#import "@preview/ilm:1.4.1": *


#show: ilm.with(
  title: [CS3231  - The Theory of Computing],
  author: "Yadunand Prem",
  // bibliography: bibliography("refs.bib"),
  table-of-contents: none,
  // figure-index: (enabled: true),
  // table-index: (enabled: true),
  // listing-index: (enabled: true),
)
#set text(lang: "en", font: ("SF Pro Condensed"))
#show raw: set text(font: "SF Mono")

== Reference
- Alphabet - Finite Non empty set of symbols, denoted by $Sigma$
  - Powers of Alphabet
    - $Sigma^2 = {00, 01, 10, 11}$
    - $Sigma^0 = {epsilon.alt}$
    - $Sigma^ lt.eq 2 = Sigma^0 union Sigma^1 union Sigma^2$
- String - Sequence of Symbols from $Sigma$, denoted by $epsilon.alt$
  - Concat - $x = 00, y = 10, x dot y = x y = 0010$
  - Substring - $a b$ is a substring of $b a b a a$, $b b$ is not.
  - Subsequence - $b b a$ is not subseq of $b a b a a $, $a b b$ is
- Length of String - Number of symbols in a string, denoted by $|w|$
- Language - Set of strings over an alphabet
  - $L = {00, 11, 01, 110}$
  - $L = emptyset$
  - $L_1 dot L_2 = L_1L_2 = {x y : x in L_1, y in L_2}$
  - $L^* = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n in NN}$
  - $L^+ = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n gt.eq 1}$