The fact that DFAs are limited, it allows us to optimize a DFA. Specifically, we ask: “does this DFA have a minimal number of states?”

Formally: can we accept the same language with a particular DFA with another DFA with less states?

For every language \(L\), there is a unique (up to state relabeling) minimal-state DFA \(M^{*}\) such that \(L(M^{*}) = L\).

Furthermore, there exists an efficient algorithm which, given DFA \(M\), will produce this unique \(M^{*}\).

Foreword

Hi there, internet traveler.

The time is 2015/2016, I was either in 5th or 6th grade. At that time, I was barely beginning to be actually comfortable using the language of English.

One of the ways I practiced English, which is also a habit I continue to do today, is to write. I write mostly expository prose now, but, back then, shining with childish naïvete, I decided to write a multi-part story as a means of practicing English.

“Doing NSM analysis is a demanding process and there is no mechanical procedure for it. Published explications have often been through a dozen or more iterations over several months” — (Heine, Narrog, and Goddard 2015)

Approach and XD

Introduction and Theory

The Natural Semantic Metalanguage (NSM) approach (Wierzbicka 1974) is a long-standing hypothetical theory in structural semantics which claims that all human languages share a common set of primitive lexical units—usually words, but, in some languages, short connected phrases—through which all other words in each language can be defined.

NUS Secondary School Other Duties

• AP Statistics Index
• AP Phys C Mech Index
• AP Phys C EM Index
• Tuning Forks
• bioinformatics
• PKM
• Intersession 2023

NUS-MATH580 QIC

NUS-CS223 Algorithms

Backlog: Finite State Machine

NUS-HIST301 American History

Backlog: New Deal, Franklin D. Roosevelt (FDR), Works Progress Administration, effects of the New Deal, Great Depression, Herber Hoover, disinformation, Guilded Age

Let’s begin. We want to create test for the linearity of a few assets, for whether or not they follow the CAPM.

Note that we will be using the Sharpe-Linter version of CAPM:

\begin{equation} E[R_{i}-R_{f}] = \beta_{im} E[(R_{m}-R_{f})] \end{equation}

\begin{equation} \beta_{im} := \frac{Cov[(R_{i}-R_{f}),(R_{m}-R_{f})]}{Var[R_{m}-R_{f}]} \end{equation}

Recall that we declare \(R_{f}\) (the risk-free rate) to be non-stochastic.

Let us begin. We will create a generic function to analyze some given stock.

We will first import our utilities