▶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=0k9iz6AaPzQ
Here we give a short video on how to return a boolean correctly (this case in Python). Many beginners make this mistake!
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=-mEQ_SWc2GE
Here we show how to achieve closure under union for regular languages, with the so-called "product construction". The idea is to "simulate" two given DFAs at the same time, because the input can only be read once. The resulting DFA has pairs of states for each of the original states in both DFAs, and transitions between them based on how the original DFAs had transitions.
Contribute:
Patreon: https://www.patreon.com/easytheory
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Live Streaming (Sundays 2PM GMT):
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(Youtube also)
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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
▶ADDITIONAL QUESTIONS◀
1. How can you show regular languages are closed under intersection?
2. Find two DFAs whose "product construction" DFA has the smallest number of states possible for that language, and another two where the resulting DFA does not.
3. How many final states are in the union-ed DFA?
▶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 efficien
...
https://www.youtube.com/watch?v=EMLuNJw3yuY
Here we give a very quick proof of the pumping lemma for regular languages. The question just asks about strings that are also accepted in a given DFA. We partition the string up into pieces (as long as the string was accepted and at least the number of states), and repeat the middle piece, yielding another accepted string. Then, we make observations about where the middle piece can be.
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. Is any one of the three conditions unnecessary?
2. Does the initial string have to be accepted?
3. Does the initial string have to be at least the number of states in length?
▶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=Ow-gfFkXPZw
Here we give a live reaction to Tom Scott's video about the Halting problem, and assess how accurate it is. His video is here: https://www.youtube.com/watch?v=eqvBaj8UYz4&ab_channel=TomScott
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
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=stRIfEqcci8
Here we give some problems on regular grammars, that deal with the conversions between them and NFAs and DFAs, such as how big the regular grammar and/or NFA/DFA will be, and is there a direct conversion between a regular grammar and DFA (without using an intermediate NFA)?
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 #gate #theory
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:
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=EH0JZp0D3UI
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
▶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=Xqp6o52lZOM
Here we introduce morphisms (also called homomorphisms) and substitutions, and briefly show that regular languages are closed under both operations. The general principle is that morphisms map strings to strings, and substitutions map strings to languages; otherwise, they behave very similarly. We can assume that each maps a single character (or epsilon) to a string (for morphisms) or language (for substitutions).
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 #gate #theory
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:
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, Ben Pritchard
▶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=_Hp7giDiS74
Here we show that the regular languages are closed under homomorphism, which is a function from Sigma* to itself that has a nice "splitting" property. We use this property in the proof by constructing an NFA for the desired "homomorphism" language, by breaking up every transition into many smaller transitions.
#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. Construct an NFA for the example homomorphism given in the video applied to a "starter" DFA.
2. Can it be possible for a finite language L to have h(L) be infinite?
3. Can it be possible for an infinite language L to have h(L) be finite?
▶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 reasonin
...
https://www.youtube.com/watch?v=U_cdiPfykTI
Credit: https://cs.stackexchange.com/a/60791
Here we give an involved proof to give strong evidence that there is no "pumping lemma for context-sensitive languages." The idea is that if there is one, then one can show that the "infinity" problem for that model is recognizable, but this is impossible for CSLs because that problem is unrecognizable (as we prove with linear bounded automata).
Timeline:
0:00 - Intro
1:20 - What does a "pumping lemma" mean?
6:45 - If the predicate exists, then Infinity Problem is recognizable
13:43 - Infinity Problem for LBAs is not recognizable
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:
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=nOJlfXGoqEQ