Editing The Ehrenfeucht-Fraiss' Game for Semijoin Algebra

Title: The Ehrenfeucht-Fraiss' Game for Semijoin Algebra

Abstract: This research article introduces an Ehrenfeucht-Fraiss' game that characterizes the discerning power of the semijoin algebra. The semijoin algebra is a variant of the full relational algebra obtained by replacing the join operator with the semijoin operator. The game is played between two players, the spoiler and the duplicator, who choose tuples from the databases and projections of these. The main research question addressed in this study is: What is the borderline of expressibility of the semijoin algebra? The results obtained from the game show that the semijoin algebra can be used to express a wide range of queries, but there are also limitations to its capabilities. The implications of these findings are discussed, and the research provides a clear understanding of the capabilities and limitations of semijoins in database query processing.

Keywords: Database, Relational Algebra, Semijoin, Ehrenfeucht-Fraiss' Game

Introduction:
Semijoins are an important concept in database query processing. They are used to eliminate dangling tuples and to optimize query processing. The semijoin algebra, which is a variant of the full relational algebra, is obtained by replacing the join operator with the semijoin operator. This study aims to characterize the discerning power of the semijoin algebra using an Ehrenfeucht-Fraiss' game.

The Ehrenfeucht-Fraiss' Game:
The game is played between two players, the spoiler and the duplicator, who choose tuples from the databases and projections of these. At each stage in the game, there is a tuple a chosen by the spoiler and a tuple b chosen by the duplicator. The game continues until one of the following conditions is met:

1. The spoiler cannot make a legal move.
2. The duplicator cannot make a legal move.
3. The duplicator wins the game.

The game is won by the duplicator if he can duplicate the spoiler's strategy throughout the game, meaning that the duplicator can always choose a tuple that matches the spoiler's tuple at each stage.

Results:
The game shows that the semijoin algebra can be used to express a wide range of queries. However, there are also limitations to its capabilities. The game provides a clear boundary for the expressibility of the semijoin algebra, which can help database designers and query processors to better understand the limitations and possibilities of semijoins.

Conclusion:
The Ehrenfeucht-Fraiss' game for the semijoin algebra provides a clear understanding of the capabilities and limitations of semijoins in database query processing. The game shows that the semijoin algebra can be used to express a wide range of queries, but there are also limitations to its capabilities. The results obtained from the game can help database designers and query processors to better optimize query processing and to avoid unnecessary computations.

Link to Article: https://arxiv.org/abs/0308014v2
Authors: 
arXiv ID: 0308014v2

[[Category:Computer Science]]
[[Category:Game]]
[[Category:Semijoin]]
[[Category:Algebra]]
[[Category:Duplicator]]
[[Category:Can]]