▶SEND ME THEORY QUESTIONS◀ ryan.e.dougherty@icloud.com
▶ABOUT ME◀ I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes. ... https://www.youtube.com/watch?v=9hr-ndN0eWE
Here we prove the following problem about languages: if L1, L2, and L3 are languages, then (L1 intersect L2) concat L3 = (L1 concat L3) intersect (L2 concat L3).
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below.
Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
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Merch:
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about it. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
The views expressed in this video are not reflective of any of my current or former employers.
...
https://www.youtube.com/watch?v=DzIDCZfcIEU
Here we give four proofs of languages not being context-free:
1) {a^n b^n c^n : n at least 0}
2) {a^i b^j c^k : i at most j, j at most k}
3) {ww : w in {0,1}*}
4) {w in {a,b,c,d}* : w has more c's than a's, b's, or d's}
In each, we go through a proof to show that each language is not context-free by first assuming that it is context-free, then using the fact that there is a pumping constant p for each language, finding a string that cannot be pumped.
Timestamps:
0:00 - Intro
1:00 - Main steps in proofs
3:30 - {a^n b^n c^n : n at least 0}
14:20 - {a^i b^j c^k : i at most j, j at most k}
24:00 - {ww : w in {0,1}*}
37:30 - {w in {a,b,c,d}* : w has more c's than a's, b's, or d's}
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
Facebook group: https://www.facebook.com/groups/easytheory/
Twitter: https://twitter.com/EasyTheory
Merch:
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If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=v4ZjggNXW3Q
Thanks for a million - onto the next one.
Easy Theory shirts: https://my-store-82c891.creator-spring.com/listing/easy-theory
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below.
Dolev Abuhazira, Josh Hibschman, Micah Wood, Morgan Jones, Patrik Keinonen, Simone Glinz, Tao Su, Timothy Gorden, unit220, Valentine Eben
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about it. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
The views expressed in this video are not reflective of any of my current or former employers.
...
https://www.youtube.com/watch?v=uJisgVH8y5k
Here we give two examples on how to minimize a DFA. The main video is here: https://www.youtube.com/watch?v=685Wn0xFCrs. The idea is to "group" states together based on "equivalence" and then to refine the groups until no longer possible.
#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem
Contribute:
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Live Streaming (Sundays 2PM GMT, 2 hours):
Twitch: https://www.twitch.tv/easytheory
(Youtube also)
Mixer: https://mixer.com/easytheory
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
Facebook group: https://www.facebook.com/groups/easytheory/
Twitter: https://twitter.com/EasyTheory
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
Ultimate Supporters: (none)
Diamond Supporters: (none)
Platinum Supporters: (none)
Gold Supporters: Anonymous (x1), Micah Wood, Ben Pritchard
Silver Supporters: Timmy Gy
Supporters: Yash Singhal
▶ADDITIONAL QUESTIONS◀
1. For each positive integer n, find an example DFA where the minimum number of states is n.
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at two different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=tVF1CQnGPEY
Here we give a slightly more complicated example on the NFA to regex conversion that uses nondeterminism. The main video of this method is here: https://youtu.be/HUolNKq7v3k
#easytheory #nfa #dfa #gate #gateconcept #theoryofcomputing #turingmachine #nfatoregex #cfg #pda #undecidable #ricestheorem
Contribute:
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Live Streaming (Sundays 2PM GMT, 2 hours):
Twitch: https://www.twitch.tv/easytheory
(Youtube also)
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
Facebook group: https://www.facebook.com/groups/easytheory/
Twitter: https://twitter.com/EasyTheory
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
Gold Supporters: Micah Wood
Silver Supporters: Timmy Gy
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=Gfa3WUFVsJA
Here we show that the language of all strings of the form 0^n 1^m where n is strictly less than 3m is not regular. This is a standard pumping lemma proof, other than picking the right string at the beginning!
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
#easytheory
Youtube Live Streaming (Sundays) - subscribe for when these occur.
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=N3G2CX2p_po
Here we go over a GATE exam problem about a language of Turing Machines that accept some string of length 2020. We then classify this language as being undecidable but recognizable. The proof of undecidability is supposing a decider for it exists, then obtaining a decider for A_TM from that, which we know cannot exist. The proof of recognizable comes from "brute force" parallel simulation of all strings of length 2020, and accepting if any such string is accepted.
Patreon: https://www.patreon.com/easytheory
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ADDITIONAL QUESTIONS◀
1. Could we have applied Rice's Theorem to this problem?
2. What can we say about the complement of L?
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.
...
https://www.youtube.com/watch?v=YSgmw9t7OQs
Here we go over the product construction for DFAs, which shows that regular languages are closed under union and intersection.
Timeline:
0:00 - Intro
3:20 - Operations on Languages (Union/Intersection/Complement)
10:30 - DFA Example 1 (Complement, not exactly two 0s)
16:50 - DFA Example 2 (Intersection, even number of 0s, exactly one or two 1s)
32:00 - DFA Example 3 (Union, even 0s or number 1s not a multiple of 3)
47:00 - DFA Example 4 (Symmetric Difference, exactly two 0s or one 1, but not both)
Thanks to the following supporters of the channel for helping support this video. If you want to contribute, links are below. Names are listed in alphabetical order by surname.
Platinum: Micah Wood
Silver: Timmy Gy, Josh Hibschman, Patrik Keinonen, Travis Schnider, and Tao Su
Easy Theory Website: https://www.easytheory.org
Become a member: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg/join
Donation (appears on streams): https://streamlabs.com/easytheory1/tip
Paypal: https://paypal.me/easytheory
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught many courses at several different universities, including several sections of undergraduate and graduate theory-level classes.
...
https://www.youtube.com/watch?v=uEe-uwvnMC8
Here we show the counterintuitive fact that for ANY unary language L, L* is regular! The idea exploits the fact that L is unary by looking at the lengths of the strings and not the strings themselves, and we can reduce this question to looking at the greatest common divisor of the lengths in the language (and reducing to a smaller case if necessary).
Contribute:
Patreon: https://www.patreon.com/easytheory
Discord: https://discord.gg/SD4U3hs
Live Streaming (Saturdays, Sundays 2PM GMT):
Twitch: https://www.twitch.tv/easytheory
(Youtube also)
Mixer: https://mixer.com/easytheory
Social Media:
Facebook Page: https://www.facebook.com/easytheory/
Facebook group: https://www.facebook.com/groups/easytheory/
Twitter: https://twitter.com/EasyTheory
Merch:
Language Hierarchy Apparel: https://teespring.com/language-hierarchy?pid=2&cid=2122
Pumping Lemma Apparel: https://teespring.com/pumping-lemma-for-regular-lang
If you like this content, please consider subscribing to my channel: https://www.youtube.com/channel/UC3VY6RTXegnoSD_q446oBdg?sub_confirmation=1
▶ADDITIONAL QUESTIONS◀
1. Can you prove that if gcd(x,y) = 1, then any number at least (x-1)(y-1)-1 can be reached?
2. What about for binary languages?
▶SEND ME THEORY QUESTIONS◀
ryan.e.dougherty@icloud.com
▶ABOUT ME◀
I am a professor of Computer Science, and am passionate about CS theory. I have taught over 12 courses at Arizona State University, as well as Colgate University, including several sections of undergraduate theory.
▶ABOUT THIS CHANNEL◀
The theory of computation is perhaps the fundamental theory of computer science. It sets out to define, mathematically, what exactly computation is, what is feasible to solve using a computer, and also what is not possible to solve using a computer. The main objective is to define a computer mathematically, without the reliance on real-world computers, hardware or software, or the plethora of programming languages we have in use today. The notion of a Turing machine serves this purpose and defines what we believe is the crux of all computable functions.
This channel is also about weaker forms of computation, concentrating on two classes: regular languages and context-free languages. These two models help understand what we can do with restricted means of computation, and offer a rich theory using which you can hone your mathematical skills in reasoning with simple machines and the languages they define.
However, they are not simply there as a weak form of computation--the most attractive aspect of them is that problems formulated on them are tractable, i.e. we can build efficient algorithms to reason with objects such as finite automata, context-free grammars and pushdown automata. For example, we can model a piece of hardware (a circuit)
...
https://www.youtube.com/watch?v=H-GYBjDpT6U