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ericung / languageofpolynomials

A language of polynomials.
https://ericung.com/Articles/languageofpolynomials
MIT License
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Figuring out a definition #6

Closed ericung closed 4 months ago

ericung commented 4 months ago

induction for the equivalence proof.

ericung commented 4 months ago

K[x] and K[[x]]. S is an element of K[[x]]

S = Sigma{n>=0}a_n*x^n

This is a finite automata on cyclic loop.

image

ericung commented 4 months ago

on the third step, we reduce or remove the special state down

ericung commented 4 months ago

conversion of turing machine to monomial decider.

turing machine definition that focuses on outcomes: accept,reject,loop, with loop - it only moves forward and doesn't go backwards just like looping in conventional programming given a finite alphabet, the natural numbers is infinite, used int in compiled languages, the trick is that it has 32 bits which is still finite.