Pairwise Disjointness Test: Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → a i and A → a j . If the intersection of First ( a i ) and First ( a j ) is equivalent to the ∅ , it means pair pass the disjointness test.

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here is a diagram code : graph LR subgraph Inputs [Inputs] A[Input C (Complete Data)] --> TeacherModel B[Input M (Missing Data)] --> StudentA A --> StudentB end subgraph TeacherModel [Teacher Model (Pretrained)] C[Transformer Encoder T] --> D{Teacher Prediction y_t} C --> E[Internal Features f_t] end subgraph StudentA [Student Model A (Trainable - Handles Missing Input)] F[Transformer Encoder S_A] --> G{Student A Prediction y_s^A} B --> F end subgraph StudentB [Student Model B (Trainable - Handles Missing Labels)] H[Transformer Encoder S_B] --> I{Student B Prediction y_s^B} A --> H end subgraph GroundTruth [Ground Truth RUL (Partial Labels)] J[RUL Labels] end subgraph KnowledgeDistillationA [Knowledge Distillation Block for Student A] K[Prediction Distillation Loss (y_s^A vs y_t)] L[Feature Alignment Loss (f_s^A vs f_t)] D -- Prediction Guidance --> K E -- Feature Guidance --> L G --> K F --> L J -- Supervised Guidance (if available) --> G K…

Answer 1

Question

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

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here is a diagram code : graph LR subgraph Inputs [Inputs] A[Input C (Complete Data)] --> TeacherModel B[Input M (Missing Data)] --> StudentA A --> StudentB end subgraph TeacherModel [Teacher Model (Pretrained)] C[Transformer Encoder T] --> D{Teacher Prediction y_t} C --> E[Internal Features f_t] end subgraph StudentA [Student Model A (Trainable - Handles Missing Input)] F[Transformer Encoder S_A] --> G{Student A Prediction y_s^A} B --> F end subgraph StudentB [Student Model B (Trainable - Handles Missing Labels)] H[Transformer Encoder S_B] --> I{Student B Prediction y_s^B} A --> H end subgraph GroundTruth [Ground Truth RUL (Partial Labels)] J[RUL Labels] end subgraph KnowledgeDistillationA [Knowledge Distillation Block for Student A] K[Prediction Distillation Loss (y_s^A vs y_t)] L[Feature Alignment Loss (f_s^A vs f_t)] D -- Prediction Guidance --> K E -- Feature Guidance --> L G --> K F --> L J -- Supervised Guidance (if available) --> G K…

details explanation and background We solve this using a Teacher–Student knowledge distillation framework: We train a Teacher model on a clean and complete dataset where both inputs and labels are available. We then use that Teacher to teach two separate Student models: Student A learns from incomplete input (some sensor values missing). Student B learns from incomplete labels (RUL labels missing for some samples). We use knowledge distillation to guide both students, even when labels are missing. Why We Use Two Students Student A handles Missing Input Features: It receives input with some features masked out. Since it cannot see the full input, we help it by transferring internal features (feature distillation) and predictions from the teacher. Student B handles Missing RUL Labels: It receives full input but does not always have a ground-truth RUL label. We guide it using the predictions of the teacher model (prediction distillation). Using two students allows each to specialize in…

We are doing a custom JSTL custom tag to make display page to access a tag handler. Write two custom tags: 1) A single tag which prints a number (from 0-99) as words. Ex: <abc:numAsWords val="32"/> --> produces: thirty-two 2) A paired tag which puts the body in a DIV with our team colors. Ex: <abc:teamColors school="gophers" reverse="true"> <p>Big game today</p> <p>Bring your lucky hat</p> <-- these will be green text on blue background </abc:teamColors> Details: The attribute for numAsWords will be just val, from 0 to 99 - spelling, etc... isn't important here. Print "twenty-six" or "Twenty six" ... . Attributes for teamColors are: school, a "required" string, and reversed, a non-required boolean. - pick any four schools. I picked gophers, cyclones, hawkeyes and cornhuskers - each school has two colors. Pick whatever seems best. For oine I picked "cyclones" and red text on a gold body - if…

Answer 2

Question

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

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Answer 3

Question

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

Expert Solution & Answer

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Answer 4

Question

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

Expert Solution & Answer

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Answer 5

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

Answer 6

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Answer 7

Chapter 4, Problem 2PS

Program Plan Intro

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Answer 8

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Answer 9

Explanation of Solution

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Answer 10

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

Answer 11

Explanation of Solution

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </

Answer 12

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Answer 13

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Ch. 4 - Prob. 1RQ Ch. 4 - Prob. 2RQ Ch. 4 - Prob. 3RQ Ch. 4 - Prob. 4RQ Ch. 4 - Prob. 5RQ Ch. 4 - Prob. 6RQ Ch. 4 - Prob. 7RQ Ch. 4 - Prob. 8RQ Ch. 4 - Prob. 9RQ Ch. 4 - Prob. 10RQ

Pairwise Disjointness Test: Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → a i and A → a j . If the intersection of First ( a i ) and First ( a j ) is equivalent to the ∅ , it means pair pass the disjointness test.

Pairwise Disjointness Test: Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj. If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

Explanation of Solution

b) A→B{aB}|a Consider the above grammar to perform pairwise disjointness. Find the First set for Right Hand Side of non-terminal symbol A. FIRST (b{aB}) = {b} FIRST (a) = {a} Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

Explanation of Solution

c) B→aB | a Find the First set for Right Hand Side of non-terminal symbol B. FIRST (aB) = {a} FIRST (a) = {a} Now, perform the intersection of FIRST (aB) ∩ FIRST </

Chapter 4 Solutions

Pairwise Disjointness Test:

Perform the pairwise disjointness test on the following grammar rules, for each pair of rules find the disjoint such as A → ai and A → aj.

If the intersection of First(ai) and First(aj) is equivalent to the ∅, it means pair pass the disjointness test.

b) A→B{aB}|a

Consider the above grammar to perform pairwise disjointness.

Find the First set for Right Hand Side of non-terminal symbol A.

FIRST (b{aB}) = {b}

FIRST (a) = {a}

Now, perform the intersection of FIRST (b{aB}) ∩ FIRST&#

c) B→aB | a

Find the First set for Right Hand Side of non-terminal symbol B.

FIRST (aB) = {a}

FIRST (a) = {a}

Now, perform the intersection of FIRST (aB) ∩ FIRST </