$$ \newcommand{\bsth}{{\boldsymbol\theta}} \newcommand{\nptime}{\textsf{NP}} \newcommand{\ptime}{\textsf{P}} \newcommand{\disteq}{\overset{d}{=}} %linalg \newcommand{\mat}[1]{\begin{pmatrix} #1 \end{pmatrix}} \newcommand{\detmat}[1]{\begin{vmatrix} #1 \end{vmatrix}} \newcommand{\spanb}[1]{\text{span}\{ #1 \}} \DeclareMathOperator{\conv}{conv} % convex hull \DeclareMathOperator{\cone}{cone} \DeclareMathOperator{\vectorize}{vec} \DeclareMathOperator{\matricize}{mat} \DeclareMathOperator{\adj}{adj} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\argmin}{argmin} \DeclareMathOperator*{\proj}{proj} % brackets, norms, cardinalities \newcommand{\pa}[1]{ \left({#1}\right) } \newcommand{\ha}[1]{ \left[{#1}\right] } \newcommand{\ca}[1]{ \left\{{#1}\right\} } \newcommand{\inner}[1]{\left\langle #1 \right\rangle} \newcommand{\innercpy}[1]{\inner{ #1, #1 }} \newcommand{\norm}[1]{\left\| #1 \right\|} \newcommand{\abs}[1]{\left|{#1}\right|} \newcommand{\card}[1]{\left\vert{#1}\right\vert} % math vectors \newcommand{\va}{\textbf{a}} \newcommand{\vb}{\textbf{b}} \newcommand{\vc}{\textbf{c}} \newcommand{\vd}{\textbf{d}} \newcommand{\ve}{\textbf{e}} \newcommand{\vf}{\textbf{f}} \newcommand{\vg}{\textbf{g}} \newcommand{\vh}{\textbf{h}} \newcommand{\vi}{\textbf{i}} \newcommand{\vj}{\textbf{j}} \newcommand{\vk}{\textbf{k}} \newcommand{\vl}{\textbf{l}} \newcommand{\vm}{\textbf{m}} \newcommand{\vn}{\textbf{n}} \newcommand{\vo}{\textbf{o}} \newcommand{\vp}{\textbf{p}} \newcommand{\vq}{\textbf{q}} \newcommand{\vr}{\textbf{r}} \newcommand{\vs}{\textbf{s}} \newcommand{\vt}{\textbf{t}} \newcommand{\vu}{\textbf{u}} \newcommand{\vv}{\textbf{v}} \newcommand{\vw}{\textbf{w}} \newcommand{\vx}{\textbf{x}} \newcommand{\vy}{\textbf{y}} \newcommand{\vz}{\textbf{z}} \newcommand{\vzero}{\textbf{0}} \newcommand{\vone}{\textbf{1}} \newcommand{\valpha}{{\boldsymbol\alpha}} \newcommand{\vepsilon}{{\boldsymbol\epsilon}} \newcommand{\vnu}{{\boldsymbol\nu}} \newcommand{\vpi}{{\boldsymbol\pi}} \newcommand{\veta}{{\boldsymbol\eta}} \newcommand{\vsigma}{ {\boldsymbol\sigma}} \newcommand{\vbeta}{ {\boldsymbol\beta}} \newcommand{\vtheta}{ {\boldsymbol\theta}} \newcommand{\vdelta}{ {\boldsymbol\delta}} \newcommand{\vlambda}{ {\boldsymbol\lambda}} \newcommand{\vmu}{ {\boldsymbol\mu}} % common math sets \newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\N}{\mathbb{N}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\F}{\mathbb{F}} \newcommand{\T}{\mathbb{T}} % limits \def\sumn{\sum_{n=0}^\infty} \def\limn{\lim_{n\rightarrow\infty}} \def\prodn{\prod_{n=0}^\infty} % mathcal \newcommand{\mcA}{\mathcal{A}} \newcommand{\mcB}{\mathcal{B}} \newcommand{\mcC}{\mathcal{C}} \newcommand{\mcD}{\mathcal{D}} \newcommand{\mcE}{\mathcal{E}} \newcommand{\mcF}{\mathcal{F}} \newcommand{\mcG}{\mathcal{G}} \newcommand{\mcH}{\mathcal{H}} \newcommand{\mcI}{\mathcal{I}} \newcommand{\mcJ}{\mathcal{J}} \newcommand{\mcK}{\mathcal{K}} \newcommand{\mcL}{\mathcal{L}} \newcommand{\mcM}{\mathcal{M}} \newcommand{\mcN}{\mathcal{N}} \newcommand{\mcO}{\mathcal{O}} \newcommand{\mcP}{\mathcal{P}} \newcommand{\mcQ}{\mathcal{Q}} \newcommand{\mcR}{\mathcal{R}} \newcommand{\mcS}{\mathcal{S}} \newcommand{\mcT}{\mathcal{T}} \newcommand{\mcU}{\mathcal{U}} \newcommand{\mcV}{\mathcal{V}} \newcommand{\mcW}{\mathcal{W}} \newcommand{\mcX}{\mathcal{X}} \newcommand{\mcY}{\mathcal{Y}} \newcommand{\mcZ}{\mathcal{Z}} % distribs, probability \newcommand{\disteq}{\overset{d}{=}} \newcommand\independent{\perp \!\!\! \perp} \DeclareMathOperator{\Laplace}{Laplace} \DeclareMathOperator{\Poisson}{Poisson} \DeclareMathOperator{\Exponential}{Exponential} \DeclareMathOperator{\Multinomial}{Multinomial} \DeclareMathOperator{\Bernoulli}{Bernoulli} \DeclareMathOperator{\Categorical}{Categorical} \DeclareMathOperator{\Uniform}{Uniform} \DeclareMathOperator{\Binomial}{Binomial} \DeclareMathOperator{\Hypergeometric}{Hypergeometric} \DeclareMathOperator{\GammaDist}{Gamma} \DeclareMathOperator{\NegativeBinomial}{NegativeBinomial} \DeclareMathOperator\sub{sub} \renewcommand{\d}[1]{\mathop{\mathrm{d} #1 }} \newcommand{\dkl}[2]{\mathop{D_\mathrm{KL}}\left({#1}\;\middle\|\;{#2}\right)} \newcommand{\sg}{\mathop{\mathrm{SG}}} \newcommand{\se}{\mathop{\mathrm{SE}}} %operators \DeclareMathOperator{\power}{{\mathcal{P}}} \DeclareMathOperator{\var}{var} \DeclareMathOperator{\cov}{cov} \DeclareMathOperator\mathProb{\mathbb{P}} \DeclareMathOperator\mathExp{\mathbb{E}} \DeclareMathOperator*\mathExpUnder{\mathbb{E}} \DeclareMathOperator*\fat{fat} \renewcommand{\P}{\mathProb} % need to overwrite stupid paragraph symbol \newcommand{\E}{\mathExp} % need to overwrite stupid paragraph symbol \newcommand{\set}[2]{ \left\{ #1 \,\middle|\, #2 \right\} } \newcommand{\CE}[2]{ \mathExp\left[ #1 \,\middle|\, #2 \right] } \renewcommand{\CP}[2]{ \mathProb\left\{ #1 \,\middle|\, #2 \right\} } $$

Articles by category: interview-question

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graph-processing parallel distributed-systems online-learning machine-learning my-whitepapers hardware-acceleration interview-question tools optimization deep-learning numpy-gems joke-post philosophy causal statistics numpy tricks history

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The Semaphore Barrier (Solution)

25 Jan 2017

The Semaphore BarrierThis is the answer post to the question posed here.A Useful FormalismReasoning about parallel systems is tough, so to make sure that our solution is correct we’ll have to introduce a formalism for parallel execution.The notion is the following. Given some instructions for threads \(\{t_i\}_{i=0}^{n-1}\), we expect each thread’s individual instructions to execute in sequence, but instructions between threads can be interleaved arbitrarily.In our simplified execution model ... Read More

The Semaphore Barrier

24 Jan 2017

The Semaphore BarrierI wanted to share an interview question I came up with. The idea came from my operating and distributed systems classes, where we were expected to implement synchronization primitives and reason about concurrency, respectively.Synchronization primitives can be used to coordinate across multiple threads working on a task in parallel.Most primitives can be implemented through the use of a condition variable and lock, but I was wondering about implementing other primitives i... Read More