33 lines
1.2 KiB
Plaintext
33 lines
1.2 KiB
Plaintext
#import "@preview/ilm:1.4.1": *
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#show: ilm.with(
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title: [CS3231 - The Theory of Computing],
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author: "Yadunand Prem",
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// bibliography: bibliography("refs.bib"),
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table-of-contents: none,
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// figure-index: (enabled: true),
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// table-index: (enabled: true),
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// listing-index: (enabled: true),
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)
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#set text(lang: "en", font: ("SF Pro Condensed"))
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#show raw: set text(font: "SF Mono")
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== Reference
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- Alphabet - Finite Non empty set of symbols, denoted by $Sigma$
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- Powers of Alphabet
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- $Sigma^2 = {00, 01, 10, 11}$
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- $Sigma^0 = {epsilon.alt}$
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- $Sigma^ lt.eq 2 = Sigma^0 union Sigma^1 union Sigma^2$
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- String - Sequence of Symbols from $Sigma$, denoted by $epsilon.alt$
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- Concat - $x = 00, y = 10, x dot y = x y = 0010$
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- Substring - $a b$ is a substring of $b a b a a$, $b b$ is not.
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- Subsequence - $b b a$ is not subseq of $b a b a a $, $a b b$ is
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- Length of String - Number of symbols in a string, denoted by $|w|$
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- Language - Set of strings over an alphabet
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- $L = {00, 11, 01, 110}$
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- $L = emptyset$
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- $L_1 dot L_2 = L_1L_2 = {x y : x in L_1, y in L_2}$
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- $L^* = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n in NN}$
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- $L^+ = {x_1x_2...x_n : x_1, x_2, ... x_n in L, n gt.eq 1}$
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