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

Content Provider	IEEE Xplore Digital Library
Author	Yingxu Wang
Copyright Year	2006
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Calgary Univ., Alta. (Yingxu Wang)
Abstract	The iterative and recursive control structures are the most fundamental mechanisms of computing, because they 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. Although a wide variety of ways have been proposed for describing iterations, there is still a lack of a unified mathematical notation that may be used to express the notion of repetitive, recursive, and predicative behaviors and architectures in computing. This paper 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 realtime process algebra (RTPA) and its supporting tools. A wide range of applications of the big-R notation are identified for rigorously describing iterations and recursions in computing and software engineering. 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
Starting Page	132
Ending Page	140
File Size	1501342
Page Count	9
File Format	PDF
ISBN	1424404754
DOI	10.1109/COGINF.2006.365688
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2006-07-17
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Computer languages Mathematical model Software engineering Computer architecture Algebra Application software Cognitive informatics Drives Modems Linear code formal methods Computing cognitive informatics basic control structures mathematical notations the big-R notation iteration recursion loop syntax semantics RTPA
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Transforming RTPA Mathematical Models of System Behaviors Into C++

Formal Linguistics and the Deductive Grammar

Operational semantics of visual notations (1997).

Specification of the RTPA grammar and its recognition

Elgot algebras † (2006).

Elgot algebras

Formalization of UML Models by RTPA

Formal description of an ATM system by RTPA

Cognitive fit: an empirical study of recursion and iteration

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

Similar Documents

Transforming RTPA Mathematical Models of System Behaviors Into C++

Formal Linguistics and the Deductive Grammar

Operational semantics of visual notations (1997).

Specification of the RTPA grammar and its recognition

Elgot algebras † (2006).

Elgot algebras

Formalization of UML Models by RTPA

Formal description of an ATM system by RTPA

Cognitive fit: an empirical study of recursion and iteration

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