-
Emil Leon Post
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Emil Leon Post
=======Image-Copyright-Info=======
Image is in public domainImage Source: https://en.wikipedia.org/wiki/File:Emil_Leon_Post.jpg
=======Image-Copyright-Info========
☆Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
published: 06 Jan 2016
-
Celebrating Emil Post & His "Intractable Problem" of Tag: 100 Years Later
100 years after combinators were first presented, Stephen Wolfram unveils the latest computational results along with some special guests. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More: https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more
Get involved with Charity Engine + Wolfram https://www.charityengine.com/wolfram
Post Tag System on GitHub: https://github.com/maxitg/PostTagSystem
See the announcement blog for the combinator centennial: https://writings.stephenwolfram.com/2020/12/combinators-a-centennial-view/
Combinators and the Story of Computation: https://writings.stephenwolfram.com/2020/12/combinators-and-the-story-of...
published: 19 May 2021
-
Marvin Minsky - Solving Emil Post's problem (72/151)
To hear more of Marvin Minsky’s stories, go to the playlist: https://www.youtube.com/watch?v=CB2SsvcECzI&list=PLVV0r6CmEsFxJatFYBb7P4NZscvJw1f0r
The scientist, Marvin Minsky (1927-2016) was one of the pioneers of the field of Artificial Intelligence, having founded the MIT AI Lab in 1970. Since the 1950s, his work involved trying to uncover human thinking processes and replicate them in machines. [Listener: Christopher Sykes; date recorded: 2011]
TRANSCRIPT: I’m trying to think of a few parallels, but generally, if you’re very good at something and you find somebody who’s better, then you should figure out something else your skill set is good for and it turned out that I was also interested in the foundations of logic and computation and I had discovered some interesting things about th...
published: 01 Nov 2016
-
The Post Correspondence Problem
TOC: The Post Correspondence Problem
Topics discussed:
1. The Post Correspondence Problem
2. Examples of The Post Correspondence Problem
3. Undecidability of The Post Correspondence Problem
Contribute: http://www.nesoacademy.org/donate
Website ► http://www.nesoacademy.org/
Forum ► http://forum.nesoacademy.org/
Facebook ► https://goo.gl/Nt0PmB
Twitter ► https://twitter.com/nesoacademy
Pinterest ► http://www.pinterest.com/nesoacademy/
Music:
Axol x Alex Skrindo - You [NCS Release]
published: 08 Feb 2018
-
Robotic Tag System (Post machine)
A "tag system" is a formal grammar system proposed by Emil L. Post in 1920 to prove computability and undecidability. The system is based on substitution of binary symbols with binary strings. The robot is constructed with modular robots (Cubelets) and LEGO pieces.
The robot executes four operations of the Post tag system: 0 - 00, 1 - 1101, v=3, starting with the string 1001 which becomes periodic in the fourth iteration.
1001
11101
011101
10100
001101 *
10100
We analyze four different initial conditions from which the robot can reach one of the following states:
00011 - halt
100 - periodic
1001 - periodic
10011 - ?
Note that a robotic Turing machine was constructed with Cubelets, published in https://youtu.be/GIQDA5Gnxkc
References.
1. Post, E.L. (1921). Introdu...
published: 30 Aug 2021
-
The Post Correspondence Problem (PCP)
In this video, we discuss another Turing complete computation model which is based on dominoes. It is known as the Post Correspondence Problem, or PCP for short. PCP is interesting because we can study several PCP variants. Some of these variants are powerful enough to include undecidable problems, others are NP-complete, and others can be solved efficiently with a simple algorithm. So PCP nicely spans the whole spectrum of computation.
published: 15 Dec 2022
-
Computation ep34: The Post Correspondence Problem (Apr 25, 2023)
This is a recording of a live class for Theory of Computation (Math 3342), an undergraduate course for math and computing majors at Fairfield University, Spring 2023.
Class website: http://faculty.fairfield.edu/cstaecker/courses/2023s3342/
Videos playlist: https://www.youtube.com/playlist?list=PLqObMWX4M-IfnvzJtNzlnLMyYLy0G9cwi
Chris Staecker main Youtube channel: https://www.youtube.com/chrisstaecker
Past courses playlists:
Mathematics: an Exploration (Fall 2022): A mathematical topics course for nontechnical majors. Includes voting, gerrymandering, and graph theory. https://www.youtube.com/playlist?list=PLqObMWX4M-If62VzwYaqrzYylGLqnHj6t
Applied Calculus 1 (Spring 2021): mostly derivatives and integrals, meant for business, health, science students. https://www.youtube.com/playlist?...
published: 25 Apr 2023
-
Post Correspondence Problem: A Fun and Easy Way to Learn About Computational Complexity
In this video, we will discuss the Post Correspondence Problem (PCP). The PCP is an undecidable decision problem that was introduced by Emil Post in 1946.
The PCP is defined as follows:
Given a set of strings, is there a way to match them up so that the corresponding symbols are equal?
For example, the following set of strings can be matched up:
Code snippet
aabb
ccdd
Use code with caution. Learn more
We can match them up as follows:
Code snippet
a ↔ c
b ↔ c
b ↔ d
Use code with caution. Learn more
The corresponding symbols are equal in each case, so this is a valid match.
However, the following set of strings cannot be matched up:
Code snippet
aabb
ccdd
ee
Use code with caution. Learn more
There is no way to match up these strings so that the corresponding symbols are equal.
The PC...
published: 31 May 2023
-
CS422 Theory of Computation, Chapter 2e
Post's Problem and Friedberg/Muchnik Finite Injury Priority Diagonalization
published: 15 Oct 2021
-
Theory of Computation - Post Correspondence Problem
published: 07 Jun 2021
5:43
Emil Leon Post
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Emil Leon Post
=======Image-Copy...
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Emil Leon Post
=======Image-Copyright-Info=======
Image is in public domainImage Source: https://en.wikipedia.org/wiki/File:Emil_Leon_Post.jpg
=======Image-Copyright-Info========
☆Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://wn.com/Emil_Leon_Post
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Emil Leon Post
=======Image-Copyright-Info=======
Image is in public domainImage Source: https://en.wikipedia.org/wiki/File:Emil_Leon_Post.jpg
=======Image-Copyright-Info========
☆Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
- published: 06 Jan 2016
- views: 389
3:42:00
Celebrating Emil Post & His "Intractable Problem" of Tag: 100 Years Later
100 years after combinators were first presented, Stephen Wolfram unveils the latest computational results along with some special guests. After 100 Years, Can ...
100 years after combinators were first presented, Stephen Wolfram unveils the latest computational results along with some special guests. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More: https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more
Get involved with Charity Engine + Wolfram https://www.charityengine.com/wolfram
Post Tag System on GitHub: https://github.com/maxitg/PostTagSystem
See the announcement blog for the combinator centennial: https://writings.stephenwolfram.com/2020/12/combinators-a-centennial-view/
Combinators and the Story of Computation: https://writings.stephenwolfram.com/2020/12/combinators-and-the-story-of-computation/
Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel: https://writings.stephenwolfram.com/2020/12/where-did-combinators-come-from-hunting-the-story-of-moses-schonfinkel/
Originally livestreamed at: https://twitch.tv/stephen_wolfram
Follow us on our official social media channels.
Twitter: https://twitter.com/WolframResearch/
Facebook: https://www.facebook.com/wolframresearch/
Instagram: https://www.instagram.com/wolframresearch/
LinkedIn: https://www.linkedin.com/company/wolfram-research/
Contribute to the official Wolfram Community: https://community.wolfram.com/
Stay up-to-date on the latest interest at Wolfram Research through our blog: https://blog.wolfram.com/
Follow Stephen Wolfram's life, interests, and what makes him tick on his blog: https://writings.stephenwolfram.com/
https://wn.com/Celebrating_Emil_Post_His_Intractable_Problem_Of_Tag_100_Years_Later
100 years after combinators were first presented, Stephen Wolfram unveils the latest computational results along with some special guests. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More: https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more
Get involved with Charity Engine + Wolfram https://www.charityengine.com/wolfram
Post Tag System on GitHub: https://github.com/maxitg/PostTagSystem
See the announcement blog for the combinator centennial: https://writings.stephenwolfram.com/2020/12/combinators-a-centennial-view/
Combinators and the Story of Computation: https://writings.stephenwolfram.com/2020/12/combinators-and-the-story-of-computation/
Where Did Combinators Come From? Hunting the Story of Moses Schönfinkel: https://writings.stephenwolfram.com/2020/12/where-did-combinators-come-from-hunting-the-story-of-moses-schonfinkel/
Originally livestreamed at: https://twitch.tv/stephen_wolfram
Follow us on our official social media channels.
Twitter: https://twitter.com/WolframResearch/
Facebook: https://www.facebook.com/wolframresearch/
Instagram: https://www.instagram.com/wolframresearch/
LinkedIn: https://www.linkedin.com/company/wolfram-research/
Contribute to the official Wolfram Community: https://community.wolfram.com/
Stay up-to-date on the latest interest at Wolfram Research through our blog: https://blog.wolfram.com/
Follow Stephen Wolfram's life, interests, and what makes him tick on his blog: https://writings.stephenwolfram.com/
- published: 19 May 2021
- views: 121187
3:01
Marvin Minsky - Solving Emil Post's problem (72/151)
To hear more of Marvin Minsky’s stories, go to the playlist: https://www.youtube.com/watch?v=CB2SsvcECzI&list=PLVV0r6CmEsFxJatFYBb7P4NZscvJw1f0r
The scientist,...
To hear more of Marvin Minsky’s stories, go to the playlist: https://www.youtube.com/watch?v=CB2SsvcECzI&list=PLVV0r6CmEsFxJatFYBb7P4NZscvJw1f0r
The scientist, Marvin Minsky (1927-2016) was one of the pioneers of the field of Artificial Intelligence, having founded the MIT AI Lab in 1970. Since the 1950s, his work involved trying to uncover human thinking processes and replicate them in machines. [Listener: Christopher Sykes; date recorded: 2011]
TRANSCRIPT: I’m trying to think of a few parallels, but generally, if you’re very good at something and you find somebody who’s better, then you should figure out something else your skill set is good for and it turned out that I was also interested in the foundations of logic and computation and I had discovered some interesting things about that... and then... a mathematician named Martin Davis, who had been a friend of mine for some years, told me about a problem that was... had been generated by a professor at NYU, Emil Post, in the 1920s and he wrote a paper in 1923 conjecturing something about a certain kind of logical system and... long before Alan Turing had published anything, Post had published something about how he thought maybe this was an unsolvable problem. Also Gödel had... Gödel was 1931 and Gödel had the first proof of what’s called a recursively unsolvable problem, but Post had sort of pioneered in that area in the 1920s and discovered something which he conjectured was unsolvable, but Gödel was the first one to prove anything and then Turing in 1936 – Alan Turing – had come up with a much simpler proof of an unsolvable problem that... something that a computer couldn’t do and I didn’t know about Post’s work, but Martin Davis had been a student of him at... at NYU and out of the blue Davis phoned me and said: 'There’s a problem that Emil Post and I couldn’t solve, but I think you might have the skill set for that.' The funny part is that I mentioned this to Davis a few years ago and he said: 'I... I never did that, I don’t remember telling you.' But I remember fairly clearly that I never heard of Post’s problem and that Davis told me about it because he thought that I might be able to solve it and indeed I did. So I published a paper in 1961 solving this interesting old problem of Emil Post.
https://wn.com/Marvin_Minsky_Solving_Emil_Post's_Problem_(72_151)
To hear more of Marvin Minsky’s stories, go to the playlist: https://www.youtube.com/watch?v=CB2SsvcECzI&list=PLVV0r6CmEsFxJatFYBb7P4NZscvJw1f0r
The scientist, Marvin Minsky (1927-2016) was one of the pioneers of the field of Artificial Intelligence, having founded the MIT AI Lab in 1970. Since the 1950s, his work involved trying to uncover human thinking processes and replicate them in machines. [Listener: Christopher Sykes; date recorded: 2011]
TRANSCRIPT: I’m trying to think of a few parallels, but generally, if you’re very good at something and you find somebody who’s better, then you should figure out something else your skill set is good for and it turned out that I was also interested in the foundations of logic and computation and I had discovered some interesting things about that... and then... a mathematician named Martin Davis, who had been a friend of mine for some years, told me about a problem that was... had been generated by a professor at NYU, Emil Post, in the 1920s and he wrote a paper in 1923 conjecturing something about a certain kind of logical system and... long before Alan Turing had published anything, Post had published something about how he thought maybe this was an unsolvable problem. Also Gödel had... Gödel was 1931 and Gödel had the first proof of what’s called a recursively unsolvable problem, but Post had sort of pioneered in that area in the 1920s and discovered something which he conjectured was unsolvable, but Gödel was the first one to prove anything and then Turing in 1936 – Alan Turing – had come up with a much simpler proof of an unsolvable problem that... something that a computer couldn’t do and I didn’t know about Post’s work, but Martin Davis had been a student of him at... at NYU and out of the blue Davis phoned me and said: 'There’s a problem that Emil Post and I couldn’t solve, but I think you might have the skill set for that.' The funny part is that I mentioned this to Davis a few years ago and he said: 'I... I never did that, I don’t remember telling you.' But I remember fairly clearly that I never heard of Post’s problem and that Davis told me about it because he thought that I might be able to solve it and indeed I did. So I published a paper in 1961 solving this interesting old problem of Emil Post.
- published: 01 Nov 2016
- views: 5028
14:29
The Post Correspondence Problem
TOC: The Post Correspondence Problem
Topics discussed:
1. The Post Correspondence Problem
2. Examples of The Post Correspondence Problem
3. Undecidability of Th...
TOC: The Post Correspondence Problem
Topics discussed:
1. The Post Correspondence Problem
2. Examples of The Post Correspondence Problem
3. Undecidability of The Post Correspondence Problem
Contribute: http://www.nesoacademy.org/donate
Website ► http://www.nesoacademy.org/
Forum ► http://forum.nesoacademy.org/
Facebook ► https://goo.gl/Nt0PmB
Twitter ► https://twitter.com/nesoacademy
Pinterest ► http://www.pinterest.com/nesoacademy/
Music:
Axol x Alex Skrindo - You [NCS Release]
https://wn.com/The_Post_Correspondence_Problem
TOC: The Post Correspondence Problem
Topics discussed:
1. The Post Correspondence Problem
2. Examples of The Post Correspondence Problem
3. Undecidability of The Post Correspondence Problem
Contribute: http://www.nesoacademy.org/donate
Website ► http://www.nesoacademy.org/
Forum ► http://forum.nesoacademy.org/
Facebook ► https://goo.gl/Nt0PmB
Twitter ► https://twitter.com/nesoacademy
Pinterest ► http://www.pinterest.com/nesoacademy/
Music:
Axol x Alex Skrindo - You [NCS Release]
- published: 08 Feb 2018
- views: 330922
4:15
Robotic Tag System (Post machine)
A "tag system" is a formal grammar system proposed by Emil L. Post in 1920 to prove computability and undecidability. The system is based on substitution of bin...
A "tag system" is a formal grammar system proposed by Emil L. Post in 1920 to prove computability and undecidability. The system is based on substitution of binary symbols with binary strings. The robot is constructed with modular robots (Cubelets) and LEGO pieces.
The robot executes four operations of the Post tag system: 0 - 00, 1 - 1101, v=3, starting with the string 1001 which becomes periodic in the fourth iteration.
1001
11101
011101
10100
001101 *
10100
We analyze four different initial conditions from which the robot can reach one of the following states:
00011 - halt
100 - periodic
1001 - periodic
10011 - ?
Note that a robotic Turing machine was constructed with Cubelets, published in https://youtu.be/GIQDA5Gnxkc
References.
1. Post, E.L. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics, 43(3), 163-185.
2. Post, E.L. (1943). Formal reductions of the general combinatorial decision problem. American Journal of Mathematics, 65(2), 197-215.
3. Davis, M. (Ed.) (1994). Solvability, Provability, Definability: The Collected Works of Emil L. Post. Birkhauser.
4. Figueroa, R.Q., Zamorano, D.A., Martínez, G.J., & Adamatzky, A. (2019). A Turing machine constructed with Cubelets robots. Journal of Robotics, Networking and Artificial Life, 5(4), 265-268.
5. Celebrating Emil Post & His "Intractable Problem" of Tag: 100 Years Later. YouTube: https://youtu.be/ultMxODJE7o
6. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More. URL: https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more/
https://wn.com/Robotic_Tag_System_(Post_Machine)
A "tag system" is a formal grammar system proposed by Emil L. Post in 1920 to prove computability and undecidability. The system is based on substitution of binary symbols with binary strings. The robot is constructed with modular robots (Cubelets) and LEGO pieces.
The robot executes four operations of the Post tag system: 0 - 00, 1 - 1101, v=3, starting with the string 1001 which becomes periodic in the fourth iteration.
1001
11101
011101
10100
001101 *
10100
We analyze four different initial conditions from which the robot can reach one of the following states:
00011 - halt
100 - periodic
1001 - periodic
10011 - ?
Note that a robotic Turing machine was constructed with Cubelets, published in https://youtu.be/GIQDA5Gnxkc
References.
1. Post, E.L. (1921). Introduction to a general theory of elementary propositions. American Journal of Mathematics, 43(3), 163-185.
2. Post, E.L. (1943). Formal reductions of the general combinatorial decision problem. American Journal of Mathematics, 65(2), 197-215.
3. Davis, M. (Ed.) (1994). Solvability, Provability, Definability: The Collected Works of Emil L. Post. Birkhauser.
4. Figueroa, R.Q., Zamorano, D.A., Martínez, G.J., & Adamatzky, A. (2019). A Turing machine constructed with Cubelets robots. Journal of Robotics, Networking and Artificial Life, 5(4), 265-268.
5. Celebrating Emil Post & His "Intractable Problem" of Tag: 100 Years Later. YouTube: https://youtu.be/ultMxODJE7o
6. After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More. URL: https://writings.stephenwolfram.com/2021/03/after-100-years-can-we-finally-crack-posts-problem-of-tag-a-story-of-computational-irreducibility-and-more/
- published: 30 Aug 2021
- views: 401
7:47
The Post Correspondence Problem (PCP)
In this video, we discuss another Turing complete computation model which is based on dominoes. It is known as the Post Correspondence Problem, or PCP for short...
In this video, we discuss another Turing complete computation model which is based on dominoes. It is known as the Post Correspondence Problem, or PCP for short. PCP is interesting because we can study several PCP variants. Some of these variants are powerful enough to include undecidable problems, others are NP-complete, and others can be solved efficiently with a simple algorithm. So PCP nicely spans the whole spectrum of computation.
https://wn.com/The_Post_Correspondence_Problem_(Pcp)
In this video, we discuss another Turing complete computation model which is based on dominoes. It is known as the Post Correspondence Problem, or PCP for short. PCP is interesting because we can study several PCP variants. Some of these variants are powerful enough to include undecidable problems, others are NP-complete, and others can be solved efficiently with a simple algorithm. So PCP nicely spans the whole spectrum of computation.
- published: 15 Dec 2022
- views: 2223
44:18
Computation ep34: The Post Correspondence Problem (Apr 25, 2023)
This is a recording of a live class for Theory of Computation (Math 3342), an undergraduate course for math and computing majors at Fairfield University, Spring...
This is a recording of a live class for Theory of Computation (Math 3342), an undergraduate course for math and computing majors at Fairfield University, Spring 2023.
Class website: http://faculty.fairfield.edu/cstaecker/courses/2023s3342/
Videos playlist: https://www.youtube.com/playlist?list=PLqObMWX4M-IfnvzJtNzlnLMyYLy0G9cwi
Chris Staecker main Youtube channel: https://www.youtube.com/chrisstaecker
Past courses playlists:
Mathematics: an Exploration (Fall 2022): A mathematical topics course for nontechnical majors. Includes voting, gerrymandering, and graph theory. https://www.youtube.com/playlist?list=PLqObMWX4M-If62VzwYaqrzYylGLqnHj6t
Applied Calculus 1 (Spring 2021): mostly derivatives and integrals, meant for business, health, science students. https://www.youtube.com/playlist?list=PLLFpXNanTP9XxRDr5SKZnUyrnhBztrcm5
Calculus 1 (Fall 2021): more theoretical calculus sequence, following Stewart's book closely. Limits, derivatives and integrals. https://www.youtube.com/playlist?list=PLLFpXNanTP9XNyWrue3PPjsih23EHmCGc
Calculus 2 (Spring 2021): continuation of the above. More integration, sequences & series. https://www.youtube.com/playlist?list=PLLFpXNanTP9V_gQsHSnfcR5Rs0Qg-joK0
Real Analysis (Fall 2022): first semester course in real analysis for upper-level math undergraduates. https://www.youtube.com/playlist?list=PLqObMWX4M-If-BQGaUP3eJhqbygoNy_kN
https://wn.com/Computation_Ep34_The_Post_Correspondence_Problem_(Apr_25,_2023)
This is a recording of a live class for Theory of Computation (Math 3342), an undergraduate course for math and computing majors at Fairfield University, Spring 2023.
Class website: http://faculty.fairfield.edu/cstaecker/courses/2023s3342/
Videos playlist: https://www.youtube.com/playlist?list=PLqObMWX4M-IfnvzJtNzlnLMyYLy0G9cwi
Chris Staecker main Youtube channel: https://www.youtube.com/chrisstaecker
Past courses playlists:
Mathematics: an Exploration (Fall 2022): A mathematical topics course for nontechnical majors. Includes voting, gerrymandering, and graph theory. https://www.youtube.com/playlist?list=PLqObMWX4M-If62VzwYaqrzYylGLqnHj6t
Applied Calculus 1 (Spring 2021): mostly derivatives and integrals, meant for business, health, science students. https://www.youtube.com/playlist?list=PLLFpXNanTP9XxRDr5SKZnUyrnhBztrcm5
Calculus 1 (Fall 2021): more theoretical calculus sequence, following Stewart's book closely. Limits, derivatives and integrals. https://www.youtube.com/playlist?list=PLLFpXNanTP9XNyWrue3PPjsih23EHmCGc
Calculus 2 (Spring 2021): continuation of the above. More integration, sequences & series. https://www.youtube.com/playlist?list=PLLFpXNanTP9V_gQsHSnfcR5Rs0Qg-joK0
Real Analysis (Fall 2022): first semester course in real analysis for upper-level math undergraduates. https://www.youtube.com/playlist?list=PLqObMWX4M-If-BQGaUP3eJhqbygoNy_kN
- published: 25 Apr 2023
- views: 86
12:13
Post Correspondence Problem: A Fun and Easy Way to Learn About Computational Complexity
In this video, we will discuss the Post Correspondence Problem (PCP). The PCP is an undecidable decision problem that was introduced by Emil Post in 1946.
The ...
In this video, we will discuss the Post Correspondence Problem (PCP). The PCP is an undecidable decision problem that was introduced by Emil Post in 1946.
The PCP is defined as follows:
Given a set of strings, is there a way to match them up so that the corresponding symbols are equal?
For example, the following set of strings can be matched up:
Code snippet
aabb
ccdd
Use code with caution. Learn more
We can match them up as follows:
Code snippet
a ↔ c
b ↔ c
b ↔ d
Use code with caution. Learn more
The corresponding symbols are equal in each case, so this is a valid match.
However, the following set of strings cannot be matched up:
Code snippet
aabb
ccdd
ee
Use code with caution. Learn more
There is no way to match up these strings so that the corresponding symbols are equal.
The PCP is undecidable, which means that there is no algorithm that can determine, given a set of strings, whether or not they can be matched up.
The PCP is an important problem in theoretical computer science. It is used to prove the undecidability of other problems, such as the halting problem.
If you are interested in learning more about the Post Correspondence Problem, this video is a great place to start.
https://wn.com/Post_Correspondence_Problem_A_Fun_And_Easy_Way_To_Learn_About_Computational_Complexity
In this video, we will discuss the Post Correspondence Problem (PCP). The PCP is an undecidable decision problem that was introduced by Emil Post in 1946.
The PCP is defined as follows:
Given a set of strings, is there a way to match them up so that the corresponding symbols are equal?
For example, the following set of strings can be matched up:
Code snippet
aabb
ccdd
Use code with caution. Learn more
We can match them up as follows:
Code snippet
a ↔ c
b ↔ c
b ↔ d
Use code with caution. Learn more
The corresponding symbols are equal in each case, so this is a valid match.
However, the following set of strings cannot be matched up:
Code snippet
aabb
ccdd
ee
Use code with caution. Learn more
There is no way to match up these strings so that the corresponding symbols are equal.
The PCP is undecidable, which means that there is no algorithm that can determine, given a set of strings, whether or not they can be matched up.
The PCP is an important problem in theoretical computer science. It is used to prove the undecidability of other problems, such as the halting problem.
If you are interested in learning more about the Post Correspondence Problem, this video is a great place to start.
- published: 31 May 2023
- views: 15
1:13:19
CS422 Theory of Computation, Chapter 2e
Post's Problem and Friedberg/Muchnik Finite Injury Priority Diagonalization
Post's Problem and Friedberg/Muchnik Finite Injury Priority Diagonalization
https://wn.com/Cs422_Theory_Of_Computation,_Chapter_2E
Post's Problem and Friedberg/Muchnik Finite Injury Priority Diagonalization
- published: 15 Oct 2021
- views: 176