Suppose that G is a CFG without any productions that have € as the right side. If w is in L(G), the length of w is n, and w has a derivation of m steps, show that w has a parse tree with n + m nodes.

Answers

Answer 1

A parse tree is a hierarchical structure that represents the syntactic structure of a sentence or expression in a formal language. It is used in natural language processing and compilers to analyze and understand the grammar of a language.

To show that w has a parse tree with n + m nodes, we can use induction on m, the number of steps in the derivation of w.

Base case: If m = 0, then w is a starting symbol of G and has a parse tree with only one node, which is w itself. Therefore, the number of nodes in the parse tree is n + 0 = n.

Inductive step: Assume that for any derivation of length k < m, any string in L(G) with length n has a parse tree with n + k nodes.

Let S be the starting symbol of G and let w be a string in L(G) with length n that has a derivation of m steps. Let the last production used in the derivation be A -> x, where A is a nonterminal symbol and x is a string of terminals and/or nonterminals.

Since G has no productions with € on the right side, x cannot be €. Therefore, x has at least one symbol in it. Let that symbol be B, which is the leftmost nonterminal in x. Then we can write x as x = yBz, where y and z are strings of terminals and/or nonterminals and B -> y is a production in G.

We can construct a parse tree for w as follows:

1. The root of the parse tree is the starting symbol S.
2. The children of S are the nonterminal symbols in the first production used in the derivation of w, which is S -> x. Therefore, the children of S are x's symbols, which are yBz.
3. The left child of S is a subtree that corresponds to the derivation of y. By the inductive hypothesis, this subtree has y nodes.
4. The right child of S is a subtree that corresponds to the derivation of Bz. This subtree has m-1 steps, since it is the remainder of the derivation of w after the first step. By the inductive hypothesis, this subtree has |Bz| + (m-1) nodes.
5. The left child of yBz is a subtree that corresponds to the derivation of y. By the inductive hypothesis, this subtree has y nodes.
6. The right child of yBz is a subtree that corresponds to the derivation of Bz. This subtree has m-1 steps, since it is the remainder of the derivation of w after the first step. By the inductive hypothesis, this subtree has |Bz| + (m-1) nodes.

Therefore, the parse tree for w has n + m nodes, since it has one node for each symbol in w and one node for each step in its derivation.

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In this case, in computer, the guidelines that should be followed prior to ordering and installing memory in an hp business pc or notebook is to verify that the network cable is plugged in. This is important to allow for easy installation.

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Answers

Answer:

user_num >= 1

while true do

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Explanation:

First, you write that the user_num is equal to or is greater than 1. Then you write in the while loop that while that's true, print user_num divided by two.

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Explanation:

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Which selection tool should be used to fill a vacancy that requires managing multiple priorities and working under pressure?

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The telephone system is an example of a circuit-switched network.

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Lucy is trying to decide what sources to use in her literature review. The type of sources Lucy will use in her literature review will depend on which of the following?

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If you forget to put a closing quotation mark on a string, what kind of error will be raised?

Answers

If you forget to put a closing quotation mark on a string, compilation (syntax) error is the kind of error that will be raised.

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Therefore,  If you forget to put a closing quotation mark on a string, compilation (syntax) error is the kind of error that will be raised.

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One of the many roles of the security compliance committee is to focus on controls that are widely used across a large population of applications, systems, and operations. These types of controls are known as ___________________.

Answers

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Answers

Answer:

A database application is a set of one or more computer programs that serves as an intermediary between the user and the DBMS.

Explanation:

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9.1% complete Question A government agency is getting rid of older workstations. The agency will donate these workstations, along with other excess computer systems, to nearby schools. Management reminds the systems administrators about data sanitization and security concerns. What actions secure the systems prior to donating to the schools?

Answers

The action that can secure the systems prior to donating to the schools is that they should use a data sanitization tool and also replace the hard drive with an empty one .

What is the aim of a data sanitization tool?

The aim of data sanitization is for the full or total clearing of devices and getting rid of all sensitive data only if the storage device is not been used or is said to be transferred to another Information system .

Hence, The action that can secure the systems prior to donating to the schools is that they should use a data sanitization tool and also replace the hard drive with an empty one .

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Theorem: for any two real numbers, x and y, if x and y are both rational then x y is also rational. Which facts are assumed and which facts are proven in a proof by contrapositive of the theorem?

Answers

The facts that are assumed and the facts  that are proven in a direct proof of the theorem is that option a) Assumed: x is rational and y is rational and Proven: x + y is rational.

What is a theorem?

The term known as theorem is known to be a kind of a formula, or statement that is seen in a lot of mathematics field and it also known top  be the logic deduced.

Note that it is also seen as the result that is said to have been proved to be true (through the use of operations and facts that are said to be already known).

Therefore, The facts that are assumed and the facts  that are proven in a direct proof of the theorem is that option a) Assumed: x is rational and y is rational and Proven: x + y is rational.

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See full question below

Theorem: For any two real numbers, x and y, if x and y are both rational then x + y is also rational. Which facts are assumed and which facts are proven in a direct proof of the theorem?

a) Assumed: x is rational and y is rational

Proven: x + y is rational

b) Assumed: x + y is irrational

Proven: x is irrational and y is irrational

c) Assumed: x + y is rational

Proven: x is rational or y is rational

d) Assumed: x is rational or y is rational

Proven: x + y is rational

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Answers

Wikis is the one on which should you be most careful about trusting the information you come across as it may seem academically reviewed but in fact is not.

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A wiki is known to be a form of a collaborative tool that is used and one that aids students to make their own contribution and change one or more pages of course linked materials.

Note that based on the above, Wikis is the one on which should you be most careful about trusting the information you come across as it may seem academically reviewed but in fact is not.

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Illuminate all lamps and leds, remove fuses, and verify that trouble signals occur when testing

Answers

Illuminate all lamps and leds, remove fuses, and verify that trouble signals occur when testing for voltage.

What tool can Technicians use to check the lighting and accessory circuits?

The technician can use a Voltmeter, ohmmeter, or continuity test and this is one that can best be used to test the  above circuits.

Hence, Illuminate all lamps and leds, remove fuses, and verify that trouble signals occur when testing for voltage.

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