Proving Correctness of Deterministic Finite Automata, State Invariants (Theory of Computing)

Channel:

PageWizard Games, Learning & Entertainment

Subscribers:

780

Published on January 30, 2023 2:30:13 PM ● Video Link: https://www.youtube.com/watch?v=egKyycczjak

Duration: 1:04:16

39 views

3

Today we explore how to prove a deterministic finite automaton (DFA) is correct. To do this we explore the concept of invariants, and how we can use induction in relation to them. Then, I present a general framework for arguing the correctness of DFAs. We will see two more examples in the next lectures!

Time Stamps:
0:00 Recap and opening
0:35 What does it mean for a DFA to be "correct"? Correctness, and the technique of using invariants.
6:30 Proving a DFA that accepts binary strings with an odd number of 0s is correct using state invariants (which we will discuss more after the example). Note that the invariants are much (much) stronger than is required to prove this claim.
44:35 State Invariants, what are they are how/why are they helpful for proving the correctness of DFAs. The sketch/framework of proving DFAs are correct using state invariants.
55:29 Some remarks about state invariants.
1:03:57 Closing

Note: I have a fun typo in the title within the video. It should be DFAs, not DFA.

Have a beautiful day!

Supporters (to date of publication, by tier (top to bottom)):
----------------------------------------------------------
Patreon Supporters (General Support):
Draikou
Patreon Supporters (Basic Support):
Patreon Supporters (Supporter Access!):
Eric R
-----------------------------------------------------------
Become a supporter today! To support my work and mission to provide free or accessible Computer Science education (especially in theory), subscribe to the channel, share my videos. Please donate and contribute to support my work for more content:
PATREON: https://www.patreon.com/PageWizard
SUBSCRIBESTAR: https://www.subscribestar.com/drpage
PAYPAL: https://paypal.me/pagewizard

Follow also at:
FACEBOOK: https://www.facebook.com/DanielRPage
TWITTER: https://twitter.com/PageWizardGLE
QUORA: https://www.quora.com/profile/Daniel-R-Page
TWITCH: https://www.twitch.tv/pagewizard

#ComputerScience
#theoryofcomputation
#finiteautomata