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Theory of Computation: Partially Computable and Computable Functions (Part 01)
Theory of Computation: Partially Computable and Computable Functions (Part 01) -
Theory of Computation: Partially Computable and Computable Functions (Part 02)
Theory of Computation: Partially Computable and Computable Functions (Part 02)Theory of Computation: Partially Computable and Computable Functions (Part 02)
1) Partially computable functions 2) Computable functions 3) Class web page is at http://vkedco.blogspot.com/2011/08/theory-of-computation-home.html 4) Video... -
Computable Functions
Computable FunctionsComputable Functions
Computable Functions -
All About - Computable function
All About - Computable functionAll About - Computable function
What is Computable function? A report all about Computable function for homework/assignment Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithm. They are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions.Particular models of computability that give rise to the set of computable functions are the Turing-computa -
Lambda Calculus Then and Now
Lambda Calculus Then and NowLambda Calculus Then and Now
Talk by ACM A.M. Turing Laureate Dana S. Scott during the ACM A.M. Turing Centenary Celebration, June, 2012. Abstract: A very fast development in the early 1... -
Math 574, Lesson 2-4: Computable Functions
Math 574, Lesson 2-4: Computable FunctionsMath 574, Lesson 2-4: Computable Functions
Math 574, Topics in Logic Penn State, Spring 2014 Instructor: Jan Reimann -
Mod-11 Lec-02 Turing Computable Functions
Mod-11 Lec-02 Turing Computable FunctionsMod-11 Lec-02 Turing Computable Functions
Formal Languages and Automata Theory by Dr. Diganta Goswami & Dr. K.V. Krishna,Department of Mathematics,IIT Guwahati.For more details on NPTEL visit http://nptel.ac.in. -
Primitive recursive function
Primitive recursive functionPrimitive recursive function
In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive). Primitive recursive functions form an important building block on the way to a full formalization of computability. These functions are also important in proof theory. The term was coined by Rózsa Péter. Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all prim -
All About - Computability theory
All About - Computability theoryAll About - Computability theory
What is Computability theory? A report all about Computability theory for homework/assignment Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. Intro/Outro music: Discovery Hit/Chucky the Construction Worker - Kevin MacLeod (incompetech.com) Licensed under CC-BY-3.0 Text derived from: http://en.wikipedia.org/wiki/Computability_theory Text to Speech powered by voice-rss.com Images are Public Domain or CC-BY-3.0: 700px-Theoretical_computer_science.s -
Theory of Computation: Composition and Recursion (Part 01)
Theory of Computation: Composition and Recursion (Part 01)Theory of Computation: Composition and Recursion (Part 01)
1) Scientific theories, primitives, and constructive devices 2) Function composition 3) Function composition of partially computable functions is partially c... -
Theory of Computation: Composition and Recursion (Part 02)
Theory of Computation: Composition and Recursion (Part 02)Theory of Computation: Composition and Recursion (Part 02)
1. Examples of showing that functions obtained from computable functions by composition are computable 2. Definition of primitive recursion (recursion) 3. Vi... -
Theory of Computation: Composition and Recursion (Part 04)
Theory of Computation: Composition and Recursion (Part 04)Theory of Computation: Composition and Recursion (Part 04)
1. A constructive method of obtaining a total function from two other total functions by primitive recursion 2. Primitive recursion preserves computability: ... -
Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)
Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)
1. Composition and primitive recursion as constructive methods 2. Does primitive recursion define computability? 3. Three primitives of the theory of primiti... -
MindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theorem
MindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theoremMindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theorem
A quick summary of Kripke's recent argument that the Church-Turing thesis, which is the claim that any effectively or algorithmically computable function can...
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11:18
Theory of Computation: Partially Computable and Computable Functions (Part 01)
1. Partial functions 2. Partially computable functions 3. Class web page is at http://vked...
published: 05 Oct 2011
author: vkedco
Theory of Computation: Partially Computable and Computable Functions (Part 01)
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Theory of Computation: Partially Computable and Computable Functions (Part 01)
- published: 05 Oct 2011
- views: 1621
- author: vkedco
1. Partial functions 2. Partially computable functions 3. Class web page is at http://vkedco.blogspot.com/2011/08/theory-of-computation-home.html 4. Referenc...
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8:35
Theory of Computation: Partially Computable and Computable Functions (Part 02)
1) Partially computable functions 2) Computable functions 3) Class web page is at http://v...
published: 05 Oct 2011
author: vkedco
Theory of Computation: Partially Computable and Computable Functions (Part 02)
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Theory of Computation: Partially Computable and Computable Functions (Part 02)
- published: 05 Oct 2011
- views: 374
- author: vkedco
1) Partially computable functions 2) Computable functions 3) Class web page is at http://vkedco.blogspot.com/2011/08/theory-of-computation-home.html 4) Video...
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1:49
Computable Functions
Computable Functions...
published: 13 Nov 2014
Computable Functions
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3:02
All About - Computable function
What is Computable function?
A report all about Computable function for homework/assignme...
published: 09 Dec 2014
All About - Computable function
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All About - Computable function
- published: 09 Dec 2014
- views: 1
What is Computable function? A report all about Computable function for homework/assignment Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithm. They are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions.Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the μ-recursive functions. Intro/Outro music: Discovery Hit/Chucky the Construction Worker - Kevin MacLeod (incompetech.com) Licensed under CC-BY-3.0 Text derived from: http://en.wikipedia.org/wiki/Computable_function Text to Speech powered by voice-rss.com Images are Public Domain or CC-BY-3.0: 8586176dbfebb230dc8e4e0db9aa4367.png from http://en.wikipedia.org/wiki/Halting_problem d5b3e6a28a5ec1f8bdacb84a160cf3fe.png from http://en.wikipedia.org/wiki/Computable_number e7710ec5d5880a8b7114bc4471b84da7.png from http://en.wikipedia.org/wiki/Computable_number 500px-Universal_Turing_machine.svg.png from http://en.wikipedia.org/wiki/Universal_Turing_machine 9dd6c05179403906880d2c028164cea8.png from http://en.wikipedia.org/wiki/Computable_function
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30:08
Lambda Calculus Then and Now
Talk by ACM A.M. Turing Laureate Dana S. Scott during the ACM A.M. Turing Centenary Celebr...
published: 23 Jan 2013
author: TheOfficialACM
Lambda Calculus Then and Now
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Lambda Calculus Then and Now
- published: 23 Jan 2013
- views: 2050
- author: TheOfficialACM
Talk by ACM A.M. Turing Laureate Dana S. Scott during the ACM A.M. Turing Centenary Celebration, June, 2012. Abstract: A very fast development in the early 1...
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19:55
Math 574, Lesson 2-4: Computable Functions
Math 574, Topics in Logic
Penn State, Spring 2014
Instructor: Jan Reimann...
published: 13 Feb 2015
Math 574, Lesson 2-4: Computable Functions
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Math 574, Lesson 2-4: Computable Functions
- published: 13 Feb 2015
- views: 17
Math 574, Topics in Logic Penn State, Spring 2014 Instructor: Jan Reimann
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54:27
Mod-11 Lec-02 Turing Computable Functions
Formal Languages and Automata Theory by Dr. Diganta Goswami & Dr. K.V. Krishna,Department ...
published: 26 Nov 2014
Mod-11 Lec-02 Turing Computable Functions
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Mod-11 Lec-02 Turing Computable Functions
- published: 26 Nov 2014
- views: 27
Formal Languages and Automata Theory by Dr. Diganta Goswami & Dr. K.V. Krishna,Department of Mathematics,IIT Guwahati.For more details on NPTEL visit http://nptel.ac.in.
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24:25
Primitive recursive function
In computability theory, primitive recursive functions are a class of functions that are d...
published: 14 Nov 2014
Primitive recursive function
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Primitive recursive function
- published: 14 Nov 2014
- views: 13
In computability theory, primitive recursive functions are a class of functions that are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive). Primitive recursive functions form an important building block on the way to a full formalization of computability. These functions are also important in proof theory. The term was coined by Rózsa Péter. Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a computable function that is not primitive recursive, although some are known (see the section on Limitations below). The set of primitive recursive functions is known as PR in computational complexity theory. This video is targeted to blind users. Attribution: Article text available under CC-BY-SA Creative Commons image source in video
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3:42
All About - Computability theory
What is Computability theory?
A report all about Computability theory for homework/assign...
published: 09 Dec 2014
All About - Computability theory
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All About - Computability theory
- published: 09 Dec 2014
- views: 0
What is Computability theory? A report all about Computability theory for homework/assignment Computability theory, also called recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. Intro/Outro music: Discovery Hit/Chucky the Construction Worker - Kevin MacLeod (incompetech.com) Licensed under CC-BY-3.0 Text derived from: http://en.wikipedia.org/wiki/Computability_theory Text to Speech powered by voice-rss.com Images are Public Domain or CC-BY-3.0: 700px-Theoretical_computer_science.svg.png from http://en.wikipedia.org/wiki/Computational_complexity_theory da5c99015af56028f27cac4d03bc634f.png from http://en.wikipedia.org/wiki/Computability_theory Barry_Cooper.jpg from http://en.wikipedia.org/wiki/S._Barry_Cooper Maquina.png from http://en.wikipedia.org/wiki/Theory_of_computation 1200px-Theoretical_computer_science.svg.png from http://en.wikipedia.org/wiki/Wikipedia_talk:WikiProject_Computer_science/Archive_8 64cb0da20570d65cab34484bf9a17a41.png from http://en.wikipedia.org/wiki/Low_basis_theorem 79ab2d1eb181c17ad36b507fd313bf4d.png from http://en.wikipedia.org/wiki/Counting_problem_(complexity)
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13:46
Theory of Computation: Composition and Recursion (Part 01)
1) Scientific theories, primitives, and constructive devices 2) Function composition 3) Fu...
published: 05 Oct 2011
author: vkedco
Theory of Computation: Composition and Recursion (Part 01)
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Theory of Computation: Composition and Recursion (Part 01)
- published: 05 Oct 2011
- views: 1273
- author: vkedco
1) Scientific theories, primitives, and constructive devices 2) Function composition 3) Function composition of partially computable functions is partially c...
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12:12
Theory of Computation: Composition and Recursion (Part 02)
1. Examples of showing that functions obtained from computable functions by composition ar...
published: 10 Oct 2011
author: vkedco
Theory of Computation: Composition and Recursion (Part 02)
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Theory of Computation: Composition and Recursion (Part 02)
- published: 10 Oct 2011
- views: 468
- author: vkedco
1. Examples of showing that functions obtained from computable functions by composition are computable 2. Definition of primitive recursion (recursion) 3. Vi...
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9:52
Theory of Computation: Composition and Recursion (Part 04)
1. A constructive method of obtaining a total function from two other total functions by p...
published: 19 Oct 2011
author: vkedco
Theory of Computation: Composition and Recursion (Part 04)
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Theory of Computation: Composition and Recursion (Part 04)
- published: 19 Oct 2011
- views: 346
- author: vkedco
1. A constructive method of obtaining a total function from two other total functions by primitive recursion 2. Primitive recursion preserves computability: ...
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14:13
Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)
1. Composition and primitive recursion as constructive methods 2. Does primitive recursion...
published: 20 Oct 2011
author: vkedco
Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)
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Theory of Computation: Primitive Recrusively Closed Classes of Functions (Part 01)
- published: 20 Oct 2011
- views: 592
- author: vkedco
1. Composition and primitive recursion as constructive methods 2. Does primitive recursion define computability? 3. Three primitives of the theory of primiti...
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1:07
MindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theorem
A quick summary of Kripke's recent argument that the Church-Turing thesis, which is the cl...
published: 24 May 2014
author: spacetimemind
MindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theorem
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MindChunk: Kripke on the Church-Turing Thesis as a corollary of Goedel's Completeness theorem
- published: 24 May 2014
- views: 37
- author: spacetimemind
A quick summary of Kripke's recent argument that the Church-Turing thesis, which is the claim that any effectively or algorithmically computable function can...
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12:37
Theory of Computation: Composition and Primitive Recursion (Part 03)
1. Primitive recursion 2. If a function is obtained from a computable function by primitiv...
published: 17 Oct 2011
author: vkedco
Theory of Computation: Composition and Primitive Recursion (Part 03)
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Theory of Computation: Composition and Primitive Recursion (Part 03)
- published: 17 Oct 2011
- views: 417
- author: vkedco
1. Primitive recursion 2. If a function is obtained from a computable function by primitive recursion, the function is computable 3. Course web page is at ht...
Theory of Computation: Composition and Primitive Recursion (Part 03)
Published: 17 Oct 2011
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53:24
CSEDays. Theory 2013. Kolmogorov complexity and bacis things (Alexander Shen). 1day (part I)
Kolmogorov complexity of a binary string x is defined as the minimal length of a program t...
published: 19 Jul 2013
CSEDays. Theory 2013. Kolmogorov complexity and bacis things (Alexander Shen). 1day (part I)
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CSEDays. Theory 2013. Kolmogorov complexity and bacis things (Alexander Shen). 1day (part I)
- published: 19 Jul 2013
- views: 744
Kolmogorov complexity of a binary string x is defined as the minimal length of a program that produces x. This quantity depends on the programming language, but the difference is O(1) if we choose different optimal languages. The Kolmogorov complexity K(x), informally speaking, is the quantity of information in x, measured in bits. It can be used to define other information notions; for example, the amount of mutual information between x and y can be defined as K(x)+K(y)-K(x,y). In this way we get an information theory version for individual strings which is somehow parallel to the Shannon information theory (for random variables). We can prove some information inequalities (in fact, the same that are true for Shannon entropy, as Romashchenko has shown); some other results (e.g., Slepian-Wolf theorem about conditional coding, or the problem of common information) also have interesting counterparts in algorithmic information theory. Kolmogorov complexity theory can be considered as a part of general computation theory (=recursion theory); for example, one can show that Kolmogorov complexity is not a computable function, and, moreover, we can solve halting program if somebody tells us Kolmogorov complexities of all strings. The classical probability theory is a well-established mathematical theory, but its relation to the "real world" is not so clear. Why we reject the hypothesis of a fair coin seeing the sequence 010101010... of 1000 alternating zeros and ones, and at the same time are ready to believe in the fairness of the coin for some other sequences of observations? Any two sequences have the same probability, so why some of them are random-looking while others are not? One of the explanations is the difference in complexity. One can formally define a notion of a random individual (infinite) sequence of zeros and ones (it was done by Martin-L), and this notion can be equivalently characterized in terms of complexity. The Kolmogorov complexity can be used as a language that replaces probabilistic arguments in the existence proofs (and this sometimes makes them easier or more intuitive). For example, there is a very nice proof of effective Lovasz local lemma that uses Kolmogorov complexity. After introducing the basic notions, I will try to cover some of these results (depending on the interests of the audience). No special background is assumed, but you should not be afraid of words "computable function" or "random variable".
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45:19
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part I)
Kolmogorov complexity of a binary string x is defined as the minimal length of a program t...
published: 02 Aug 2013
author: Контур Студент
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part I)
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CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part I)
- published: 02 Aug 2013
- views: 100
- author: Контур Студент
Kolmogorov complexity of a binary string x is defined as the minimal length of a program that produces x. This quantity depends on the programming language, ...
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45:50
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 2day (part I)
Kolmogorov complexity of a binary string x is defined as the minimal length of a program t...
published: 02 Aug 2013
author: Контур Студент
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 2day (part I)
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CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 2day (part I)
- published: 02 Aug 2013
- views: 229
- author: Контур Студент
Kolmogorov complexity of a binary string x is defined as the minimal length of a program that produces x. This quantity depends on the programming language, ...
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55:00
BalCCon2k14 - Bernd Fix - Post-Quantum Crypto
The security of asymmetric crypto algorithms today like RSA and ECC is based on mathematic...
published: 13 Dec 2014
BalCCon2k14 - Bernd Fix - Post-Quantum Crypto
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BalCCon2k14 - Bernd Fix - Post-Quantum Crypto
- published: 13 Dec 2014
- views: 26
The security of asymmetric crypto algorithms today like RSA and ECC is based on mathematical operations, that have no computable "reverse function" in classical mathematics. Shor (1994) has shown that both algorithms can be broken by using a quantum computer – and the development in this field has speed up during the last years commercial systems today work with 500 and more Q bits (although adiabatic and not as an ideal quantum computer). Therefore it is time to focus our attention on post-quantum cryptology that is not compromised by quantum computers. If we don't start today, we will probably not be ready if we really need the new algorithms…
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6:12
Teori Bahasa dan Otomata - Mesin Turing
Teori Bahasa dan Otomata - Mesin Turing
Mesin Turing adalah model komputasi teoritis yang...
published: 12 Jan 2015
Teori Bahasa dan Otomata - Mesin Turing
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Teori Bahasa dan Otomata - Mesin Turing
- published: 12 Jan 2015
- views: 2
Teori Bahasa dan Otomata - Mesin Turing Mesin Turing adalah model komputasi teoritis yang ditemukan oleh Alan Turing, berfungsi sebagai model ideal untuk melakukan perhitungan matematis. Walaupun model ideal ini diperkenalkan sebelum komputer nyata dibangun, model ini tetap diterima kalangan ilmu komputer sebagai model komputer yang sesuai untuk menentukan apakah suatu fungsi dapat selesaikan oleh komputer atau tidak (menentukan computable function). Mesin Turing terkenal dengan ungkapan ” Apapun yang bisa dilakukan oleh Mesin Turing pasti bisa dilakukan oleh komputer.”
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17:57
Busy Beaver Turing Machines - Computerphile
The Busy Beaver game, pointless? Or a lesson in the problems of computability? - How do yo...
published: 02 Sep 2014
author: Computerphile
Busy Beaver Turing Machines - Computerphile
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Busy Beaver Turing Machines - Computerphile
- published: 02 Sep 2014
- views: 28992
- author: Computerphile
The Busy Beaver game, pointless? Or a lesson in the problems of computability? - How do you decide if something can be computed or not? Professor Brailsford's code and further reading: http://bit....
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39:32
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 1day (part II)
Kolmogorov complexity of a binary string x is defined as the minimal length of a program t...
published: 02 Aug 2013
author: Контур Студент
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 1day (part II)
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CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 1day (part II)
- published: 02 Aug 2013
- views: 133
- author: Контур Студент
Kolmogorov complexity of a binary string x is defined as the minimal length of a program that produces x. This quantity depends on the programming language, ...
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8:31
ULTRATERRESTRIAL TRANSPONDER LIVE: "THIS IS NEW ATLANTIS" (1/4)
"The Shiv tattava (Divine Consciousness as Shiva) is inactive, while the Shakti tattava (D...
published: 23 Nov 2011
author: hhhuman
ULTRATERRESTRIAL TRANSPONDER LIVE: "THIS IS NEW ATLANTIS" (1/4)
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ULTRATERRESTRIAL TRANSPONDER LIVE: "THIS IS NEW ATLANTIS" (1/4)
- published: 23 Nov 2011
- views: 138
- author: hhhuman
"The Shiv tattava (Divine Consciousness as Shiva) is inactive, while the Shakti tattava (Divine Energy as Kali) is active. Shiva, or Mahadeva represents Brah...
ULTRATERRESTRIAL TRANSPONDER LIVE: "THIS IS NEW ATLANTIS" (1/4)
Published: 23 Nov 2011
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46:38
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part II)
Kolmogorov complexity of a binary string x is defined as the minimal length of a program t...
published: 02 Aug 2013
author: Контур Студент
CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part II)
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CSEDays. Theory 2013. Kolmogorov complexity (Alexander Shen). 3day (part II)
- published: 02 Aug 2013
- views: 68
- author: Контур Студент
Kolmogorov complexity of a binary string x is defined as the minimal length of a program that produces x. This quantity depends on the programming language, ...
Computable functions are the basic objects of study in computability theory. Computable functions are the formalized analogue of the intuitive notion of algorithm. They are used to discuss computability without referring to any concrete model of computation such as Turing machines or register machines. Any definition, however, must make reference to some specific model of computation but all valid definitions yield the same class of functions. Particular models of computability that give rise to the set of computable functions are the Turing-computable functions and the μ-recursive functions.
Before the precise definition of computable function, mathematicians often used the informal term effectively calculable. This term has since come to be identified with the computable functions. Note that the effective computability of these functions does not imply that they can be efficiently computed (i.e. computed within a reasonable amount of time). In fact, for some effectively calculable functions it can be shown that any algorithm that computes them will be very inefficient in the sense that the running time of the algorithm increases exponentially (or even superexponentially) with the length of the input. The fields of feasible computability and computational complexity study functions that can be computed efficiently.
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http://en.wikipedia.org/wiki/Computable_function
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This article is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License, which means that you can copy and modify it as long as the entire work (including additions) remains under this license.
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