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Proceedings ArticleDOI

Some new properties of lists and a framework of a list theoretic relation model

26 Oct 2012-pp 165-170
TL;DR: The design of a list theory based relational database model using position function approach is proposed and how query processing can be realized for the relational algebraic operation of 'Selection' on it, using the 'filter' operation is illustrated.
Abstract: The concept of list is of very much importance in the field of computer science as a data structure [6] and in programming languages like LISP [7]. The concept was redefined by Jena, Tripathy and Ghosh [10] in 2001, in an attempt to introduce it as an extension of the concept of characteristic function for sets and count function for multisets. Since then, many concepts related to list theory have been introduced from the new angle and many properties are established ([11], [12] and [13]). In this paper, we continue this effort and define three new concepts of filter, zip* and indexlist. We establish many properties of these notions. Particularly, the concept of filter is of enough importance and interest. It has many applications in array manipulation in data structure [1, 4, 8] and query realization from databases [5, 14]. We propose the design of a list theory based relational database model using position function approach and illustrate how query processing can be realized for the relational algebraic operation of 'Selection' on it, using the 'filter' operation.
Citations
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Book ChapterDOI
01 Jan 2013
TL;DR: Another application of the concept of position function to define lists is provided in defining data structures like Stack, Queue and Array to the context of fuzzy lists and intuitionistic fuzzy lists.
Abstract: Following the approach of defining a set through its characteristic function and a multiset (bag) through its count function, Tripathy, Ghosh and Jena ([3]) introduced the concept of position function to define lists. The new definition has much rigor than the earlier one used in computer science in general and functional programming ([2]) in particular. Several of the concepts in the form of operations, operators and properties have been established in a sequence of papers by Tripathy and his coauthors ([3, 6, 7, 8]. Also, the concepts of fuzzy lists ([4]) and that of intuitionistic fuzzy lists ([5]) have been defined and studied by them. Recently an application to develop list theoretic relational databases and operations on them has been put forth by Tripathy and Gantayat ([9]). In the present article we provide another application of this approach in defining data structures like Stack, Queue and Array. One of the major advantages of this approach is the ease in extending all the concepts for basic lists to the context of fuzzy lists and intuitionistic fuzzy lists. We also illustrate this approach in the present paper.

1 citations


Cites background or methods from "Some new properties of lists and a ..."

  • ...Recently, as an application of the new definition of lists, a framework of relational data model and some operations on it have been defined by Tripathy et al ([9])....

    [...]

  • ...INSERT(15, 4, A) = take(4 - 1, A) ╫ [15] ╫ drop(4 -1, A) = take(3, A) ╫ [15] ╫ drop(3, A) = [1, 5, 3] ╫ [15] ╫ [1, 6, 8, 9] = [1, 5, 3, 15, 1, 6, 8, 9] (iv) To find the next and previous element at the position i = 4: NEXT( 4, A) = hd(take(5, A) – take (4, A))...

    [...]

  • ...The notions of fuzzy bags and fuzzy lists were not considered in literature before these were defined by Tripathy et al [4]....

    [...]

  • ...2 Deletion Operation (i) Deletion from the beginning: B-DELETE(A) = tl(A) = tl [1, 5, 3, 1, 6, 8, 9] = [5, 3, 1, 6, 8, 9] (ii) Deletion from the end: E-DELETE(A) = init(A)...

    [...]

  • ...Recently an application to develop list theoretic relational databases and operations on them has been put forth by Tripathy and Gantayat ([9])....

    [...]

Book ChapterDOI
01 Jan 2014
TL;DR: In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations.
Abstract: The concept of list is very important in functional programming and data structures in computer science. The classical definition of lists was redefined by Jena, Tripathy, and Ghosh (2001) by using the notion of position functions, which is an extension of the concept of count function of multisets and of characteristic function of sets. Several concepts related to lists have been defined from this new angle and properties are proved further in subsequent articles. In this chapter, the authors focus on crisp lists and present all the concepts and properties developed so far. Recently, the functional approach to realization of relational databases and realization of operations on them has been proposed. In this chapter, a list theory-based relational database model using position function approach is designed to illustrate how query processing can be realized for some of the relational algebraic operations. The authors also develop a list theoretic relational algebra (LRA) and realize analysis of Petri nets using this LRA.

1 citations

Journal ArticleDOI
TL;DR: The notions of fuzzy lists and intuitionistic fuzzy lists are new and least attended concepts and the works in this paper opens a new application area to develop fuzzy and intuitionistically fuzzy data structures.
Abstract: The concept of a set can be defined through its characteristic function and that of a bag is defined through the count function. Following this approach, Tripathy, Ghosh and Jena introduced the concept of position function to define lists. The new definition has much rigor than the earlier one used in computer science in general and functional programming ([2]) in particular. Several of the concepts in the form of operations, operators and properties have been established in a sequence of papers by Tripathy and his coauthors ([4, 7, 8]. Also, the concepts of fuzzy lists ([5]) and that of intuitionistic fuzzy lists ([6]) have been defined and studied by them. Recently an application to develop list theoretic relational databases and operations on them has been put forth by Tripathy and Gantayat ([9]). In the present article we provide another application of this approach in defining data structures like Stack, Queue and Array and establishing operations on them. One of the major advantages of this approach is the ease in extending all the concepts for basic lists to the context of fuzzy lists [5] and intuitionistic fuzzy lists [6]. In this paper, we illustrate how this can be done. The notions of fuzzy lists and intuitionistic fuzzy lists are new and least attended concepts and the works in this paper opens a new application area to develop fuzzy and intuitionistic fuzzy data structures.

1 citations

References
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Book ChapterDOI
01 Jan 2014
TL;DR: This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation.
Abstract: Algorithms are important tools for solving problems computationally. All computation involves algorithms, and the efficiency of an algorithm largely determines its usefulness. This chapter provides an overview of the fundamentals of algorithms and their links to self-organization, exploration, and exploitation. A brief history of recent nature-inspired algorithms for optimization is outlined in this chapter.

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E. F. Codd1
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01 Jan 1983
TL;DR: The basis of this book is the material contained in the first six chapters of the earlier work, The Design and Analysis of Computer Algorithms, and has added material on algorithms for external storage and memory management.
Abstract: From the Publisher: This book presents the data structures and algorithms that underpin much of today's computer programming. The basis of this book is the material contained in the first six chapters of our earlier work, The Design and Analysis of Computer Algorithms. We have expanded that coverage and have added material on algorithms for external storage and memory management. As a consequence, this book should be suitable as a text for a first course on data structures and algorithms. The only prerequisite we assume is familiarity with some high-level programming language such as Pascal.

2,690 citations