Questions tagged [derivation]

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Can a grammar that has only one leftmost derivation tree for every sentence, have more than one rightmost derivation tree for some sentence?

I'm currently studying the book Engineering a Compiler by Keith Cooper, and in chapter 3, there is the following definition: A grammar G is ambiguous if some sentence in L(G) has more than one ...
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How to calculate image gradient with respect to homogeneous coordinate vector?

I want to use the direct method of computing the homography between two images to estimate the plane parameters (normal and depth [= distance from camera]) of a 3D plane. If we have two images of the ...
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179 views

Binary cross Entropy derivative?

I am just learning backpropagation algorithm for NN and currently I am stuck with the right derivative of Binary Cross Entropy as loss function. Here it is: ...
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How to derive the worst case time complexity of Heapify algorithm?

I would like to know how to derive the time complexity for the Heapify Algorithm for Heap Data Structure. I am asking this question in the light of the book "Fundamentals of Computer Algorithms&...
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Use or Importance of $\Rightarrow^*$ operator

Particularly, there are 2 variants of $\Rightarrow$, one is $\Rightarrow^*$ and another is $\Rightarrow^+$ which are used in derivation of strings using the productions of the grammar. As stated here,...
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Simple back propagation example

Sorry if this is too simplistic of a question, but over the last couple of months I have been working through the course mathematical foundations of machine learning at my college. I think I am really ...
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21 views

Variable derives itself

In Sipser's Introduction to the theory of computation (3rd edition), I found the following claim. Consider the grammar: $$ \begin{align*} &R \to XRX \mid S \\ &S \to aTb \mid bTa \\ &T \...
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When and what must be present on the left-hand side of the turnstile in metalogics?

Let me show the problem on an example... An actual task from one of the former exams: Consider a simple functional language: $$e::= x|n|e_1e_2|\lambda x.e$$ With typing rules: $$\tau ::= \mathtt{int} ...
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The rightmost derivation is possible with the same rule of leftmost derivation

Can someone please help me in understanding the statement. What does it exactly mean? What I think it means is that: the derivation produces by the leftmost derivation is also possible with rightmost ...