the functions disjunction, parity or threshold.

Hierarchical program diagram editor based on attribute graph grammar

The hierarchical program diagram editor is a tool for visual program environments. We propose a model of a syntax-directed diagram editor using an attribute graph grammar We formalize and define editor commands by using productions of the attribute graph grammar which defines the hierarchical program diagram. This guarantees that any diagram that is grammatically correct can be generated and that there will be no syntax errors in the program generation and editing processes with the editor. We have implemented our editor based on the editor command definitions. The system is the first practical program diagram editor supporting complete syntax-directed commands and efficient automatic layouts by using attribute graph grammars. The methods should be applicable to development environments for various tree-structured diagrams.

Ridge Detection with the Steepest Ascent Method

We propose a new method to detect ridges from digital elevation map (DEM) data. We call it “the steepest ascent method” which is based on steepest ascent lines obtained by selecting the maximum inclined direction from eight neighbors. Then ridge lines are extracted by their steepest ascent lines on a surface. In this paper it is shown that our method is able to detect ridge lines sharply. Besides we claim that our algorithm is simple and suitable for huge area such as the entire area of Japan. Finally, we give the ridge detected terrain map of the entire area of Japan and Korea by applying “the steepest ascent method”.

An NCE context-sensitive graph grammar for visual design languages

An NCE context-sensitive graph grammar, that is, a context-sensitive graph grammar with neighborhood controlled embedding has been developed. It is an expansion of the well-known NCE (context-free) graph grammar. Because it has a quite general embedding mechanism, it can be used to formalize the graph-syntax rules of visual objects with much flexibility. The composition of its production copies is discussed. It is theoretically and practically significant for defining graph-rewriting rules that can be (re)used to embed sub-graphs of particular structures, such as the feedback structure of control systems and the frequently-used sub-diagrams of program diagrams. The confluence property of NCE context-sensitive graph grammars is also studied. This property maintains that the result of a derivation does not depend on the order in which the production copies were applied. This is very important for guaranteeing the validity of the application of composite production copies and for developing efficient parsing algorithms. This formalization of subgraph reuse on, the basis of composite production copies is widely applicable to visual design languages based on graph grammars.

Block diagram generation and parsing based on graph grammar

A block diagram is a graphical model with which it is possible to concisely visualize a system structure and is widely used in control engineering and other fields. However, there are few studies that try to formulate a syntax of block diagrams. In this research, we define a block diagram grammar which generates block diagrams by means of subgraph rewriting of a graph grammar. It includes some context-sensitive productions and is very concise. We have also developed a parser based on this block diagram grammar that parses a diagram in a bottom-up parallel method. It decides whether a diagram is valid for the grammar or not, and returns a production instance sequence for a valid diagram.

Identification of partial disjunction, parity, and threshold functions

Let F be a class of functions obtained by replacing some inputs of a Boolean function of a fixed type with some constants. The problem considered in this paper, which is called attribute efficient learning, is to identify “efficiently” a Boolean function g out of F by asking for the value of g at chosen inputs, where “efficiency” is measured in terms of the number of essential variables. We study the query complexity of attribute-efficient learning for three function classes that are, respectively, obtained from disjunction, parity, and threshold functions. In many cases, we obtain almost optimal upper and lower bound on the number of queries.

8k-ary Grid graph models of tabular forms

Tabular forms are commonly used in software. Those tabular forms are represented as rectangular dissections. In rectangular dissections, ruled line oriented operations such as cell merge, line and column operations are often used. With respect to ruled line oriented operations, 8k-ary grid graphs have been introduced as models of rectangular dissections that provide fast algorithms. This paper surveys octal and hexa-decimal grid graph models of rectangular dissections. First, octal grids, called octgrids, for single layer rectangular dissections and related algorithms are introduced. Next, hexa-decimal grid graphs for multiple layer rectangular dissections, called hexadeci-grids, and related algorithms are introduced. Furthermore, tetraicosa-grid graphs for rectangular solid dissections for CG applications, called tetraicosa-grids and related algorithms are introduced.

Multi-input/multi-output block diagram grammar

A multi-input/multi-output block diagram grammar for a block diagram with multiple inputs and/or multiple outputs is formalized in terms of a context-sensitive graph grammar. This grammar is defined by adding to the single-input, single-output block diagram grammar we proposed previously dummy nodes and new productions for dealing with multiple inputs and/or multiple outputs. A parser based on the multi-input/multi-output block diagram grammar is also implemented; it uses a bottom-up parallel algorithm to parse diagrams with multiple inputs and/or multiple outputs. The block diagram grammar defined in this paper makes a fundamental and important formal model for system analysis and design using block diagrams on a computer.

Block diagram grammar and structure recognition based on graph rewriting

A block diagram grammar is presented that is a formal model generating block diagrams. It is formalized as a context-sensitive graph grammar with subgraph rewriting based on subgraph isomorphism. We implement a block diagram parser that decides whether a diagram is valid for the block diagram grammar in a bottomup-parallel method, and that returns the production instance sequence for a valid diagram. A function of structure recognition is also implemented into the parser by means of template matching and subgraph rewriting. This enables the parser to find and return the structure information of series connections, parallel connections, feedback connections and so forth, in the parsed diagram.

Generation of UML package diagrams based on an attribute graph grammar

Abstract Graphical representations are often used in software design and development because of their expressiveness. So far, various graphical program description languages have been reported. The Unified Modeling Language (UML), developed for modeling in software development was proposed recently, and in 2005 was standardized as the ISO/IEC 19501 standard. Some tools for drawing UML diagrams have been proposed in recent years. However, it is hard for developers to draw UML diagrams using the UML tool because diagram layouts generally should be manually adjusted. Of course, there are tools that can automatically provide layout diagrams, though, sometimes such functions provide unexpected layouts. In order to automate the drawing of these graphical representations aesthetically, a syntax for program diagrams must first be defined. We propose a framework for specifying these diagrams using a graph grammar, and a syntax-directed editor based on the graph grammar.