Suggestions for a method of analyzing binary images using Langlet's parity logic

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Suggestions for a method of analyzing binary images using Langlet's parity logic

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International Conference on APL archive
Proceedings of the 2001 conference on APL: an arrays odyssey table of contents

New Haven, Connecticut

Pages: 115 - 124

Year of Publication: 2001

ISBN:1-58113-419-3

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Author

Stuart Smith

University of Massachusetts Lowell, Lowell, MA

Sponsors

: NY Special Interest Group for the APL Programming Language (the NYC area APL chapter of ACM)
SIGAPL: ACM Special Interest Group on APL Programming Language

Publisher

ACM New York, NY, USA

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ABSTRACT

This paper describes an extension to the system of parity logic operations developed by Gerard Langlet and subsequently elaborated by Michael Zaus. Two operations, A and B, are introduced which can be used both to analyze and to synthesize arbitrary patterns of l's and O's in square Boolean matrices. The A and B operations are, like most of the operations in Langlet's system, completely reversible (i.e., the input to A or B can be exactly reconstructed its output). The B operation is shown to be connected with Langlet's Helical and Cognitive transforms. Manipulations of binary images are used to illustrate the properties of A and B, but no claim made that they have real-world applications at this time. The A and B algorithms, their supporting operations, and the programming examples are in Q'Nial; however, they can be easily translated APL, J, or other may programming language.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Gérard A. Langlet, Building the APL atlas of natural shapes, Proceedings of the international conference on APL, p.134-147, August 15-19, 1993, Toronto, Ontario, Canada
	2	Gérard A. Langlet, Not-equal scan as a matter of faith?, ACM SIGAPL APL Quote Quad, v.23 n.2, p.23-27, Dec., 1992 [doi>10.1145/155919.155923]
	3	Gérard A. Langlet, Towards the ultimate APL-TOE, Proceedings of the international conference on APL, p.118-134, July 06-10, 1992, St. Petersburg, Russia
	4	Michael Zaus. Crisp and Soft Computing with Hypercubical Calculus. New York: Springer Verlag, 1999.