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”.

  • lemmesayOPEnglish
    24·
    1 year ago

    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.