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sigma star

image transcription:

an image incorporating two famous memes. on top is the title “learning about Σ* in theory of computation.”

in the centre is a close-up of Chad face – often used when talking about sigma males – cropped in a five-pointed star shape.

below are two soyjaks pointing towards the aforementioned Chad face. those soyjaks are labeled “me” and “my brain”.

TheyCallMeHacked ,

It’s funny, I never associated formal languages as part of the theory of computation. We only learnt about them from the perspective of automata/state machine theory

kogasa ,
@kogasa@programming.dev avatar

Automata and formal languages were pretty much my entire “Theory of Computation” class. It’s what’s in Sipser.

Mars ,
@Mars@beehaw.org avatar

Didn’t you go into Turing machines and the Halting problem from that?

That was my intro into computation: regex, automatas, state machines, stack state machines, formal languages, grammars, Turing machines, Hanting Problem, P NP.

TheyCallMeHacked ,

No, we went Automata, Finite State Machines, regex, grammars, set-theoretical and other mathematical formalisms

PlexSheep ,
@PlexSheep@feddit.de avatar

Can images work as formal Languages?

lemmesay OP ,
@lemmesay@discuss.tchncs.de avatar

what’d a symbol be? a pixel?

aside from this, they say a picture is worth a 1000 words. so maybe a big language.

Mars ,
@Mars@beehaw.org avatar

A tree can be seen as a formal language. Look into L-systems.

If you generalize what a symbol is (the rgb value of a pixel) you can write a grammar that ends producing a list of pixels. You can then place it in a 2d matrix and you have an image.

I guess a better approach would be wave function colapse, but seems to me like it could be formally described as a grammar (CS or CF, dunno, would have to look into it)

fl42v ,

Sum asterisk or something? 🙃

lemmesay OP ,
@lemmesay@discuss.tchncs.de avatar

sigma star.

if you haven’t heard about theory of computation, let me define some keywords:

  • symbol: smallest unit. denoted by any character(a,b,c, etc.) or number (0,1, etc.)
  • alphabet: set of symbols. denoted by Σ(sigma). e.g.: {a, b, c}
  • string: sequence of symbols. eg: a, aa, aaab, etc.
  • language: set of strings. e.g.: {a, as, aaab, …}

now, sigma has powers. Σ² is set of all strings of length 2. e.g.: {aa, ab, bb, …}. you can generalise this to Σ^n.
Σ* is union of all powers of sigma. i.e., Σ¹ + Σ² + …

so, a language is basically a subset of Σ*.

as for why theory of computation even exists, you basically try to define what a computer can/cannot do.
and you try to mathematically define a computer. then you try to define what a language is(in case of programming , you need it to form languages and compilers). hence the need for this.

AlmightySnoo ,
@AlmightySnoo@lemmy.world avatar

wait until you learn about sigma-algebras in measure theory

lemmesay OP ,
@lemmesay@discuss.tchncs.de avatar

thanks for sharing. can’t wait to go insane :')

FishFace ,

They don’t have anything to do with alphabets in theory of computation…

AlmightySnoo ,
@AlmightySnoo@lemmy.world avatar

correct, but will come up if OP chooses to study measure-theoretic probability theory

Rentlar ,

This is just a representation of your feelings in Big-O notation.

AlmightySnoo ,
@AlmightySnoo@lemmy.world avatar

neither an understatement nor an overstatement, a Big-Theta

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