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On the Big-R Notation for Describing Iterative and Recursive Behaviors

On the Big-R Notation for Describing Iterative and Recursive Behaviors

Yingxu Wang
Copyright: © 2010 |Pages: 16
ISBN13: 9781605669021|ISBN10: 1605669024|ISBN13 Softcover: 9781616924140|EISBN13: 9781605669038
DOI: 10.4018/978-1-60566-902-1.ch015
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MLA

Wang, Yingxu. "On the Big-R Notation for Describing Iterative and Recursive Behaviors." Discoveries and Breakthroughs in Cognitive Informatics and Natural Intelligence, edited by Yingxu Wang, IGI Global, 2010, pp. 292-307. https://doi.org/10.4018/978-1-60566-902-1.ch015

APA

Wang, Y. (2010). On the Big-R Notation for Describing Iterative and Recursive Behaviors. In Y. Wang (Ed.), Discoveries and Breakthroughs in Cognitive Informatics and Natural Intelligence (pp. 292-307). IGI Global. https://doi.org/10.4018/978-1-60566-902-1.ch015

Chicago

Wang, Yingxu. "On the Big-R Notation for Describing Iterative and Recursive Behaviors." In Discoveries and Breakthroughs in Cognitive Informatics and Natural Intelligence, edited by Yingxu Wang, 292-307. Hershey, PA: IGI Global, 2010. https://doi.org/10.4018/978-1-60566-902-1.ch015

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Abstract

Iterative and recursive control structures are the most fundamental mechanisms of computing that make programming more effective and expressive. However, these constructs are perhaps the most diverse and confusable instructions in programming languages at both syntactic and semantic levels. This article introduces the big-R notation that provides a unifying mathematical treatment of iterations and recursions in computing. Mathematical models of iterations and recursions are developed using logical inductions. Based on the mathematical model of the big-R notation, fundamental properties of iterative and recursive behaviors of software are comparatively analyzed. The big-R notation has been adopted and implemented in Real-Time Process Algebra (RTPA) and its supporting tools. Case studies demonstrate that a convenient notation may dramatically reduce the difficulty and complexity in expressing a frequently used and highly recurring concept and notion in computing and software engineering.

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