Hi, I’m Saad, I love maths and I love to backpack in the woods. Welcome to my blog! Here’s my story and if you are technically inclined, here’s my notebook.

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# My Takeaways from “Endure,” by Alex Hutchinson

# Notes on the PCP Theorem and the Hardness of Approximation: Part 1

## PCP Theorem: the Interactive Proof View

# What I Learned from “Never Split the Difference,” a Book by Chris Voss

# Impagliazzo’s Hardcore Lemma: a Proof

# What Is Your Excuse Today?

# Const-Pointer and Pointer-to-Const in C / C++

Wir müssen wissen — wir werden wissen!

I finished listening to the book “Endure” by Alex Hutchinson. It is one of the most important books that I have read. I have had multiple important realizations from it.

Brain sets an expectation. Giving up is almost always a choice.

**Brain sets an expectation.** You know it or not, feel it or not, your brain sets an expectation at a physiological as well as a psychological level. Try as we may, the brain controls your actions (again, at both the physiological and psychological levels) so that you meet the expectation, but don’t exceed it.

Therefore, **these expectations matter**. Sometimes these expectations are conscious, in that we can spell them out. Other times, they are at a subconscious or even unconscious level. Are you aware of what you expect of yourself? Expect does not mean hope: what do you really, really expect of yourself?

Continue reading “My Takeaways from “Endure,” by Alex Hutchinson”

In this note, we are going to state the PCP theorem and its relation to the hardness of approximating some NP-hard problem.

Intuitively, a PCP (Probabilistically Checkable Proof) system is an interactive proof system where the verifier is given random bits and he is allowed to look into the proof in many locations. If the string is indeed in the language, then there exists a proof so that the verifier always accepts. However, if is not in the language, no prover can convince this verier with probability more than . The proof has to be short i.e., of size at most . This class of language is designated as **PCP[r(n), q(n)].**

Theorem A (PCP theorem).Every NP language has a highly efficient PCP verifier. In particular,.

Continue reading “Notes on the PCP Theorem and the Hardness of Approximation: Part 1”

*[In a hurry? Jump straight to the bullet points.]*

**HBO charged me $15 via Amazon for my subscription that I forgot to cancel** after the Game of Thrones was over. Upon writing to Amazon, the representative said:

As per policy we are unable to issue refund for the previous month charge (September) for your HBO subscription.

However, I am able to make an exception for youand have issued you a promotional credit of $15.14 in your account.

**Walmart manager said he would not accept my returns (worth $107) without a receipt.** Although the first guy said he would give me a gift card, the system didn’t let him proceed. The manager came in and told me they wouldn’t take these returns. Why? Because they have recently changed the rule: without a receipt, I can return items worth only up to $25.

Continue reading “What I Learned from “Never Split the Difference,” a Book by Chris Voss”

Informally speaking, Impagliazzo’s hardcore lemma says that if a boolean function is “hard to compute on average” by small circuits, then there exists a set of inputs on which the same function is “extremely hard to compute on average” by slightly smaller circuits.

In this post, I am going to explain how I understand the proof of the hardcore lemma presented in the Arora-Barak complexity book (here). Because the formal proof can be found in the book I intend to write in an informal way. I think some subtleties are involved in turning the context of the lemma into a suitable two-player zero-sum game. Doing so enables one to use von Neumann’s minimax theorem to effectively “exchange the quantifiers” in the contrapositive statement of the lemma. Although the Arora-Barak proof mentions these subtleties, I am going to explore these in more detail and in a more accessible way for a beginner like me.

I changed my mind before entering the blue doors of the weight room in my gym. There was the soothing sound of water trickling down from the fountain. I felt more thirsty as I waited.

— “Hey, Saad!” exclaimed a low voice. I looked to my right. He just came out of that blue door of the weight room.

— “You used to be my TA !” he said. It always feels good to meet your past students, especially ones that still remember you. I looked hard. Remembering my students’ names used to be my forte, but probably not anymore. Continue reading “What Is Your Excuse Today?”

You must have known it already, but I can’t stop myself from showing off the interplay of const with pointers in C/C++.

Here goes the code. It’s simple.

void main() { int arr[]={1,2,3,4}; // data const int *p1 = &arr[0]; // non-const ptr to const data int const *p2 = &arr[0]; // non-const ptr to const data int* const p3 = &arr[0]; // const ptr to non-const data const int* const p4 = &arr[0]; // const ptr to const data p1++; // ok p1[0]++; // compile error: modifying const data p2++; // ok p2[0]++; // compile error: modifying const data p3++; // compile error: modifying const ptr p3[0]++; // ok p4++; // compile error: modifying const ptr p4[0]++; // compile error: modifying const data }

Continue reading “Const-Pointer and Pointer-to-Const in C / C++”