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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

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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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems. This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | automata | computability | computability | complexity | complexity | mathematical models | mathematical models | computation | computation | finite representation | finite representation | infinite objects | infinite objects | finite automata | finite automata | regular languages | regular languages | context-free languages | context-free languages | Turing machines | Turing machines | partial recursive functions | partial recursive functions | Church's Thesis | Church's Thesis | undecidability | undecidability | reducibility | reducibility | completeness | completeness | time complexity | time complexity | NP-completeness | NP-completeness | probabilistic computation | probabilistic computation | interactive proof systems | interactive proof systems | 6.045 | 6.045 | 18.400 | 18.400

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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6.045J Automata, Computability, and Complexity (MIT) 6.045J Automata, Computability, and Complexity (MIT)

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. 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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6.045J Automata, Computability, and Complexity (MIT)

Description

This course is offered to undergraduates and introduces basic mathematical models of computation and the finite representation of infinite objects. The course is slower paced than 6.840J/18.404J. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | computability | complexity | mathematical models | computation | finite representation | infinite objects | finite automata | regular languages | context-free languages | Turing machines | partial recursive functions | Church's Thesis | undecidability | reducibility | completeness | time complexity | NP-completeness | probabilistic computation | interactive proof systems | 6.045 | 18.400

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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6.045J Automata, Computability, and Complexity (MIT)

Description

This course introduces basic mathematical models of computation and the finite representation of infinite objects. Topics covered include: finite automata and regular languages, context-free languages, Turing machines, partial recursive functions, Church's Thesis, undecidability, reducibility and completeness, time complexity and NP-completeness, probabilistic computation, and interactive proof systems.

Subjects

automata | computability | complexity | mathematical models | computation | finite representation | infinite objects | finite automata | regular languages | context-free languages | Turing machines | partial recursive functions | Church's Thesis | undecidability | reducibility | completeness | time complexity | NP-completeness | probabilistic computation | interactive proof systems | 6.045 | 18.400

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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https://ocw.mit.edu/rss/all/mit-allarchivedcourses.xml

Attribution

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6.045J Automata, Computability, and Complexity (MIT)

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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