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Here is how we can test ef ciently if an attribute is extraneous Let R be the relation schema, and let F be the given set of functional dependencies that hold on R Consider an attribute A in a dependency If A , to check if A is extraneous consider the set F = (F { }) { ( A)} and check if A can be inferred from F To do so, compute + (the closure of ) under F ; if + includes A, then A is extraneous in If A , to check if A is extraneous, let = {A}, and check if can be inferred from F To do so, compute + (the closure of ) under F ; if + includes all attributes in , then A is extraneous in For example, suppose F contains AB CD, A E, and E C To check if C is extraneous in AB CD, we compute the attribute closure of AB under F = {AB D, A E, and E C} The closure is ABCDE, which includes CD, so we infer that C is extraneous A canonical cover Fc for F is a set of dependencies such that F logically implies all dependencies in Fc , and Fc logically implies all dependencies in F Furthermore, Fc must have the following properties: No functional dependency in Fc contains an extraneous attribute Each left side of a functional dependency in Fc is unique That is, there are no two dependencies 1 1 and 2 2 in Fc such that 1 = 2 A canonical cover for a set of functional dependencies F can be computed as depicted in Figure 78 It is important to note that when checking if an attribute is extraneous, the check uses the dependencies in the current value of Fc , and not the dependencies in F If a functional dependency contains only one attribute in its right-hand side, for example A C, and that attribute is found to be extraneous, we would get a functional dependency with an empty right-hand side Such functional dependencies should be deleted The canonical cover of F , Fc , can be shown to have the same closure as F ; hence, testing whether Fc is satis ed is equivalent to testing whether F is satis ed However, Fc is minimal in a certain sense it does not contain extraneous attributes, and it Fc = F repeat Use the union rule to replace any dependencies in Fc of the form 1 1 and 1 2 with 1 1 2 Find a functional dependency in Fc with an extraneous attribute either in or in /* Note: the test for extraneous attributes is done using Fc , not F */ If an extraneous attribute is found, delete it from until Fc does not change Figure 78 Computing canonical cover.

g = 2(RTH + R L )

Since it is far easier to use the menu creation tools than if you try to create menus from scratch, we ll use those tools to add our menu to the timeline Figure 8-2 shows the basic steps to get you started Let s go through the steps to add the menu:

The McGraw Hill Companies, 2001

the construction of sophisticated user interfaces, beyond what is possible with just HTML, interfaces that can be used without downloading and installing any software Thus, Web interfaces are powerful and visually attractive, and are likely to eclipse special-purpose interfaces for all except a small class of users

Here we review some of the fundamental technology behind the World Wide Web, for readers who are not familiar with it

Giving (RTH + R L )2 2R L (RTH + R L ) = 0

A uniform resource locator (URL) is a globally unique name for each document that can be accessed on the Web An example of a URL is http://wwwbell-labscom/topic/book/db-book The rst part of the URL indicates how the document is to be accessed: http indicates that the document is to be accessed by the HyperText Transfer Protocol, which is a protocol for transferring HTML documents The second part gives the unique name of a machine that has a Web server The rest of the URL is the path name of the le on the machine, or other unique identi er of the document within the machine Much data on the Web is dynamically generated A URL can contain the identi er of a program located on the Web server machine, as well as arguments to be given to the program An example of such a URL is http://wwwgooglecom/search q=silberschatz which says that the program search on the server wwwgooglecom should be executed with the argument q=silberschatz The program executes, using the given arguments, and returns an HTML document, which is then sent to the front end

Drag your selection onto the timeline and drop it FIGURE 8-2

Figure 211 is an example of the source of an HTML document Figure 212 shows the displayed image that this document creates The gures show how HTML can display a table and a simple form that allows users to select the type (account or loan) from a menu and to input a number in a text box HTML also supports several other input types Clicking on the submit button causes the program BankQuery (speci ed in the form action eld) to be executed with the user-provided values for the arguments type and number (speci ed in the select and input elds) The program generates an HTML document, which is then sent back and displayed to the user; we will see how to construct such programs in Sections 2113, 2114, and 2115 HTML supports stylesheets, which can alter the default de nitions of how an HTML formatting construct is displayed, as well as other display attributes such as background color of the page The cascading stylesheet (css) standard allows the same

The McGraw Hill Companies, 2001

21

Solving, we nd that the load resistance that results in maximum power transfer is R L = RTH (103)

CHAPTER 8: