Description

A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems. A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Subjects

computability | computability | computational complexity theory | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | Decidable and undecidable problems | reducibility | reducibility | recursive function theory | recursive function theory | Time and space measures on computation | Time and space measures on computation | completeness | completeness | hierarchy theorems | hierarchy theorems | inherently complex problems | inherently complex problems | oracles | oracles | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 18.404 | 18.404 | 6.840 | 6.840

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier. This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier.

Subjects

quantum computational complexity theory | quantum computational complexity theory | quantum computers | quantum computers | complexity classes | complexity classes | lower bounds | lower bounds | communication complexity | communication complexity | interactive proof systems | interactive proof systems | BQP | BQP | quantum algorithms | quantum algorithms | QMA | QMA | quantum Merlin Arthur | quantum Merlin Arthur

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements. This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements.

Subjects

modern cryptography | modern cryptography | fundamental cryptographic primitives | fundamental cryptographic primitives | public-key encryption | public-key encryption | digital signatures | digital signatures | pseudo-random number generation | pseudo-random number generation | basic protocols | basic protocols | computational complexity | computational complexity | two-party protocols | two-party protocols | zero-knowledge | zero-knowledge

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power. This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Subjects

finite automata | finite automata | Turing machine | Turing machine | halting problem | halting problem | computability | computability | computational complexity | computational complexity | polynomial time | polynomial time | P | P | NP | NP | NP complete | NP complete | probabilistic algorithms | probabilistic algorithms | private-key cryptography | private-key cryptography | public-key cryptography | public-key cryptography | randomness | randomness

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory. This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Computability | computational complexity theory | Regular and context-free languages | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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The Braining IT course brings together the topics of neuroanatomy and computational complexity allowing students to compare biological and electronic computational systems.

Subjects

sfsoer | ukoer | neuroscience | biology | human biology | systems | networks | computational complexity | Physical sciences | F000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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A more extensive and theoretical treatment of the material in 18.400J, Automata, Computability, and Complexity, emphasizing computability and computational complexity theory. Regular and context-free languages. Decidable and undecidable problems, reducibility, recursive function theory. Time and space measures on computation, completeness, hierarchy theorems, inherently complex problems, oracles, probabilistic computation, and interactive proof systems.

Subjects

computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | interactive proof systems | 18.404 | 6.840

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Description

This course is an introduction to quantum computational complexity theory, the study of the fundamental capabilities and limitations of quantum computers. Topics include complexity classes, lower bounds, communication complexity, proofs, advice, and interactive proof systems in the quantum world. The objective is to bring students to the research frontier.

Subjects

quantum computational complexity theory | quantum computers | complexity classes | lower bounds | communication complexity | interactive proof systems | BQP | quantum algorithms | QMA | quantum Merlin Arthur

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Description

This course features a rigorous introduction to modern cryptography, with an emphasis on the fundamental cryptographic primitives of public-key encryption, digital signatures, pseudo-random number generation, and basic protocols and their computational complexity requirements.

Subjects

modern cryptography | fundamental cryptographic primitives | public-key encryption | digital signatures | pseudo-random number generation | basic protocols | computational complexity | two-party protocols | zero-knowledge

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Recorded May 14, 2013. How are magnetic materials related to issues in biology and computerscience? Professor Chuck Newman will share how spin glasses or -- "disordered magnets with frustrated interactions --" play a role in neural networks, evolution, and immune systems as well as in computational complexity and social network modeling. Based on the recent book, Spin Glasses and Complexity, by NYU's Dr. Daniel Stein and Dr. Newman, this talk will introduce the application of spin glass concepts in future immunological and technological breakthroughs.

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http://creativecommons.org/licenses/by-sa/3.0/

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Description

This graduate level course is more extensive and theoretical treatment of the material in Computability, and Complexity (6.045J / 18.400J). Topics include Automata and Language Theory, Computability Theory, and Complexity Theory.

Subjects

Computability | computational complexity theory | Regular and context-free languages | Decidable and undecidable problems | reducibility | recursive function theory | Time and space measures on computation | completeness | hierarchy theorems | inherently complex problems | oracles | probabilistic computation | and interactive proof systems

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Description

This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Subjects

finite automata | Turing machine | halting problem | computability | computational complexity | polynomial time | P | NP | NP complete | probabilistic algorithms | private-key cryptography | public-key cryptography | randomness

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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This graduate-level course focuses on current research topics in computational complexity theory. Topics include: Nondeterministic, alternating, probabilistic, and parallel computation models; Boolean circuits; Complexity classes and complete sets; The polynomial-time hierarchy; Interactive proof systems; Relativization; Definitions of randomness; Pseudo-randomness and derandomizations;Interactive proof systems and probabilistically checkable proofs.

Subjects

18.405 | 6.841 | Polynomial hierarchy | time-space lower bounds | approximate counting | ?s Theorem | Relativization | Baker-Gill-Solovay | switching lemma | Razborov-Smolensky | NEXP vs. ACC0 | Communication complexity | PCP theorem | Hadamard code | Gap amplification | Natural proofs

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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