A simple text processing tool which allows positioning of lines within a document is presented using the formal specification language Z. Implementation details such as the use of tab characters and newline sequences ...
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A simple text processing tool which allows positioning of lines within a document is presented using the formal specification language Z. Implementation details such as the use of tab characters and newline sequences are covered. The program has been implemented under the UNIX operating system. It is hoped that the use of similar techniques will become widespread in the field of software engineering.
A specification of the UNIX filing system is presented that uses a notation based on elementary mathematical set theory. The notation involves very few of its own special constructs. The specification is sufficientl...
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A specification of the UNIX filing system is presented that uses a notation based on elementary mathematical set theory. The notation involves very few of its own special constructs. The specification is sufficiently detailed to capture the filing system's behavior at the system call level, yet abstracts from issues of data representation, whether in programs or on the storage medium, and from the description of any algorithms that might be employed to implement the system. The specification is presented in several stages, each new stage building on the previous one; major concepts are introduced separately to make them easily understood. The notation used permits these separate stages to be linked together to provide a complete description of each filing system operation, including its error conditions. Features of the specification are explained as they are used. Appendices.
Two systolic arrays for recursive digital filtering are presented. Both have a rectangular structure and produce output for a particular computation in consecutive cycles. Their performance is analyzed and the design ...
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Two systolic arrays for recursive digital filtering are presented. Both have a rectangular structure and produce output for a particular computation in consecutive cycles. Their performance is analyzed and the design tradeoffs are discussed.
The properties of a set theory, RZF, defined in a logic weaker than intuitionistic logic are investigated, using natural models. RZF is intended to act as a framework for fuzzy set theory, more general and applicable ...
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The properties of a set theory, RZF, defined in a logic weaker than intuitionistic logic are investigated, using natural models. RZF is intended to act as a framework for fuzzy set theory, more general and applicable than Heyting valued structures such as Topoi. The theory RZF contains an interpretation of classical set theory, and is consistent relative to this theory. It is also a suitable theory for the expression of attributes of uncertainty and vagueness, since a certain subclass of the sets definable in this theory are `crisp' or two-valued, and behave classically, whereas sets in general obey only residuated logic, of which the Lukasiewicz semantics on [0, 1], the real interval, is a particular realisation.
Two classes of systolic array for the implementation of recursive digital filters are presented, which overcome some of the limitations of earlier designs. The trade-off resulting from varying the degree of pipelining...
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Two classes of systolic array for the implementation of recursive digital filters are presented, which overcome some of the limitations of earlier designs. The trade-off resulting from varying the degree of pipelining is discussed.
One of the concepts from topology that has found use in image processing is the so called Fundamental group of an image. A definition for the digital fundamental group of a binary picture was introduced by Kong in A d...
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One of the concepts from topology that has found use in image processing is the so called Fundamental group of an image. A definition for the digital fundamental group of a binary picture was introduced by Kong in A digital fundamental group [4]. This paper introduces a fundamental group for greyscale images. We also describe Poincare's classical method for computing a representation of the fundamental group and extend this to work with our greyscale version.
This paper discusses applications of a formal set-theoretic foundation for fuzzy set theory [23] to problems of approximate and uncertain reasoning, and also looks at other formalisms, such as the classical Alternativ...
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This paper discusses applications of a formal set-theoretic foundation for fuzzy set theory [23] to problems of approximate and uncertain reasoning, and also looks at other formalisms, such as the classical Alternative Set Theory 139) and its Intuitionistic version [21, 20] for uncertain reasoning. Formal definitions of these frameworks will be given. Many suggestions for semantic operations on values of formulae involving intermediate truth have been made;[41, 40] contain a survey of these. There are two main problems: how to reconcile the use of the linear order [0, 1] as the value space when in reality degrees of truth are often incomparable, and secondly, within this simplified range of values, to select operations which are both logically coherent with each other and intuitively reasonable. We will derive general semantic constraints on operations which will motivate the formal frameworks that we define.
In image processing, workers sometimes wish to display three dimensional objects on a CRT screen, and so tools for detecting surfaces by computer need to be developed. In recent papers[ D. G. Morgenthaler and A. Rosen...
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In image processing, workers sometimes wish to display three dimensional objects on a CRT screen, and so tools for detecting surfaces by computer need to be developed. In recent papers[ D. G. Morgenthaler and A. Rosenfeld, Information and Control 51 , 1981 , 227–247; G. M. Reed and A. Rosenfeld, submitted for publication; G. M. Reed, Computer Vision, Graphics, and Image Processing 25 , 1984 , 226–235] Morgenthaler, Reed, and Rosenfeld have introduced the concept of a simple surface point of a subset of Z 3 . But simple surface points are defined by means of axioms, and the axioms do not reveal what simple surface points “look like.” In this paper eight of the nine varieties of simple surface points are shown to have natural “continuous analogs,” and the one remaining variety is shown to be very different from the other types. This work yields substantial generalizations of the main theorems on simple surface points that were proved by Morgenthaler, Reed, and Rosenfeld.
We present a very general language for expressing tactic programs. The paper describes some essential tactic combinators (tacticals), and gives them a formal semantics. Those definitions are used to produce a complete...
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We present a very general language for expressing tactic programs. The paper describes some essential tactic combinators (tacticals), and gives them a formal semantics. Those definitions are used to produce a complete calculus for reasoning about tactics written in this language. The language is extended to cover structural combinators which enable the tactics to be precisely targeted upon particular sub-expressions.
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